Ending the Era of the U.S. Survey Foot | Hacker News Reader

Ending the Era of the U.S. Survey Foot

nist.gov

104 pointsamjaeger158 comments

> In 1959, the relationship of the foot to the meter was officially refined as 1 foot = 0.304 8 meter exactly.

We can thank one man for this: Carl Edvard Johansson from Sweden. When making gauge blocks, he decided to round off the inch to exactly 25.4mm, and people around the world used his blocks to manufacture everything. The 1959 change just reflected what industry was already doing.

- http://mitutoyo.com/wp-content/uploads/2013/07/E12016-Histor...

- https://books.google.com/books?id=3rUaAQAAMAAJ&lpg=PA293&ots...

An interesting factoid is that if you rummage around in a machine shop, you will find a pair of gears in a drawer somewhere, with 50 and 127 teeth. Those are for converting an old fashioned manual lathe to cut metric screw threads.

Just FYI, a 'factoid' is something believed to be true, when it probably isn't. I assumed you meant 'fact', but otherwise your comment could be confusing.

That is indeed one sense of the word factoid, but in common North American usage it also can mean “small or trivial piece of information”, which is the sense I believe the parent poster is using.

For reference, a US survey foot is legally defined as 1200⁄3937 meters, which is ~0.304801 meters.

The difference is usually written as 2ppm, for practical purposes. (To match units for survey equipment accuracy.)

It frustrates my sense of aesthetics to no end that the inch isn't defined as 25.6 mm.

That would make the imperial system a base-two variant of the SI system.

This would have made the mile around 42 (current) feet longer, which is a non-starter; I just wish the foot had been a little longer, somehow.

At least you can't blame Johansson for that; 25.6mm would've been so far off (0.8% versus 0.0002%) that people wouldn't have bought his product.

Now I'm wondering how the ratio landed so close to 25.4 in the first place; 25.4000508 and 25.399977 have too many 0s and 9s for random chance.

Johansson rounded the inches, but previous legal definition was in yards. The Mendenhall Order was the US agreeing to define it's units in terms of the metric pegs, instead of the UK's (which were unreliably changing). The US survey of the coast (today the national geodetic survey), defined conversion values for the yard and pound.

1 (survey) yard = 3600⁄3937 meters

Reduces to:

1 (survey) foot = 1200⁄3937 meters

1 (survey) inch = 1/39.37 meters ~ 25.4000508 mm

https://en.m.wikipedia.org/wiki/Mendenhall_Order

If it helps, the miles-to-kilometers ratio is approximately the golden ratio... (1.609 vs 1.618.)

So, as a level N nerd, you can convert miles to kilometers by rounding to a nearby fibonacci number, and then finding the NEXT fibonacci number (and maybe fudging a bit in the direction of rounding).

Then, as a Level N+1 Nerd, you can realize that the Fibonacci Base exists, in which any integer can be represented as a collection of distinct fibonacci numbers. (for example, 43 = 34 + 8 + 1, or, using a binary string to show which Fibs are involved, 42 = 10010001.) The conversion of miles to kilometers is then just a bit-shift operation.

Well, almost, anyway.

It doesn't help! If the inch were 25.6mm, the ratio would be 1.622!

That's a lot closer! argh!

Gauge blocks are quite interesting, particularly how they stick to each other: https://en.wikipedia.org/wiki/Gauge_block#Wringing (mention on HN a few months ago IIRC)

As an example of a problem that can occur: Client wants to survey the elevations of a parcel of land for building a house. The surveyor goes out and collects data with gps survey equipment, which produces a .csv file of northing,easting,and elevation values relative to some National Geodetic Survey benchmark. The engineer imports this .csv into his cad software, produces a grading plan .csv file. The earthmoving contractor imports the grading plan into his software and grades the site.

Client gets house built, moves in and discovers that the front yard turns into a swamp after every rain.

Somewhere in the chain of importing and exporting .csv files, software A was using survey feet and software B was using international feet.

This can also cause problems like structures built in the wrong spot, fences built on neighbors land, etc.

The difference is .0002%. your examples would barely add up to an inch over a mile.

Sometimes the benchmark for northing/easting/elev is many miles away from the actual site. This is especially true with gps surveys.

It only takes a few inches to wind up with a substantial drainage problem.

Wouldn't the elevation difference between benchmark and site be the important bit here? If so, then the difference would rarely be more than a mile, and the resulting error would be at most an 1/8"

It's that you're in the wrong e, n location, which may be at an entirely different elevation than where you want to be.

It has been 20 years since I worked in this area so likely I have some details wrong. If elevation is distance to the center of the earth 1/8" per mile is 40 feet!

From the link below you can see the noaa benchmark is using both elevation in feet above sea level and in meters from the center of the earth.

https://www.ngs.noaa.gov/cgi-bin/ds_mark.prl?PidBox=aa3449

If you're not converting H (gps orthometric height) to E (local elevation datum to "sea level") first, you're doing it wrong, for a number of practical reasons.

Usually there's not even a reason to use H directly anymore, since elevations should reference a local benchmark.

GPS has changed things, but surveyors are still obscenely practical when it comes to procedures for eliminating systematic error.

Using an RTK-GNSS requires a gravitational model of the earth to measure mean sea level (MSL). Using your position, you use the GEOID model to figure out the delta of the nav satellite's orbit to the MSL.

Yes, That's what I mean by going straight from H to e first. The geoid is that conversion.

