vs.

the “Imperial” (or “English”) System(s)

First published in March 1997

The following is an actual excerpt of a conversation I found in a newsgroup. Names have been changed to protect the uneducated.

Ernö: I vote for the emperical system to be superiour. When you go to the market and you need a quarter of a foot of fabric, then that will be exactly 4 inches. When you would have needed a third, that would be exactly 3 inches.

Kristian (

aside): Actually, a quarter is 3 and a third is 4, but point made.

Ernö: When you would have liked to have a quarter metre, it would be 25 cm, and a third metre, would be 33,33333 cm. The empirical system is based on the numbre 12 (12 inches to a foot) because that can be divided by 2,3,4,6. Whereas 10 can only be divided by 2 and 5. So the empirical system is superiour, when you are not good at maths.

José: Yes, this is the only good thing about the empirical system.

Kristian: It’s not just for people not good at math. Empirical is good for those good at spatial geometry, ie. the relation of things and objects and the ratios of proportion.

Give someone an unmarked stick precisely one meter and ask him to turn it into a metric ruler, with nothing more than a pen and piece of string, it’ll be virtually impossible.

Like people make their own rulers on a regular basis?
Nevertheless, if I also have a piece of blank paper, I can very easily make a
metric ruler. This reminds me of the old guy to
tried to tell me that clocks with hands were superior to digital because you
could *see* “quarter of five” on a manual^{*}
clock. (No, not “analog.” See the footnote.)

Duh. I always say “four forty-five”
*because* I use digital. Manual is only
“better” when you make sure to bias the question. (Actually, I say sixteen
forty-five, but that’s another matter.)

The “third of a foot of fabric” is the same specious argument. If you work in metric, you don’t go “Gosh, I need a third of a foot,” you go “Gosh, I need ten centimeters here.” 1/3 of a foot is 10.16cm. I think we can safely round down one and a half millimeters for a scarf.

Now I need to make nineteen of these scarves. How much fabric do I need? 1/3 foot times 19? Er, 19/1 × 1/3 = 19/3 = 6 1/3 feet. But fabric is sold by the yard. A foot is 1/3 of a yard, so (19/3) ÷ 3 = 2 1/9 yards. Or maybe I knew that the scarves were four inches wide. 4 inches × 19 = 76 inches ÷ 36 inches per yard = 2 1/9 yards. Unlike the previous formulas, I can’t do that last division in my head. 19/3, (6 1/3) ÷ 3 and 4 × 19 also require careful thinking, as opposed to the answer just popping up.

Now, nineteen metric scarves: 10cm × 19 = 190cm = 1.90m. A no-brainer. I left out the “divide cm by 100” because I didn’t divide. I moved the decimal point, which might sound the same, but requires a different, much easier, thought process. To find out how many km of fabric, I wouldn’t go “Hmm, what’s 1.9 ÷ 1000?” I’d go “move the point three to the left.” Metric transformations frequently skip division entirely, using the decimal shift trick instead.

What are the conversion factors you need to know to turn tablespoons into quarts? I know 1 qt = 2 cups, but I haven’t memorized the number of Tbsp. in a cup. How many milliliters in a liter? The question is the answer. Metric rules for distance (“millimeter is 1/1000 of a meter”) map to volume (“milliliter is 1/1000 of a liter”), whereas knowing how many feet in a mile doesn’t give the slightest clue for the tablespoon question.

How many ounces in a ton? You’d better know two more conversions: ounces in a pound (16), and pounds in a ton (2000). How many centigrams in a megagram? Voila! Once I’ve learned the prefixes for distance (centi is 1/100, mega is one million), I can also convert weight as well as volume.

Here’s one I personally have to
fiddle with a lot: I need to drill a hole. I have a 3/4′′ drill bit, and a
23/32′′ drill bit.^{†} Which one’s bigger? I need to drill a hole. I have a
19mm drill, and an 18mm drill. Which one’s bigger?

Is 70lb/ream text paper heavier
(that is, thicker) than 60lb/ream cover? No. Is 244mg/m^{2}
paper thicker than 198mg/m^{2}? Yes.

An 11′′ × 17′′ (“ledger” size) sheet of paper has twice the surface area of an 8.5′′ × 11′′ (“letter” size), and can be cut into two letter size sheets. Can I enlarge a letter-sized poster to fit on the ledger-sized sheet? No. Ledger sized paper has a proportion of 1:1.55, but letter size’s ratio is 1:1.3. The rectangles have different proportions.

