How unit conversion works: a simple guide
Quick answer: to convert a unit, multiply by a conversion factor, a number that says how many of one unit fit in another. The trick is knowing whether to multiply or divide, and you can check that with a simple rule.
The idea: a conversion factor is a ratio
Every conversion factor comes from a fact like “1 inch = 2.54 centimeters”. Written as a fraction, it equals 1, because the top and bottom describe the same length:
2.54 cm / 1 in = 1
Multiplying by 1 does not change the size of something, only the unit you describe it in. That is the whole idea.
The multiply-or-divide rule
Ask yourself: am I going to a smaller unit or a bigger unit?
- Bigger unit to smaller unit (cups to milliliters): the number gets larger, so you multiply.
- Smaller unit to bigger unit (milliliters to cups): the number gets smaller, so you divide.
A quick sense-check catches most errors. If you convert 3 cups to milliliters and get 0.0127, you divided when you should have multiplied.
A worked example
Convert 3 cups to milliliters. One US cup is 236.588 ml.
3 x 236.588 = 709.76 ml, which we can call about 710 ml.
Convert 500 ml to cups. Going to a bigger unit, so divide:
500 / 236.588 = 2.11 cups.
Cancelling units
For longer conversions, write out the units and cancel them like fractions.
How many teaspoons are in 2 cups? One cup is 16 tablespoons, and one tablespoon is 3 teaspoons:
2 cups x (16 tbsp / 1 cup) x (3 tsp / 1 tbsp) = 96 tsp
The cups cancel, then the tablespoons cancel, leaving teaspoons. If the units do not cancel to what you want, you have the factor upside down.
Exact vs approximate factors
Some conversions are exact by definition, and others are rounded:
- 1 inch = 2.54 cm exactly
- 1 pound = 0.45359237 kg exactly
- 1 US gallon = 231 cubic inches exactly
- 1 cup = 236.588 ml is a rounded value
Our converters use the exact definitions and show up to six significant digits.
Volume is not weight
You can convert volume to volume (cups to milliliters) or weight to weight (ounces to grams) with a fixed factor. You cannot convert cups to grams without knowing the ingredient, because it depends on the density. That is why our converters only offer same-type pairs, and why cups to grams has no single answer.
Rounding sensibly
Round at the end, not in the middle, and keep as many digits as your measuring tool can use. A kitchen scale that reads to 1 gram does not need six digits, and 709.76 ml is fine as 710 ml. For land or construction, keep more.
Common mistakes
- Using fluid ounces where you need ounces of weight.
- Mixing US and UK units, for example pints or gallons. See US cup vs metric cup vs UK cup.
- Forgetting that area factors are squared. One foot is 0.3048 m, so one square foot is 0.3048 x 0.3048 = 0.0929 square meters, not 0.3048.
Try these ideas with our kitchen and area converters, or read the worked examples for grams to ounces.