Although for rtk, the delta isn't to any of the sats, it's to your base station. The deltas to the sats cancel out of the equations, which is where most of the gains in accuracy come from. But it still needs to be tied into a known elevation benchmark.

That said, most field crews will still be shooting a differential to a published benchmark, or plugging the geoid file into the data collector, or dialing into a vrs or cors that already is adjusting for the geoid. For them, H is just an extra data point asking to be plugged into the wrong data field.

Unless you're doing static observations or geodesy or manual network adjustments or direct gravity readings, the new way (22) isn't all that different from the old way (83). There's just different underlying theory of MSL and different math to adjust the network. And if you are doing any of those things, then you generally already know what you're doing.

We're not even getting to the topic of elevation (yet). The US Survey Foot is 1200/3937 which is a not a clean value that terminates after a few decimal places. With high grid coordinates (X,Y), your origin is based at 0,0 as origin. When you scale between metric and US Imperial, if you're not using enough significant digits it impacts how the model scales. This can cause a difference of 1 foot or more from my experience. Floating point operators also become an issue especially in CAD. Standardizing to one number is a great start.

There's a ppm error there as well, but that's a usually a different problem. If different units were used, it would be obvious when checking in on the benchmark.

If it's in northing and easting, the baselines are to the South and West of all coordinates covered by the projection, plus an offset. So it might start at 1000000 instead of zero, to ensure format consistency and to catch blunders.

So it's about 2ppm, multiplied by the number of feet between you and the Southern or Western most edge of your state (if single projection state) plus 10^5 or 10^6 or similar.

It's designed to make an error large enough to notice.

Vertical however is rarely a problem, as it's all based off local benchmarks.

seems like an issue that surveyors and engineers should be well acquainted with.

How often does a "should" translate into reality?

It's entirely possible that they might not be aware. Surveyors are concerned with measuring bearing and distance from an arbitrary location (5000,5000) in some cases. The distances they traverse are not enough to see differences between US Survey foot and Int'l Feet. Cartographers and GIS folks who tie into a photogrammetric basemap are probably more aware. Most Civil engineers are like 'NAD83? Ok, whatever you say~!'

This is true. I barely understand coordinate systems enough to get by and somehow I know them better than any other engineer I've talked to. Surveyors are 50/50 on whether they know all that stuff or not.

Really though, there's no excuse for errors caused by that stuff. Survey data should almost always only be used relative to itself.

I worked as a CAD operator, surveyor, and occasional field crew worker at a civil engineering firm for a few years. We never ran into issues like this - by far the more common issue was the difference between NAVD and NGVD. At the time I was surveying, the FEMA flood insurance maps in our area were only partially updated, so the base flood elevation could be in either datum, and you had to really watch it so you didn't end up about 0.7' off vertically.

I actually learned of the difference between the U.S. Survey Foot and the International Foot while working on https://plantpredict.com. For years we had infrequent but bizarre unit-conversion bugs. Calculations literally weren't adding up. We assumed it was related to precision rounding since numeric input fields showed rounded values. It turns out the imperial-to-metric feet conversion factor we picked was 1 of 2 choices, and we picked wrong!

If anyone else is curious - the "US Survey Foot" was 609nm larger than the US International Foot. Or, 0.0002% Larger.

It would take 41,708 feet for the error to add up to one inch.

Which feet?

The non-survey one

The left ones.

Sorry, I'll show myself out.

The article left me confused about what it means to have a legally binding redefinition of a term.

Does this mean that all existing, legally binding contracts are to be reinterpreted using the new definition of "foot"?

Does it mean that any new legal document (contract, legislation, etc.) that uses the term "foot" without further clarification shall be assumed to mean this new definition of "foot"?

I believe it is the latter.

In practice, since the difference is so small it does not matter in almost all cases, because no one was in a position to measure accurately enough. If you ask for 100 feet of rope, the difference between the two definitions of "foot" is much tinier than the smallest possible roundoff error you or the sales person will make.

That's fine for measuring most things, but not necessarily for survey work. Your reference points can be quite far away, and you are dealing with angles. So ever pretty tiny changes can be significant.

As a general point, I don't think contracts can have their terms adjusted after the fact without both parties agreeing to it.

This seems the only reasonable way to do it except for terms deemed unenforceable (which is why you see a lot of boilerplate about severability)

A good overview on NSRS can be found below, pretty interesting read if you're into datums.

https://www.esri.com/about/newsroom/arcuser/moving-from-stat...

Fortunately, the inch is defined as 0.0254 meter exactly. So we have consistency for the really important units.

Then which "foot" is exactly 12.000000 inches?

The International one (i.e. Non Survey Foot)

> In 1959, the relationship of the foot to the meter was officially refined as 1 foot = 0.3048 meter exactly.

So 0.0254 * 12.000000 == 0.3048

0.3048 meters / 12 = 0.254

My calculation shows 12 * 0.0254 = 0.30479999999999996 meters. That may be off a little due to IEEE floating-point inaccuracy.

2 * 4 = 8 so the last significant digit should be an ‘8’

Definitely one to cite in the "overreliance on calculators" - the comment you are replying to should have realised that multiplication can't create digits to the right like that!

(Most desktop calculators do it in BCD which would give the correct result, too)

I use Python as my desktop calculator. It has a Decimal module that would have gotten it correct, but that would have been way too much trouble.

