Conversion Factor — Definition, Formula & Examples
A conversion factor is a fraction (ratio) that equals 1 and is used to change a measurement from one unit to another without changing its actual value. For example, since 12 inches = 1 foot, the fraction is a conversion factor.
A conversion factor is a ratio derived from an equality between two different units, expressed as a fraction whose numerator and denominator represent the same quantity in different units, so that the fraction's value is exactly 1.
How It Works
To use a conversion factor, multiply your original measurement by the fraction so that the unwanted unit cancels out. Write the conversion factor with the unit you want to remove in the denominator and the unit you want to keep in the numerator. The units cancel like common factors in a fraction, leaving only the desired unit. You can chain multiple conversion factors together when converting across more than one step.
Worked Example
Problem: Convert 5 feet to inches using a conversion factor.
Identify the equality: 1 foot equals 12 inches, so the conversion factor with inches on top is:
Multiply and cancel units: Multiply 5 ft by the conversion factor. The foot units cancel, leaving inches.
Answer: 5 feet = 60 inches
Why It Matters
Conversion factors are essential in science classes whenever you need to switch between metric and imperial units or between different metric prefixes. They also appear in everyday tasks like cooking (converting cups to tablespoons) and in careers such as engineering, nursing, and construction where using the wrong unit can have serious consequences.
Common Mistakes
Mistake: Placing the conversion factor upside down so units do not cancel.
Correction: Always put the unit you want to eliminate in the denominator. If converting feet to inches, feet must be on the bottom of the fraction so it cancels with feet in the original measurement.