A conversion factor is a ratio that changes a quantity from one unit to another. It is a fraction equal to one. Multiply by the conversion factor and the units cancel, leaving the desired unit. The value stays the same. Only the label changes.

If 1 inch equals 2.54 centimeters, then the fraction 2.54 cm / 1 in is a conversion factor. Multiply 10 inches by that fraction and the inches cancel, leaving 25.4 centimeters. The method is called dimensional analysis. It works for any unit conversion, from miles to kilometers, from grams to moles, from joules to calories.

Common conversion factors

• 1 inch = 2.54 centimeters.
• 1 mile = 1.609 kilometers.
• 1 pound = 0.4536 kilograms.
• 1 gallon = 3.785 liters.
• 1 calorie = 4.184 joules.

The trick is to set up the fraction so the unwanted unit cancels. If the unit is in the numerator, put the conversion factor with that unit in the denominator. If the unit is in the denominator, flip it. Chain multiple conversion factors together to go through intermediate units. Convert miles per hour to meters per second by multiplying by kilometers per mile, meters per kilometer, and hours per second. Dimensional analysis catches errors. If the units do not cancel to the desired unit, the setup is wrong. It is one of the most useful skills in science. It turns unit conversion from a memorization task into a systematic procedure.