Surveyors almost always use tenths (of a survey foot), which is one dead giveaway to which one you're using.

Thank you 'amjaeger for removing the local-TV-news-level attempted pun from the headline.

Ah, the joy of standards.

If someone had told me this statement was part of a Monty Python script, I'd likely have believed them.

I don't see anything wrong with "truth in comedy".

A part of me believes that's how comedy works: if it wasn't true you wouldn't be laughing, and another part of me is laughing because the same truth is sad.

For those of us who came later to the discussion, what was the original title?

I was referring to the content of the post on nist.gov. But I think the title has changed, and may have been simply "U.S. Survey Foot" when I first commented.

Mildly surprising that we are not just using meters at this point.

think renaming a software library is hard? try changing units of measure!!!!!

I think that's what they did in Canada and it worked out great as far as I can tell (except that they had a silly clock based on 10 hours instead of 12 IIRC which had little to do with metric units and nobody wanted it nor was it compatible with the rest of the world).

I suppose it depends on what your goals are; despite being officially metric, my Canadian and British friends still seem to exhibit a melange of imperial and metric in everyday life.

I notice sometimes when watching British television that stones are commonly used as a unit of weight, which is interesting because it's imperial, not metric, but I've seen never it used in American contexts.

That's because we don't use the Imperial system. The system we use is called "US Customary".

“1 stone equals 14 pounds” is (also) British. It dates back to Edward III (1350). See https://en.wikipedia.org/wiki/Stone_(unit)#England.

The idea to use physical stones as reference weights is way older.

Some metric units work well, and are scaled to human everyday measurements, and some are not.

But the time thing goes to show the absurdity of people's frame of reference. The same people that judgingly ask why the US hasn't gone full metric will say how absurd the idea of base 10 time is.

https://en.wikipedia.org/wiki/Gimli_Glider

I once tried to imagine a metric time system, with a deciday of 14.4 minutes. I realized that it would never catch on, because a half-hour TV show would have to be cut to 28.8 minutes losing at least 2 commercials.

They actually tried this, during the French Revolution:

https://en.wikipedia.org/wiki/French_Republican_calendar

It didn't catch on then either.

And again in the 90s https://en.wikipedia.org/wiki/Swatch_Internet_Time

14.4 minutes is a centiday btw. For decimal time I think milliday is the most reasonable unit, being very close to conventional minute.

In practice Mars might be the best opportunity for enacting decimal time, because Earth based units would be bit awkward on Mars.

Thanks for the correction.

Saw this here somewhere previously: Sweden did something more insane: Högertrafikomläggningen. Do it once, get it over with?

https://en.wikipedia.org/wiki/Dagen_H

What would the cost be to change everything for a country the size of the USA? I imagine it would be in the trillions.

The situation is far more bizarre than "use" or "not use." As I understand it, America uses something along the lines of "converted metric units" - i.e. the entire imperial system is defined according to metric/SI. Some subset of public records have been, supposedly, converted to metric. If you have a recent car, it should have km/h alongside mph (in a smaller font, or as a different digital readout). You'll find metric all over the place if you keep an eye out for it.

US cars have had dual speedometers for decades. One example: https://www.ebay.com/itm/NOS-1980-1981-FORD-MUSTANG-85MPH-SP...

It's called "US Customary", not "imperial".

Only in the US - except for gallons/fluid ounces - those genuinely are US only

No, that's my point. The system of units that is used in the United States is not "Imperial", it has differences from Imperial. We use "US Customary".

Back in the 90s, new construction for the US Govt was supposed to all be done using the metric standard even though all of the supplies were in US/Imperial units. Can't imagine the headaches that caused.

Source: My uncle who is/was a contractor

The Comanche helicopter was subject to this dictum. The original drawings specified all metric fasteners. They found out nobody supplies aircraft grade metric bolts so everything had to be redesigned for the next size up in freedom-units with a corresponding weight penalty.

They are using metric:

https://geodesy.noaa.gov/INFO/Policy/files/SPCS2022-Policy.p...

> The meter is the unit of the defining linear parameters for SPCS2022

> SPCS2022 coordinates are published in meters

83 was also defined in metric, but most states chose to use feet for their actual grid.

We are. All of the US standards are based on metric units. A large number of the products that we buy are made from metric components such as screws. CAD software and machine tools can switch effortlessly between unit standards. There are some standards that are so unique that they might as well be arbitrary, such as spark plug threads.

Some building materials still have US dimensions, but if you measure plywood carefully, it's thicknessed in mm. And the "2 x 4" has never been 2 x 4 inches.

So I think we've made great progress towards an age when units of measure don't matter much any more.

> the "2 x 4" has never been 2 x 4 inches.

Well, it used to be pretty close, until lumber manufacturers and builders cheaped out. They've been gradually "shrinkflating" by reducing the thickness, conveniently requiring less wood. This went along with the switch to fast-growing garbage pine. I lived for a long time in an early-fifties house, and the quality of the wood was vastly superior to what you'd find today. Though, the newer measurements did make things a pain.

Here in NZ when we switched to metric nothing changed, 2x4s (well we call the 4x2s) were never quite 2x4, and 50x100s (the metric replacement) are close enough (but still not quite) that nothing really changed

four buh two

No the difference is that we process wood now. Look up dimensional lumber. Its confusing, but makes sense if looked at historically. Iy is not shrinkflation or any other such nonsense.

