Conversion factor

The conversion factor or unit factor is a conversion method that is based on multiplying by one or more fractions in which the numerator and denominator are quantities equal expressed in different units of measurement, in such a way that each fraction is equivalent to the unit. It is a very effective method for changing units and solving simple exercises without using the rule of three.

Examples

Each conversion factor is built with an equivalence (equality between two quantities).

• Example 1: pass 15 inches to centimeters (1 in ≡ 2.54 cm)

15in× × 2.54cm1in=38.1cm{displaystyle 15{text{ in}}}times {frac {2.54{text{ cm}}}}{1{text{ in}}}}}}{38.1{text{ cm}}}}}}

the unitary factor 2.54cm/1in{textstyle 2.54{text{ cm}}/1{text{ in}}} is built from the given equivalence.

• Example 2: pass 25 meters per second to kilometers per hour (equivalences: 1 kilometer ≡ 1000 meters, 1 hour ≡ 3600 seconds)

25ms× × 1km1000m× × 3600s1h=90kmh{displaystyle 25,mathrm {frac {m}{s}}} times {frac {1{text{ km}}}}{1000{text{ m}}}}}}}}}{times {frac {3600{text{ s}{1}{1{1{text{ h}}}}}}}}}{90mathrm {mathrm {

In each of the fractions between parentheses, the same measure has been used in different units so that in the end only the unit is required.

Examples showing simplification

• 2 and a half days to hours::

2,5days× × 24h1Day=2,5days× × 24h1Day=60h{displaystyle 2.5{cancel {mbox{days}}}{times {frac {24{mbox{mbox}}{1{1{mbox{dia}}}}{frac}{2,5} {cancel {mbox{days}}}{times 24{mbox{ hbox}{1}{cancel {mbox}{1}{1}{

• Spend 30 cm/s at km/h:

30cms× × 1m100cm× × 1km1000m× × 60s1min× × 60min1h=1,08km/h{cHFFFF}{cH00FF}{cH00FF}{cH00FF}{cH00FF}{cH00FF}{cH00FF}{cH00FF}{cH00}{cH00}{cH00}{cH00}{cH00FF}{cH00}{cH00}{cH00}{cH00}{cH00}{cH00}{cH00}{cH00}{cH00}{cH00}{cH00}{cH00}{cH00FF}{cH00FF}{cH00}{cH00}{cH00}{cH00}{cH00FF}{cH00}{cH00FF}{cH00}{cH00}{cH00FF}{cH00}{cH00}{cH00}{