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Unit Conversion Using Conversion Factors

A conversion factor is a fraction formed from two equivalent measurements, such as 12 inches1 foot\frac{12 \text{ inches}}{1 \text{ foot}} or 1 foot12 inches\frac{1 \text{ foot}}{12 \text{ inches}}. Because the numerator and denominator represent the same quantity expressed in different units, every conversion factor equals 11. To convert a measurement from one unit to another, multiply the given quantity by a conversion factor chosen so that the unwanted unit appears in the position (numerator or denominator) that will allow it to cancel:

given quantity×desired unitgiven unit=result in desired unit\text{given quantity} \times \frac{\text{desired unit}}{\text{given unit}} = \text{result in desired unit}

For example, to convert 55 feet to inches: 5 ft×12 in.1 ft=60 in.5 \text{ ft} \times \frac{12 \text{ in.}}{1 \text{ ft}} = 60 \text{ in.} The "ft" labels cancel, leaving only inches. This technique — sometimes called dimensional analysis — works because multiplying by a fraction equal to 11 does not change the value of the measurement, only the unit in which it is expressed.

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Updated 2026-04-21

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