3 ms·

Here in Canada, my family ran a fishing camp with a lot of US customers. I was talking with one of them about metric vs. US units and to demonstrate I said ho

Here in Canada, my family ran a fishing camp with a lot of US customers. I was talking with one of them about metric vs. US units and to demonstrate I said how about this: How many gallons in a cubic mile? And he was able to work it out in his head, and pretty quickly too. Whoa. The point I was trying to make that is than in metric (say, liters per cubic kilometer) you just need to get the number of zeroes right, but you can't argue with results.

nayuki 9mo ago
> he was able to work it out in his head, and pretty quickly That's a scary ability. I wonder if that guy is equally adept at converting acre-feet to gallons, or if he's a one-trick pony. Here's what I know without looking anything up: 1 mile = 1760 yards, 1 yard = 3 feet, 1 foot = 12 inches; 1 US gallon = 231 cubic inches (exact conversion, and a weird number at that). So 1 cubic mile = (63360 inch)^3 = 7707820032000/7 gal ≈ 1.101 trillion US gallons. Fun fact, combustion engine displacements used to be quoted in cubic inches. Note that 61 in^3 ≈ 1 litre.
mark-r 9mo ago
I was able to do something similar by using gross approximations and conversions to/from metric. My coworker had just bought a surplus stainless steel water tank for solar heating, and was wondering how much it would weigh when full. It was cylindrical, so I asked him for the diameter and the height. In my head I converted those measurements to inches, then to centimeters by multiplying by 2.5. I divided the diameter by 2, squared it, and multiplied by 3 (close enough to pi) to get the area. Then I converted the area and the height to their nearest power of 2 so I could take advantage of logarithms. Multiplying the area and height was as easy as adding the exponents, which gave me cubic centimeters. The weight of water is almost by definition 1 gram per 1 cc. Divide by 1000 to get kg by subtracting 10 from the exponent, then multiply by 2 to get approximate pounds by adding 1 to the exponent. By the time he was done telling me the dimensions, I had an answer for him. It definitely wasn't correct, but all he needed was a ballpark anyway.
mikhailfranco 9mo ago
It's not too difficult to know or calculate inches in a mile: 12 * 3 * 1760 = 12 * 5280 = 63,360 A few Americans may know how many cubic inches in a US gallon: 231 But I don't believe anyone (apart from rainman/prodigy circus performers) can do this in their head: 63360^3 / 231 = 1,101,117,147,428.571 Estimate yes; calculate no.
- MarkusWandel 9mo ago
  That's probably what it was, an engineering estimate with a couple of significant digits. It's been years.

nayuki 9mo ago

> he was able to work it out in his head, and pretty quickly That's a scary ability. I wonder if that guy is equally adept at converting acre-feet to gallons, or if he's a one-trick pony. Here's what I know without looking anything up: 1 mile = 1760 yards, 1 yard = 3 feet, 1 foot = 12 inches; 1 US gallon = 231 cubic inches (exact conversion, and a weird number at that). So 1 cubic mile = (63360 inch)^3 = 7707820032000/7 gal ≈ 1.101 trillion US gallons. Fun fact, combustion engine displacements used to be quoted in cubic inches. Note that 61 in^3 ≈ 1 litre.

mark-r 9mo ago

I was able to do something similar by using gross approximations and conversions to/from metric. My coworker had just bought a surplus stainless steel water tank for solar heating, and was wondering how much it would weigh when full. It was cylindrical, so I asked him for the diameter and the height. In my head I converted those measurements to inches, then to centimeters by multiplying by 2.5. I divided the diameter by 2, squared it, and multiplied by 3 (close enough to pi) to get the area. Then I converted the area and the height to their nearest power of 2 so I could take advantage of logarithms. Multiplying the area and height was as easy as adding the exponents, which gave me cubic centimeters. The weight of water is almost by definition 1 gram per 1 cc. Divide by 1000 to get kg by subtracting 10 from the exponent, then multiply by 2 to get approximate pounds by adding 1 to the exponent. By the time he was done telling me the dimensions, I had an answer for him. It definitely wasn't correct, but all he needed was a ballpark anyway.

mikhailfranco 9mo ago

It's not too difficult to know or calculate inches in a mile: 12 * 3 * 1760 = 12 * 5280 = 63,360 A few Americans may know how many cubic inches in a US gallon: 231 But I don't believe anyone (apart from rainman/prodigy circus performers) can do this in their head: 63360^3 / 231 = 1,101,117,147,428.571 Estimate yes; calculate no.

MarkusWandel 9mo ago
That's probably what it was, an engineering estimate with a couple of significant digits. It's been years.