Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
Techniques
Process overview
The process of conversion depends 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:
The precision and accuracy of measurement and the associated uncertainty of measurement.
The statistical confidence interval or tolerance interval of the initial measurement.
The number of significant figures of the measurement.
The intended use of the measurement including the engineering tolerances.
Historical definitions of the units and their derivatives used in old measurements; e.g., international foot vs. US survey foot.
Some conversions from one system of units to another need to be exact, without increasing or decreasing the precision of the first measurement.
This is sometimes called soft conversion.
It does not involve changing the physical configuration of the item being measured.
By contrast, a hard conversion or an adaptive conversion may not be exactly equivalent.
It changes the measurement to convenient and workable numbers and units in the new system.
It sometimes involves a slightly different configuration, or size substitution, of the item.
Nominal values are sometimes allowed and used.
Conversion factors
A conversion factor is used to change the units of a measured quantity without changing its value.
The unity bracket method of unit conversion consists of a fraction in which the denominator is equal to the numerator, but they are in different units.
Because of the identity property of multiplication, the value of a quantity will not change as long as it is multiplied by one.
Also, if the numerator and denominator of a fraction are equal to each other, then the fraction is equal to one.
So as long as the numerator and denominator of the fraction are equivalent, they will not affect the value of the measured quantity.
The following example demonstrates how the unity bracket method is used to convert the rate 5 kilometers per second to meters per second.
The symbols km, m, and s represent kilometer, meter, and second, respectively.
\frac{5 \cancel {\text {km}}}{\text {s}} \cdot\frac{{1000 }\text { m}}{{1}{\cancel {\text { km}}}}=\frac{{5000 \cdot {\text {m}}}}{{\text {s}\cdot {1}}} =\frac {5000{\text { m}}}{\text {s}}
Thus, it is found that 5 kilometers per second is equal to 5000 meters per second.
Software tools
There are many conversion tools.
They are found in the function libraries of applications such as spreadsheets databases, in calculators, and in macro packages and plugins for many other applications such as the mathematical, scientific and technical applications.
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 Linux and Windows.
Calculation involving non-SI Units
In the cases where non-SI units are used, the numerical calculation of a formula can be done by first working out the pre-factor, and then plug in the numerical values of the given/known quantities.
For example, in the study of Bose–Einstein condensate, atomic mass  is usually given in daltons, instead of kilograms, and chemical potential μ is often given in Boltzmann constant times nanokelvin.
The condensate's healing length is given by:
\xi=\frac{\hbar}{\sqrt{2m\mu}}\,.
For a 23Na condensate with chemical potential of (Boltzmann constant times) 128 nK, the calculation of healing length (in micrometres) can be done in two steps: Calculate the pre-factor
Assume that m=1 \,\text{Da},\mu=k_\text{B}\cdot 1\,\text{nK}\,, this gives
\xi=\frac{\hbar}{\sqrt{2m\mu}}=15.574 \,\mathrm{\mu} m\,,
which is our pre-factor.
Calculate the numbers
Now, make use of the fact that \xi\propto\frac{1}{\sqrt{m\mu}}.
With m=23 \,\text{Da},\mu=128\,k_\text{B}\cdot\text{nK}, \xi=\frac{15.574}{\sqrt{23\cdot128}} \,\mathrm{\mu} m=0.287\,\mathrm{\mu} m.
This method is especially useful for programming and/or making a worksheet, where input quantities are taking multiple different values; For example, with the pre-factor calculated above, it's very easy to see that the healing length of 174Yb with chemical potential 20.3 nK is \xi=\frac{15.574}{\sqrt{174\cdot20.3}} \,\mu m=0.262\,\mathrm{\mu} m.
Tables of conversion factors
This article gives lists of conversion factors for each of a number of physical quantities, which are listed in the index.
For each physical quantity, a number of different units (some only of historical interest) are shown and expressed in terms of the corresponding SI unit.
Conversions between units in the metric system are defined by their prefixes (for example, 1 kilogram = 1000 grams, 1 milligram = 0.001 grams) and are thus not listed in this article.
Exceptions are made if the unit is commonly known by another name (for example, 1 micron = 10−6 metre).
Within each table, the units are listed alphabetically, and the SI units (base or derived) are highlighted.