An A3 sheet is twice the surface
area of an A4 sheet, and can be cut into two A4 size sheets. If I enlarge an A4
size poster by 141%, will it fit on the A3 sheet? Yes. Why not 200%? Because
that would make the poster twice as big in both directions, or four times as
large in surface area. Metric paper keeps the same ratio because it’s always 1:√2.
If you enlarged an A4 poster by 200%, it would fit perfectly onto an A2 sheet (1 × √2 × √2 = 2).
Oh, and you can figure out the dimensions of *any* A-size sheet of paper if you know just
three simple facts: (1) If you cut an A(n) sheet in half across the narrow dimension, you get an A(n+1) sheet,
(2) that the proportions are 1:√2, and (3) that an A0 sheet has a
surface area of 1 square meter.

Is an A5 sheet bigger or smaller than an A3 sheet, and by how much? Is a tabloid sheet bigger or smaller than a ledger sheet, and by how much? Answers: the A5 is, as you should be able to guess, 1/4 the surface area of an A3 sheet, and “tabloid” is an alternative name for “ledger,” so they’re the same size.

Given the dimensions for “letter” sized paper, can you figure out what size “legal” must be in the U.S? No, of course not. How about in the Phillippines? Or Chile? (In the Philippines and Chile, “legal” paper is 8.5 × 13′′, not 14′′.)

Arrange the following by area, largest to smallest: Hectare, Acre, Square Mile, Circular Mil. Arrange the following by area, largest to smallest: Square Meter, Square Centimeter, Square Kilometer, Square Nanometer.

Sort by weight: an ounce of
feathers, an ounce of gold, and an ounce of ethyl alcohol. Yes, it is a trick
question, but sadly, the answer is *not*
“they’re the same.” The answer is: Gold is measured in troy ounces, and
is thus 28.35 grams, and feathers (and almost everything else but gold) are measured in avoirdupois ounces, and would be
31.1 grams. No, I am not kidding. And the alcohol? That depends: being a fluid, it should be measured
in fluid ounces, which is a unit of *volume*,
not weight. I’d need my “Handbook of Chemistry and Physics” to find
out. . . and lo, the density is in grams per milliliter. (I’ll just point out that
my copy of the Handbook is the *1959(!)* edition.) OK, one fl. oz. =
29.5737 cm^{3} (according to the handbook), which is 29.5737
milliliters. That’s not a coincidence, since the measure of volume, the liter,
is *defined* to be one cubic decimeter.
The density is .7893 g/ml, so that means 23.343 grams. This is clearly
lighter than the other two. How much lighter? 23 grams ÷ 31.1 (grams per ounce)
= about 0.75 avoirdupois ounces. Unless I really
meant “one ounce of ethyl alcohol by weight,” in which case it weighs the same
as the feathers.

About that cm^{3} = ml thing?
If I’ve got an aquarium that’s 10 × 12 × 20 inches, how many gallons will it hold?
If it’s 25 × 30 × 50 cm, then the answer is 37500 cubic cm, or 37500 ml. Move the
point three to the left, and you get 37.5 liters. It’s a good thing I’ve got
that Handbook handy to look up the conversion for gallons: 7.481 gallons per cubic foot.
Unfortunately, the only conversion factor for cubic
*inches* listed is into cubic centimeters, so I can’t find out how many gallons
the tank holds until I figure out its volume in cubic feet. Let’s see,
(10 ÷ 12) × (12 ÷ 12) × (20 ÷ 12) = .8333 × 1 × 1.6667
feet = 1.3888 cubic feet. Or, a cubic foot
contains 12^{3} cubic inches (that’s 1728), so (10 × 12 × 20 inches) ÷ 1728 =
2400 in^{3} ÷ 1728
=1.3888 ft^{3}. Either way, 1.3888 ft^{3} × 7.481 gallons
per cubic foot = 10.4 gallons.

As long as I’m filling my aquarium, maybe I should make sure the aquarium stand can handle the weight. How much does 10.4 gallons of water weigh? A friend of mine is fond of the mnemonic phrase “A pint’s a pound the world around.” How many pints in a gallon? Um, four quarts in a gallon, two pints in a quart, eight! So a gallon of water weights eight pounds! If you wanted to be precise, you might specify “at room temperature,” but then again, if you wanted to be precise, you’re already doomed, since a gallon of water at 75°F actually weights 8.34 pounds.

What does 37.5 liters of water weigh? 37.5 kilograms. That’s at 24°C, by the way. Since a gram is *based on* the mass of a cubic centimeter of water, you don’t have to worry about any lack of precision this time.