While i don't doubt they're cheating it a bit, the dimensions originally refered to rough cut, pre-dried lumber. Most of the difference came from finish cuts and drying.

My house was built in 1860. The 2x4s are basically 2x4.

My house was built in 1962, and there were some exposed studs, and spares made into things like garage shelves. The old 2x4's are bigger than new 2x4's.

Yeah, I went through a remodel and dealt with the same thing, trying to get drywall to line up on old (1970) and new walls. There's more to it than that, but it's the quick version.

On the other hand, if you find a smaller mill, usually the ones specializing in hardwood, you can still get "full size" cuts, usually without even asking.

Imagine it being 2020 and not using the metric system.

I don’t really mind that we’re not on the metric system. I just wish our measurements were consistent as they increase. E.g. foot, kilofoot, etc. instead of foot, yards, miles.

IDK, if you're going to be non-standard might as well go all the way.

What you want is metric, so 10 inches to a foot and so on. Switching makes of units isn’t so bad so long as the multipliers are 10,100,1000

Next you want your units to make sense across dimensions. You want your volume units to ALL be based on your length units. A cubic foot is ok. It then contains 1000 cubic inches. There are no quarts, gallons, pints (unless they are names for decimal quantities of cubic units).

And base-2, rather than the computer-unfriendly base-10. Aaaaactually ... with a bit of squinting the U. S. customary volume system(s) define a complete set of base-2 nouns (which could be used as prefixes):

    tbspn
    oz
    jill
    gill
    cup
    pint
    quart
    half
    gallon
    peck
    kenning
    bushel
    rundlet
    barrel
    hogshead
    butt
    tun

Where each item below the next item is exactly 2x the previous one. It turns out there's also some base-3 stuff (for measuring simplicity), like the teaspoon, etc.

I've always imagined we could redefine a few things to make a "completely rational" U.S. customary measure. That'd be:

    1 in == 2.5 centimeters (as Thomas Jefferson wanted)
    256 in^3 == 1 gallon (water at 32° F)

1 in is a bit awkwardly small. A cup-inch is ~1.3ft. A pint-inch is exactly .8125m. Luckily, a 'tun-tun-inch' (65536in) is 1.0343 miles, so we could define a a 'tun-tun-inch' to be a mile, etc., etc.

That gives you a gallon of exactly 4 liters (256 * 2.5^3 = 4000 mL). Alternatively, a quart is now just another name for a liter.

Fractional lengths in the US are commonly in base-2, ie, 1/2", 1/4", 1/8", 1/16", etc. Still annoying to remember that the next socket up from 1/2" is 9/16".

Just use Highly Composite Numbers... Babylon used base-60 and we still tell the time with it today. Base-12 is good too. It's divisible by 1,2,3,4,6,12. Base-10 is only 1,2,5,10 which is less usable for fractions.

At this point one has to point out that US gallons (and pints and cups and flu ounces) are different from the gallons/pints/cups/flu ounces used everywhere else on the planet (for reasons that mostly have to do with English kings trying to get around the parliament's limits on taxation they made some gallons smaller, the US standardised on one of the smaller ones) - fortunately most of the rest of us have stopped using those units so we don't care as much, but we do have to have to be careful with, for example, US recipes.

When visiting Starbucks I'm often tempted to ask the person behind the register "Venti? that's Italian for 20 right? 20 what?" they invariably will say "20 fluid ounces" .... of course the correct comeback is "I'm pretty sure they use the metric system in Italy, it must be litres, or maybe mililitres" - usually they will choose "litres"

Added binary teaspoon and dessert spoon, also renaming a few units:

    tspn
    dspn
    tbspn
    oz
    jill
    gill
    cup
    bottle
    quart
    half
    gallon
    peck
    jimmyjohn
    bushel
    rundlet
    barrel
    hogshead
    butt
    tun

That's not hard to imagine. Quick, what's 1/3 of a meter? The sometimes problem with metric is it's base-10. The prime factors of 10 are 2 and 5. Feet are in base-12, which has the prime factors 2 and 3. Three is much more useful than five. There are marks on your measuring tape at exactly 1/3 of a yard or 1/3 of a foot.

Metric is often easier and more convenient, but not always. So, in the US, we tend to use metric or customary units depending on which is more convenient for the task at hand. Actually, it's a lot like the UK and other countries where older systems still exist alongside metric. The difference with the US is that we don't have as many unnecessary laws mandating metric. You're an adult. You're working with other adults. You're perfectly capable of figuring out what to do without the input of lifelong politicians who've never measured a thing in their lives. Except for the amount of your money that they're going to spend. They like measuring that.

> Quick, what's 1/3 of a meter?

33.3 cm?

Oh, you rounded. Got it. ;)

Let's not pretend that any real world application of a third of a foot has infinite precision.

That's why you pick highly composite numbers to create your object. 'Quick, what's 1/3 of 12 meters?' Why do they make raised floors 600mm tiles?

Agreed. If you have ever done any type of construction you are very thankful that you can divide a foot evenly by 2, 3, 4 and 6.

Yeah, woodworking is so much easier when using feet and inches. It's so incredibly useful to be able to divide a foot into half, thirds, quarters, sixths, and twelfths.

nah, a mm is an incredibly useful unit for woodworking, it's a little less than the width of a saw cut, it's just about the right precision for most woodworking

It's not the precision. It's the divisibility. 10 can only be divided in half. It can't be divided into thirds, quarters, sixths or twelfths evenly and that ability is invaluable.

