Conversion of units is the conversion of the unit of measurement in which a quantity is expressed, typically through a multiplicative conversion factor that changes the unit without changing the quantity.
Unit conversion is often easier within a metric system such as the SI than in others, due to the system's coherence and its metric prefixes that act as power-of-10 multipliers.
The definition and choice of units in which to express a quantity may depend on the specific situation and the intended purpose.
This may be governed by regulation, contract, technical specifications or other published standards.
Engineering judgment may include such factors as: For some purposes, conversions from one system of units to another are needed to be exact, without increasing or decreasing the precision of the expressed quantity.
An adaptive conversion may not produce an exactly equivalent expression.
[2][3][4] The factor–label method is the sequential application of conversion factors expressed as fractions and arranged so that any dimensional unit appearing in both the numerator and denominator of any of the fractions can be cancelled out until only the desired set of dimensional units is obtained.
For example, 10 miles per hour can be converted to metres per second by using a sequence of conversion factors as shown below:
, "mile" will need to be the denominator in the conversion factor.
Dividing both sides of the equation by 1 mile yields
As a more complex example, the concentration of nitrogen oxides (NOx) in the flue gas from an industrial furnace can be converted to a mass flow rate expressed in grams per hour (g/h) of NOx by using the following information as shown below: After cancelling any dimensional units that appear both in the numerators and the denominators of the fractions in the above equation, the NOx concentration of 10 ppmv converts to mass flow rate of 24.63 grams per hour.
For example, check the universal gas law equation of PV = nRT, when:
As can be seen, when the dimensional units appearing in the numerator and denominator of the equation's right hand side are cancelled out, both sides of the equation have the same dimensional units.
Dimensional analysis can be used as a tool to construct equations that relate non-associated physico-chemical properties.
The equations may reveal undiscovered or overlooked properties of matter, in the form of left-over dimensions – dimensional adjusters – that can then be assigned physical significance.
It is important to point out that such 'mathematical manipulation' is neither without prior precedent, nor without considerable scientific significance.
Indeed, the Planck constant, a fundamental physical constant, was 'discovered' as a purely mathematical abstraction or representation that built on the Rayleigh–Jeans law for preventing the ultraviolet catastrophe.
It was assigned and ascended to its quantum physical significance either in tandem or post mathematical dimensional adjustment – not earlier.
The factor–label method can convert only unit quantities for which the units are in a linear relationship intersecting at 0 (ratio scale in Stevens's typology).
Thus, to convert from units of Fahrenheit to units of Celsius, one subtracts 32 °F (the offset from the point of reference), divides by 9 °F and multiplies by 5 °C (scales by the ratio of units), and adds 0 °C (the offset from the point of reference).
Reversing this yields the formula for obtaining a quantity in units of Celsius from units of Fahrenheit; one could have started with the equivalence between 100 °C and 212 °F, which yields the same formula.
Hence, to convert the numerical quantity value of a temperature T[F] in degrees Fahrenheit to a numerical quantity value T[C] in degrees Celsius, this formula may be used: To convert T[C] in degrees Celsius to T[F] in degrees Fahrenheit, this formula may be used: Starting with: replace the original unit
Or, which is just mathematically the same thing, multiply Z by unity, the product is still Z: For example, you have an expression for a physical value Z involving the unit feet per second (
): Or as an example using the metric system, you have a value of fuel economy in the unit litres per 100 kilometres and you want it in terms of the unit microlitres per metre: In the cases where non-SI units are used, the numerical calculation of a formula can be done by first working out the factor, and then plug in the numerical values of the given/known quantities.
For example, in the study of Bose–Einstein condensate,[6] atomic mass m is usually given in daltons, instead of kilograms, and chemical potential μ is often given in the Boltzmann constant times nanokelvin.
For a 23Na condensate with chemical potential of (the Boltzmann constant times) 128 nK, the calculation of healing length (in micrometres) can be done in two steps: Assume that
This method is especially useful for programming and/or making a worksheet, where input quantities are taking multiple different values; For example, with the factor calculated above, it is very easy to see that the healing length of 174Yb with chemical potential 20.3 nK is There are many conversion tools.
There are many standalone applications that offer the thousands of the various units with conversions.
For example, the free software movement offers a command line utility GNU units for GNU and Windows.
[7] The Unified Code for Units of Measure is also a popular option.