Conversion of units refers to conversion factors between different units of measurement for the same quantity.
Techniques
The simplest way to convert from one unit to another is to carry through the units themselves in the mathematical operation. To illustrate this process, consider the following examples.
You would like to convert 6 feet into metres. Consulting the table below and finding that one foot is exactly 0.3048 metre, you can now perform the mathematical conversion:
- 6 ft × 0.3048 m/ft = 1.8288 m
Notice that the "foot" units canceled out, leaving only metres, the desired result. (Since 0.3048 metre per foot have infinite precision, the precision of the answer is determined by the precision of the 6 ft figure; if, for example, you are defining the fathom, expressing it with 5 significant figures is correct. But if the 6 ft figure is a measurement, the result needs to be rounded appropriately.)
Say your height is 183 centimetres, and you wish to convert this into inches:
- 183 cm / (2.54 cm/in) = 72.0 in
To check our answer, we convert this result back into feet:
- 72 in / (12 in/ft) = 6.0 feet
which confirms the earlier result.
Multiple units can be manipulated in the same fashion:
- 7 mi/s × 1.609344 km/mi × 3600 s/h = 40,000 km/h
Thus, Earth escape velocity is about 7 miles per second, or 40,000 kilometres per hour. Notice that since the calculation started with one significant figure (the 7), the answer also has one significant figure (the 4 in 40,000).
Deciding whether to multiply or divide is determined by looking at the units and deciding which ones you want to "get rid" of. In the conversion just above, if we had divided by 3600 s/h instead of multiplying, the result would have come out in kilometre-hours per square second, clearly an incorrect and meaningless result.
Rounding of results
An important thing to remember is that the process of making a conversion cannot give you any more precise results than what you started with. While many of the conversion factors given in the tables below are exact, and others while not exact contain many significant digits, not all the numbers you get after performing calculations on a calculator or with pencil and paper are meaningful.
After using these conversion factors, be sure to round off the results appropriately.
Software tools
Units and measurements can be easily converted using software tools, but only if the units are explicitly defined and the conversion is compatible (e.g., cmHg to kPa).
One popular command-line utility is units. Another utility and programming library is UDUNITS.
For Windows users, Josh Madison offers Convert, as a downloadable .exe or .zip file.
Modern TI (Texas Instruments) calculators have unit-conversion functionality, as well as the popular math software Mathematica (in its "Miscellaneous`Units" default package).