This is the same reason why, in the old days of grid layouts, grids were 12 columns wide and not 10.

I remember when we built our holiday home - yelling out the lengths of dwangs in millimeters - they were perfect for the job, we never needed to divide them in 3

What’s so special about thirds, sixths or twelfths?

10cm = 100mm; 100mm can easily be divided by 2, 4, 5, 8 (=12.5), 10, 20, 25, ...

That’s a nice thing about metric. If you don’t like the units you can multiply them

Specifically, twelve is a superior highly composite number.[1] In plain (and probably over simplified) English, it has more factors than other numbers in a similar range.

Historically, problems of division have been harder to solve than problems of multiplication. You can observe counting systems and their radices develop in multiple civilizations to make dividing easier by providing more factors. Twelve inches to the foot. The long hundred. 360 degrees in a circle. Ancient Mesopotamian sexagesimal arithmetic.[2] The fact that 'dozen' is a word.

In the modern industrial era, we have computers (mechanical then electronic) to help with problems of division, but for most of history we didn't have those tools.

What's so special about ten? Probably that we have as many fingers, so some counting systems developed as base-10 and spread across the world for reasons that have more to do with geopolitics than utility for mathematics. Of course, you can count to twelve on your knuckles.

[1]: https://en.wikipedia.org/wiki/Superior_highly_composite_numb...

[2]: https://en.wikipedia.org/wiki/Sexagesimal

I'm surprised that people are finding the benefits of divisibility to be so hard to understand. Does using the metric system create this blind spot? I've heard of language creating blind spots in what people can easily understand and think about. I hadn't thought about mathematical things, like the metric system, also creating blind spots, but I guess it makes sense.

But a sawcut is (typically) exactly an eighth inch.

Well, architectural construction is based on the "octameter", so 12.5 cm.

That adds pretty well ;)

You've flummoxed me with this. The internet seems sure that "octameter" is a "metrical foot", which in this context is quite a pun. Without a link to confirm an architectural connection, I'll take this as a fairly obscure joke...

Haha, no, it's not a joke as I can tell you as an architect.

Sadly there are no english links, but have a look at Wikipedia [0] and you will see, that I've not dreamed that up :) Of course it has a referenece norm: the DIN 4172, which calls it the "oktametrisches Maßsystem" (_octametric system of measurement_). It is made since a brick would be 11.5 cm and the mortice 1 cm = ∑ 12.5 cm. Eight bricks with mortice are a meter. Pretty easy actually!

[0] https://de.wikipedia.org/wiki/Baurichtma%C3%9F

Thanks for the update; I would not have found that!

"Quick, what's 1/3 of a meter?"

About a foot.

My wife's family, who almost all have university degrees, who were all born and raised in the US, and who are very familiar with the imperial system NEVER seem to be able to do math with it. They ask me, a European raised with the metric system, for help.

Find out how many fl oz of milk are in a measuring cup graduated in units of cups? Ask mrb.

Convert my daughter's height from feet/inches to inches? Ask mrb.

Convert a package's weight from oz to lb/oz? Ask mrb.

Need to know how cold it needs to be outside in farenheit for water to freeze? Ask mrb.

I lost count of the number of times they accidentally mix up for example 1.3 feet with 1 ft 3 in. Sometimes it's due to miscommunication, eg. I have seen "six pound five" interpreted as 6 lb 5 oz by one when the speaker meant 6.5 lb. Or vice versa.

It's just comical to see someone trying to argue that the imperial system is "sometimes easier."

I once worked with a guy who had just bought a surplus cylindrical water tank, and wanted to get an idea of what it would weigh when filled. I asked him for the dimensions and multiplied each by 2.5 to convert to approximately centimeters. Then I multiplied the diameter by 3, approximating pi. I converted each to the nearest power of 2 so I could multiply by adding the exponents. Assuming 1 cubic cm of water is 1 gram, I had the log2 weight in grams. Then I subtracted 10 to divide by 1024, getting approximate kilograms. Then added 1 to get approximate pounds. Finally took 2 to the power of the result. By the time he finished telling me the dimensions, I had an answer for him.

How would one use the diameter to determine weight? Do we square it then divide by four?

In metric, the weight of water in grams is equal to the volume in cubic centimeters, by definition. The volume of a cylinder is the area of the circle times the length. The area of a circle is pi * r^2. So my description above skipped a step or two.

> In metric, the weight of water in grams is equal to the volume in cubic centimeters, by definition.

Just to clarify this is not exactly true. It was the original idea, but pretty quickly they realized that it wasn't a practical definition and kilogram ended up being defined by a standard reference object which was carefully stored in a vault in Paris and thus being disconnected from the meter and the density of water. Finally in 2019 kilogram was redefined again in terms of natural constants in the great SI unit upheaval. Although sadly the new definition is not very intuitive to understand.

I'm sure the updates to the Kilogram definition tried to keep it as close to the original as possible, right? The difference pales in comparison to the other shortcuts I was taking.

I have no idea what the GP is doing but you would just do

Pi * D^2 / 4 * H * 62.4

Where D is tank diameter in ft H is tank height in ft and 62.4 is the unit weight of water in lbs per cubic foot. Divide by 144 of D is in inches and 12 if H is in inches.

Or if you want to be real lazy you can see Pi/4*62.4 is ~49 and round to 50.