If you are compulsive enough to check my math, you’ll find that my U.S. aquarium is apparently half a gallon bigger than my metric aquarium. You didn’t really think that my aquarium was exactly ten inches wide, did you? I rounded all the measurements. It was actually about 9 and 27/32nds inches. I rounded the metric numbers too, but to the nearest millimeter. Which one do you think is more accurate? If I use the 32nd lines on my ruler, I would get even more precision than I can get with millimeters, but then I’m back to the indescribable delights of fractional math.

What happens if you want to get down to the nuts and bolts of the issue? In one hand, I have a 1/4′′ by 2′′ bolt. That means it’s two inches long, and has a diameter of a quarter of an inch. What’s implicit in this is that is also has a thread ratio of 20, which I guess means 20 threads per inch along the shaft. In the other hand, I have an M6x50 bolt, which has a diameter of 6mm and a length of 50mm. Implicitly, it has a thread pitch of 1 thread per mm.

So I went shopping one day for some
bolts to use with my equipment rack. I knew that 1/4 inch bolts were too big: I
needed bolts two sizes smaller. Now, for anything *larger* than 1/4 inch, in the US’s NATO-created United
National system, you specify it in fractions of an inch, so the next two sizes
up are 5/16ths and 3/8ths. We’ve already covered why that’s not such a great
system. But going down, it changes. The next two *smaller* sizes are #12 and #10.

I could tell I needed a #10 bolt,
but my #10’s didn’t fit. It turned out I needed a #10 *fine thread*,
not the standard #10 coarse thread. A normal #10 is
a 10-24 with 24 threads per inch, but a fine thread #10 is a 10-32. (So the
specification for a #10 bolt with fine threads that’s 1/2′′ long is 10-32 × 1/2.)

Metric isn’t really “better” as long as you’re just putting nuts and bolts together. A #8 is smaller than a #10, and an M3 is smaller than an M4. A coarse thread #8 is an 8-32, and a fine thread #8 is an 8-36. A coarse thread M4 has a thread every 0.7mm, and a fine thread has one every 0.5mm.

But what happens when you want to drill a hole for your bolt? What size drill bit do I use for a #8 bolt? The answer is: a 3/16ths bit. That is, I’ll be making a 0.1875′′ hole for my 0.164′′ diameter bolt. I can either look up that answer in a chart, or try to eyeball it by holding the bolt up to different drill bits until I find one that looks about right. What if I have an M5 bolt? I’ll use a 6mm drill bit, of course. How easy.

How easy. And one day, maybe even we Americans will be able to take advantage of a system where ratios are consistent, where larger sizes almost always have larger numbers attached, where fractions are rarely seen but decimal points are common.

Here’s one last comparison. Quick, tell me what you’re measuring if you’re using the “pica” as a unit of measurement, and how big is one pica? OK, so that’s a tough one. I’ll give you a two-part hint. Part one: have you ever heard of a “point”, as in “twelve point type?” Part two: a pica is likewise a unit of length.

Hmm. Well, twelve point type isn’t very big, so a point must be awfully small. But how many points in a pica, or is it picas in a point? Don’t have that one memorized? I do. I even know how many points in an inch. Oh, and a “point” in Adobe’s PostScript (and thus probably the version of “point” that your computer uses) is a different length than the “point” used by all the printing technology that came before.

Now a metric version of that puzzle: What do you measure with a “bel” and how big it is? Hint part one: ever heard of a “decibel?”

Well, hint part two would be to point out that decibels and bels are related,
but you probably already figured that out, as well as deducing that
a bel is a measure of sound,
and is ten times larger than a decibel. But even the *Handbook of Chemistry
and Physics* won’t tell you that a pica is
12 points, or 0.0830220008 of an inch, although most typographers or printing
press operators can.

There you are. 3.285 kilowords to
make a point (72.27 points in an inch!^{‡}) about the metric system.

—Dave Howell

* Yes, “manual,” not “analog.” A digital watch is called that *not* because it uses digital circuitry;
nearly all the watches made today with hands on them are also digital devices. A digital watch is called that because the display
is in digits, instead of using hands. Latin for hands is “manus,” thus “manual labor,” so a watch with hands is
a manual watch, not an analog watch. [Return]

† A bit of typographical geekery. Note that the tick marks after the number of inches are not quote marks?
Everybody *thinks* they’re quote marks, but they’re not. Properly, they’re a “prime tick,” which was different before
typewriters came along and forced everybody to make do with a sadly limited number of symbols. [Return]

‡ Unless it’s PostScript. Then it’ll be 72 points per inch, although “picas” don’t (or at least shouldn’t) use the rounded-off PostScript point. And the bel is named after Alexander Graham Bell. [Return]