Legend
Length
[[Length]]
Area
[[Surface area|Area]]
Volume
[[Volume]]
Plane angle
[[Angle|Plane angle]]
Solid angle
[[Solid angle]]
Mass
Notes:
See Weight for detail of mass/weight distinction and conversion.
Avoirdupois is a system of mass based on a pound of 16 ounces, while Troy weight is the system of mass where 12 troy ounces equals one troy pound.
In this table, the symbol  is used to denote standard gravity in order to avoid confusion with the (upright) g symbol for gram.
[[Mass]]
Density
[[Density]]
Time
[[Time]]
Frequency
Frequency
Speed or velocity
[[Speed]]
A velocity consists of a speed combined with a direction; the speed part of the velocity takes units of speed.
Flow (volume)
Flow
Acceleration
[[Acceleration]]
Force
[[Force (physics)|Force]]
Pressure or mechanical stress
[[Pressure]]
===Torque or moment of force===
[[Torque]]
===Energy===
[[Energy]]
Power or heat flow rate
[[Power (physics)|Power]]
Action
Action
Dynamic viscosity
Dynamic [[viscosity]]
Kinematic viscosity
Kinematic [[viscosity]]
Electric current
[[Electric current]]
Electric charge
[[Electric charge]]
Electric dipole
[[Electric dipole]]
Electromotive force, electric potential difference
[[Voltage]], electromotive force
Electrical resistance
[[Electrical resistance]]
Capacitance
[[Capacitor]]'s ability to store [[electric charge|charge]]
Magnetic flux
[[Magnetic flux]]
Magnetic flux density
What physicists call [[magnetic field]] is called [[magnetic flux]] density by electrical engineers and magnetic induction by applied mathematicians and electrical engineers.
Inductance
[[Inductance]]
Temperature
[[Temperature]]
Information entropy
[[Information entropy]]
Modern standards (such as ISO 80000) prefer the shannon to the bit as a unit for a quantity of information entropy, whereas the (discrete) storage space of digital devices is measured in bits.
Thus, uncompressed redundant data occupy more than one bit of storage per shannon of information entropy.
The multiples of a bit listed above are usually used with this meaning.
Luminous intensity
The candela is the preferred nomenclature for the SI unit.
[[Luminous intensity]]
Luminance
[[Luminance]]
Luminous flux
[[Luminous flux]]
Illuminance
[[Illuminance]]
Radiation – source activity
[[Radioactivity]]
Although becquerel (Bq) and hertz (Hz) both ultimately refer to the same SI base unit (s−1), Hz is used only for periodic phenomena (i.e. repetitions at regular intervals), and Bq is only used for stochastic processes (i.e. at random intervals) associated with radioactivity.
Radiation – exposure
Radiation – exposure
The roentgen is not an SI unit and the NIST strongly discourages its continued use.
Radiation – absorbed dose
Radiation – [[absorbed dose]]
Radiation – equivalent dose
Radiation – [[equivalent dose]]
Although the definitions for sievert (Sv) and gray (Gy) would seem to indicate that they measure the same quantities, this is not the case.
The effect of receiving a certain dose of radiation (given as Gy) is variable and depends on many factors, thus a new unit was needed to denote the biological effectiveness of that dose on the body; this is known as the equivalent dose and is shown in Sv.
The general relationship between absorbed dose and equivalent dose can be represented as
H = Q ⋅ D
where H is the equivalent dose, D is the absorbed dose, and Q is a dimensionless quality factor.
Thus, for any quantity of D measured in Gy, the numerical value for H measured in Sv may be different.
See also
Accuracy and precision
Conversion of units of temperature
English units
False precision
Imperial units
International System of Units
Mesures usuelles
Metric prefix (e.g. "kilo-" prefix)
Metric system
Natural units
Orders of Magnitude
Rounding
Significant figures
Unified Code for Units of Measure
United States customary units
Unit of length
Units (software)
Units conversion by factor-label
Units of measurement
Notes and references
;Notes External links
NIST Guide to SI Units Many conversion factors listed.
The Unified Code for Units of Measure
Units, Symbols, and Conversions XML Dictionary
"Instruction sur les poids et mesures républicaines:déduites de la grandeur de la terre,uniformes pour toute la République,et sur les calculs relatifs à leur division décimale"