Do most people know 62.4 lb/ft³?

The equivalent metric factor is 1 g/cm³ or 1 kg/L [1] so with D and H in centimeters the calculation is

  π D²/4 × H

kilograms of water.

[1] Assuming we're talking about a normal water tank, not a space rocket. Density varies with temperature, it's 0.9970474 g/cm³ at 25 °C.

The unit weight of water being 62.4 pcf is probably not known by most people - most people don’t think in cubic feet. The more likely (and less useful) number most people know is ~8 lbs per gallon.

This is also just an anecdote, but I'll second thomk's opinion on woodwork/manual measurement of most kinds. Twelve has one, two, three, four, six, and twelve for divisors, and that is incredibly handy when you're trying to do manual measurement. Even sixteen has one, two, four, eight, and sixteen, making for easier division of pounds to even numbers of ounces; compare this to ten, which has only one, two, five, and ten. People can't eyeball or measure tenths or fifths nearly so easily as thirds and fourths. Even eights are easy to get from measuring a quarter and taking half; good luck eyeballing a fifth. And before all the "we have computers to do it for us" people come out of the woodwork: 1. Not always and 2. High-precision floating-point arithmetic is still computationally expensive and often hard to get right. I think every one has, at one point or another, hit some weird numerical glitch due to floating-point error.

Every schoolboy learns basic unit conversion; I'm not convinced by your tales of hapless relations. It's not that hard to remember eight fluid ounces per cup. It's not that hard to multiply the feet times twelve, add the inches, and divide by twelve to get just feet. It's not that hard to divide the ounces by sixteen to get pounds and ounces. It's not hard to remember that water freezes at thirty-two degrees. I've also never heard someone describe weights as "six pound five" with either meaning; the closest I've heard are descriptions of height as, say, "six foot two". This means six feet and two inches in every case, and everyone understands this.

At this point,

In conclusion, it is sometimes easier. It's just comical to see someone trying to argue that there are literally zero cases where the customary system is sometimes easier.

150mm has 2, 3, 5, 6, 10, 15, 25, 30, 50, 75 so that works very nicely if you want something that can be combined with many combinations. European kitchen cupboards and appliances are designed with a width of N×150mm.

> My wife's family, who almost all have university degrees

Honestly, this is probably part of the problem.

If you ask the AP Calculus student to calculate these things, they probably don't have that down solid.

If you ask the sweathog vocational tech kid, they will know what the units of measure are and have no problem.

Practice makes perfect.

> Find out how many fl oz of milk are in a measuring cup graduated in units of cups? Ask mrb.

8. Volume is base 2. Two tablespoons in an ounce, 8 ounces in a cup, (there used to be other units in between, but nobody used them, like deci in si) two cups in a pint, two pints in a quart, four quarts in a gallon.

If you were going to sell me on switching units, it would be based on hexadecimal instead of base 10.

> Convert my daughter's height from feet/inches to inches? Ask mrb.

5' is 60". Add and subtract from that. 5'6” is 60"+6" = 66" inches, 4'4" is 60"-8"=52", etc. "Normal" humans cluster around 5' so this takes you pretty far.

> Convert a package's weight from oz to lb/oz? Ask mrb.

Again, base 2. As a programmer this is easy because it leverages all the same neural pathways that I use for converting between base 10 and base 2/16. Hell, maybe learning to cook in base 2 has made me a better programmer.

> Need to know how cold it needs to be outside in farenheit for water to freeze? Ask mrb.

This is definitely the worst example. 0°F is really cold. 100°F is really hot. Fahrenheit is objectively better than Celsius as a common parlance unit.

> I lost count of the number of times they accidentally mix up for example 1.3 feet with 1 ft 3 in.

I've never seen anyone do this ever. I've seen dumb computer systems do shoddy conversions on inputting numbers into a program, but that's why you normalize your inputs and show it back to the user. I've never seen or heard of a living breathing human make this mistake.

> "six pound five"

That's like saying "100 centi 57 meters". Those words have meanings on their own, but they don't have a meaning in that order. The only meaningful response to that is to be confused, and then realize they're confused.

How long did they live in the US and how long have they lived where they are now? This sounds like someone who lived in the US until they were ten and moved somewhere where they not only didn't use customary units but didn't speak English. Then spent the next few years scrambling to master the language and hit adulthood understanding neither US customary units nor metric units.

Honestly, culture, customs, and normality run deep. Those handful of nations that use , as the decimal separator and . as the thousands (or otherwise) separator would have a much easier time and much more benefit swapping their separators than the average American would switching from customary units to SI. Nearly everybody uses a 24 hour day, 60 minute hour, 60 second minute. 3600 second hour, 86400 second day, etc.

Oh did I say 24 hour day? Well I lied but it's close enough.

Astronomers happily use astronomical unit, light-year, parsec, and z= redshift to measure distance all in the same context. For me, having "dumb, arbitrary" units is way less important than having familiar units. Despite the fact that humans are dumb and arbitrary, we're still pretty clever.

Most of the people who complain strongly about customary units, which are dumb and arbitrary, speak languages where inanimate objects have gender. (for the record, I also think grammatical gender is dumb and arbitrary in English) "Auto" (meaning car) is neuter and "Wagen" (meaning car) is masculine. If one considers a scale where 100°F is really hot and 0°F is really cold a dumb, arbitrary system, you should stop to consider whether to_lower(str) and to_lower(to_upper(str)) yield the same results.

