Conversion Factor Definition and Examples

A conversion factor is the number or formula you need to convert a measurement in one set of units to the same measurement in another set of units. The number is usually given as a numerical ratio or fraction that can be used as a multiplication factor. For example, say you have a length that is measured in feet and you wish to report on it in meters. If you know that there are 3.048 feet in a meter, then you can use that as a conversion factor to determine what the same distance is in meters. 

One foot is 12 inches long, and the conversion factor of 1 foot to inches is 12. In yards, 1 foot is equal to 1/3 yard (conversion factor of 1 foot to yards is 1/3) so forth. The same length is 0.3048 meters, and it is also 30.48 centimeters.

• To convert 10 feet to inches, multiply 10 times 12 (the conversion factor) = 120 inches
• To convert 10 feet to yards, multiply 10 x 1/3 = 3.3333 yards (or 3 1/3 yards)
• To convert 10 feet to meters, multiply 10 x .3048 = 3.048 meters
• To convert 10 feet to centimeters, multiply 10 x 30.48 = 304.8 centimeters

Examples of Conversion Factors

There many different types of measurements that sometimes require conversions: length (linear), area (two dimensional) and volume (three dimensional) are the most common, but you can also use conversion factors to convert mass, speed, density, and force. Conversion factors are used for conversions within the imperial system (feet, pounds, gallons), within the International System of Units (SI, and the modern form of the metric system: meters, kilograms, liters) or across the two. 

Remember, the two values must represent the same quantity as each other. For example, it's possible to convert between two units of mass (e.g., grams to pounds), but you generally can't convert between units of mass and volume (e.g., grams to gallons).

Examples of conversion factors include:

• 1 gallon = 3.78541 liters (volume)
• 1 pound = 16 ounces (mass) 
• 1 kilogram = 1,000 grams (mass) 
• 1 pound = 453.592 grams (mass)
• 1 minute = 60000 milliseconds (time) 
• 1 square mile = 2.58999 square kilometers (area) 

Using a Conversion Factor

For example, to change a time measurement from hours to days, use a conversion factor of 1 day = 24 hours.

• time in days = time in hours x (1 day/24 hours)

The (1 day/24 hours) is the conversion factor.
Note that following the equal sign, the units for hours cancel out, leaving only the unit for days.