In the previous post I described a couple new approaches to my original compendium of stack math algorithms. Below is the updated compendium. The error is calculated using this script, which for algorithms that aren't simple multiplication or division checks the error at a few powers of ten and reports the worst accuracy.
If you have any improvements to suggest, or would like to see some additional conversions, feel free to email me.
| Conversion | Less accurate | More accurate |
|---|---|---|
Celsius → Fahrenheit 9 * 5 / 32 + | double -tenth +32(exact) | |
Fahrenheit → Celsius 32 - 5 * 9 / | -32 halve +tenth(1% error) | |
15% tip 0.15 * | tenth +half(exact) | |
Multiply by π 3.14159 * | triple +tenth(5% error) | triple +twentieth(0.3% error) |
Divide by π 3.14159 / | third -tenth(6% error) | third -twentieth(0.5% error) |
kilometers → miles 0.6214 * | two-thirds(7% error) | two-thirds -tenth +twentieth(1% error) |
miles → kilometers 1.609 * | +half(7% error) | [+half] left [tenth] right +(0.6% error) |
meters → feet 3.281 * | triple(9% error) | triple +tenth(0.6% error) |
feet → meters 3.281 / | third(9% error) | third -tenth(2% error) |
inches → centimeters 2.54 * | tenfold quarter(2% error) | |
centimeters → inches 2.54 / | tenth quadruple(2% error) | |
miles → feet 5280 * | five-thousandfold(5% error) | five-thousandfold +twentieth(0.6% error) |
feet → miles 5280 / | five-thousandth(6% error) | five-thousandth -twentieth(0.3% error) |
kilograms → pounds 2.205 * | double(9% error) | double +tenth(0.2% error) |
pounds → kilograms 2.205 / | halve(10% error) | halve -tenth(0.8% error) |
hours → seconds 3600 * | four-thousandfold(10% error) | four-thousandfold -tenth(exact) |
seconds → hours 3600 / | four-thousandth(10% error) | four-thousandth +tenth(1% error) |
mi/h → ft/s 1.467 * | +half(2% error) | |
ft/s → mi/h 1.467 / | two-thirds(2% error) | |
sq. miles → acres 640 * | seven-hundredfold(9% error) | seven-hundredfold -tenth(2% error) |
acres → sq. miles 640 / | seven-hundredth(9% error) | seven-hundredth +tenth(0.6% error) |
acres → sq. feet 43560 * | ten-thousandfold quadruple(8% error) | ten-thousandfold quadruple +tenth(1% error) |
sq. feet → acres 43560 / | ten-thousandth quarter(9% error) | ten-thousandth quarter -tenth(2% error) |
sq. kilometers → acres 247.1 * | thousandfold quarter(1% error) | |
acres → sq. kilometers 247.1 / | thousandth quadruple(1% error) | |
pounds → troy ounces 14.58 * | tenfold +half(3% error) | [tenfold +half] left [halve] right -(0.5% error) |
troy ounces → pounds 14.58 / | tenth two-thirds(3% error) | |
US cups → fluid ounces 8 * | quadruple double(exact) | |
fluid ounces → US cups 8 / | quarter halve(exact) | |
liquid gallons → US cups 16 * | quadruple quadruple(exact) | |
US cups → liquid gallons 16 / | quarter quarter(exact) | |
liquid gallons → liters 3.785 * | quadruple(6% error) | quadruple -twentieth(0.4% error) |
liters → liquid gallons 3.785 / | quarter(5% error) | quarter +twentieth(0.6% error) |
sphere radius → surface area square 4 * 3.14159 * | square tenfold +quarter(0.5% error) | |
sphere radius → volume cube 4 * 3 / 3.14159 * | cube quadruple(5% error) | cube quadruple +twentieth(0.3% error) |
sphere surface area → radius 4 / 3.14159 / sqrt | tenth -quarter sqrt(3% error) | hundredth quadruple double sqrt(0.3% error) |
sphere volume → radius 4 / 3 * 3.14159 / cube-root | quarter cube-root(2% error) |