Humans are dumb, arbitrary creatures. The fact that US customary units are tend towards base 2 units instead of base 10 is way less arbitrary than daylight savings time, or the fact that France is in the wrong time zone, or the fact that Denmark has enshrined in law its own national time basis and then completely ignores it and then refuses to change the law which is ignored by literally every single person in Denmark.

The conversion techniques you explained, I use them myself (that's why they always ask for my help, I can do it in my head.) But the fact many Americans are unable to do that is, in itself, evidence the imperial system doesn't work that well for them.

> This is definitely the worst example. 0°F is really cold. 100°F is really hot.

This might be a sufficient explanation to give to a 5-year-old, but as soon as you need to do actual work with temperatures, this doesn't work so well. Case in point: many Americans don't know the freezing and boiling point in ⁰F. So, no, it's not "objectively better."

> That's like saying "100 centi 57 meters"

No European ever says this. In contrast, many American routinely say "six pound five".

> How long did they live in the US and how long have they lived where they are now?

Their whole life. Born and raised in America.

American here. I've never once in my 40 years on this earth heard someone say "six pound five". That parlance is often used for feet and inches (almost always in reference to human height), but I've never encountered anyone using it for pounds and ounces.

I'm American, have lived in many parts of the US, and I agree: "six pound five" is not something that we say. As Gormo says, this construction is frequent for feet and inches ("six foot five"), but would not be standard for weight.

And personally, if I were to use this nonstandard construction, I'd probably pluralize "pounds". I don't know why "foot" is usually singular in the parallel construction.

The most charitable interpretation I can come up with is that your relatives are from the American South, and are actually saying "six point five", meaning 6 and half pounds, and you are mishearing them.

> But the fact many Americans are unable to do that is, in itself, evidence the imperial system doesn't work that well for them.

The set of anecdotes you have put forward about Americans you know could be evidence of any number of things. You hypothesis is that the US customary system doesn't work well for them. An equally valid hypothesis is that public education doesn't work for them.

You keep asserting that your anecdotes are broadly indicative, but multiple people are telling you the opposite (and presenting an equivalent level of anecdotal evidence with similar limits in broad applicability).

For my part, I've lived in several parts of America my entire life and never met another American:

* who says "six pound five" for weight.

* who doesn't know that water freezes at 32°F.

* who would express length/distance as tenths of feet (e.g. 1.3). [1]

But I wouldn't therefore conclude anything about Americans generally.

In fairness, you could probably take a camera and get an 'average man on the street is dumb' effect if you looked hard enough and cut a bunch of disparate interviews together. I suspect you are encountering selection bias. All the people who are bad at math (independent of measuring system or educational background) have found and glommed onto you for help. All the people who don't have trouble with unit conversion (who possibly outnumber the former group) don't trouble you with their unit conversions.

[1]: I have seen halves and quarters (X.25, X.5, X.75) of feet expressed in decimal.

Except 3 teaspoons to a tablespoon.

> nobody used them, like deci in si

What makes you believe that nobody uses them? Where I'm from, "decimeter" is in use, for example. Centimeters are way more common, sure - but it does come up when eyeballing distances, or in well-established terms such as "decimeter band".

NB your fluid calculations are for US customary measures. The Imperial system has 20 fl oz in a pint, and people never use cups or quarts. Take care if you come across an old British recipe, or drink beer in pints in Britain.

0°F is colder than the coldest temperature I've ever experienced, your definition seems very arbitrary.

I do agree with you that base-12 is easier to work with, but I think it's worth pointing out, appropos of the article, that U.S. surveyors actually talk about feet in "tenths" and "hundredths" - so, quick, what's one third of a foot? About 33 hundredths of a foot. ;)

Feet and inches aren't really in "base twelve", because it's not a positional number system. For example, what's 1/3 of an inch?

I think we'd be better off using dozenal numbers, but that ship sailed a long time ago.

> Quick, what's 1/3 of a meter?

33 cm

333 mm

333 333 micrometre

333 333 333 nm

... and so on ...

   $ units
   You have: 1|3 m
   You want: ym
    * 3.3333333e+23
    / 3e-24

> politicians

Oooooookay.

The metric system doesn't really have anything intrinsically better about it.

Sure the power of ten thing is convenient, but really that is just sticking to one unit and adding a prefix. You could call "thousandths of an inch" a "milli-inch" and it'd be about the same.

Fahrenheit is absolutely a more useful human-scale measurement than Celcius. The boiling point of water is mostly irrelevant to everyday life. At that point you might as well just do things in Kelvin.

Perhaps the usefulness of Fahrenheit is only a thing when you live in a continental climate though.

100F is about as hot as it's going to get here in Iowa.

Similarly, 0F means that it's the depths of winter. Anything above 0F is pretty manageable. When you start going below 0F you're getting into "real cold" territory.

Point being, Fahrenheit is a scale that matches well to the climate extremes (at least around here), which I think is a significant advantage for it.

As to the rest of it, a meter is basically a yard. A liter is basically a quart. A kilogram is just two pounds. Not really that difficult.

The boiling point of water may not be useful on a day-to-day basis, but the freezing point certainly is. 0C is a lot less arbitrary than 32F. Other temperature mileposts are just a matter of getting used to them; 100F is pretty hot, as is 35C.

I think you underestimate the usefulness of powers of 10.

> The boiling point of water may not be useful on a day-to-day basis, but the freezing point certainly is

The freezing point of water is interesting, but in practice it is pretty variable depending on what adulterants are mixed with it.

Realistically, any day that it gets up to the 20s F you will get some amount of snow melt.

Any time it is above ~0F the roads will de-ice during the day from the salt they put down.

I don't have any issue with people preferring C to F, but I think any choices come mainly down to what you have been exposed to.

My main point is that Fahrenheit is a very practical temperature scale.

> I think you underestimate the usefulness of powers of 10

Powers of ten are just scientific / engineering notation, they aren't really all that dependent on the underlying base units.

The fact that people gravitate toward the measurement system they were first exposed to suggests that they are both adequate in practice.

If they predict sub-zero temperatures in early spring you have to cover your plants in the garden or they are likely to die. If you leave your house for a week or longer and they predict consistent sub-zero temperatures you have to set heater to keep it above 0C or drain your pipes so they won't burst. That's pretty practical threshold if you ask me.

Nobody says in the weather prognosis "beware people it will get sub-negative 17 C at one point", they just say the lowest it will get. But they do warn if it will get sub-zero C at any point, there's a separate word for it.

> Any time it is above ~0F the roads will de-ice during the day from the salt they put down.

The ~0F for salt-water mix is a very fuzzy threshold, depending on the proportions it can be anything up to 0C in reality. In practice I just expect ice if it's sub-zero C, I don't really know if they will salt the roads before I'm there and how much of it will remain when I'm driving there.

I also don't understand why you need 100 degrees when you can't distinguish between for example 70 and 80 F. Could just as well be using dekoF without perceived loss of precision.

> Powers of ten are just scientific / engineering notation, they aren't really all that dependent on the underlying base units.

The problem is converting between feet, pounds, inches, miles, gallons, etc. It introduces ugly factors everywhere. Sure you can do it, but it turns something you can do instinctively on the fly with metric into something you have to solve on a paper or with a calculator.

Fun exercise to showcase this - how many 50x50 cm tiles to tile a 2m wide pavement 5 km long? Now do the same with 20x20 inches tiles for 5 feet wide pavement 3 miles long :)

See roman numerals vs positional system. Multiplication with roman numerals is a daunting task, while kids in primary school can multipy long numbers with positional system. Despite that there was over a century where both systems coexisted, and some people even complained that "positional system makes falsifying accounting books too easy".

Also 1 kg ~ 1 liter for most liquids is very useful for quick estimation of mass and volume, can't do that with pounds and gallons.

> If they predict sub-zero temperatures in early spring you have to cover your plants in the garden or they are likely to die

Around here they just call it a "frost warning"

> Nobody says in the weather prognosis "beware people it will get sub-negative 17 C at one point"

If it gets too cold out, they do advise people to take extra care being outside due to the danger.

> you can't distinguish between for example 70 and 80 F

You really can.

> can't do that with pounds and gallons.

A pint ~ 1 lb. So a gallon is ~8lb.

0deg F was originally set as the freezing point of sea ice, which could be recreated in the lab using a mixture that's more thermally stable than the freezing point of fresh water.

Not as arbitrary as people think. Most units have a good reason for their definition, in the context for which they're used, and are divisible by numbers that are convenient.

Without needing decimals at all.

And in my experience, the people who benefit from base 10 metric are the same people who misplace decimal points.

A milli-inch (thou) is actually a commonly used unit in precision manufacturing: https://en.wikipedia.org/wiki/Thousandth_of_an_inch

"Eschew flamebait. Don't introduce flamewar topics unless you have something genuinely new to say. Avoid unrelated controversies and generic tangents."

https://news.ycombinator.com/newsguidelines.html

Hmm... Autodesk makes a widely popular software called Revit and it started in Massachusetts. The API's base unit is in feet. How can I convince them to rewrite software so it uses SI units?

I get the impression that fractions are very much engrained in American psychi and cultural identity and thus is a strong influence for opposition to a metric system.

Yes, as an Australian I find the idea of using fractional measurements to be super weird.

People in these threads talk about 1/3rd of an inch as if that’s a real number :)

But seriously I think you are right. I never use fractional notation or thinking when I’m building something, while it seems very common when reading US sites. I have a socket set which US Customary sizes in fractional inches and mm; I cant tell which of the US sockets is bigger without comparing them, but 11mm is obviously larger than 10mm (to me).

I think your observation about cultural identity is spot on, but as always it goes both ways - I think the US system is nuts because of all these crazy fractions.

Until now I didn’t realise that this was my own cultural bias against fractions leaking in.

I knew about the survey foot because both the l00' tape measures I have are in survey feet. Messed me up on a home construction project about 13 years back. It was then I learned there are 2 differing feet definitions.

Are you sure it was the differing length of each version (about 610 nanometers), or was it because your tapes were marked in tenths of a foot instead of inches?

I have actually worked with people who didn't notice this about their 100' tapes. Even better are the tapes divided by 12 on one side and 10 on the other...

Well this was a false memory I may now remember as false. No, it wasn't tenths. I think more likely it had to do with the claw at the start of the tape for attaching to your starting point, which does not stay at a rigid 90 degrees. My memory is that over several tens of feet I was off by 1/8 inch.

Over the length of a 100’ tape, the difference is about 61 um, ie 0.061 mm. How could that difference have any effect?

Reply on news.ycombinator.com