Conversion of units
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.
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.
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 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 is often given in Boltzmann constant times nanokelvin. The condensate's healing length is given by:
For a 23Na condensate with chemical potential of 128 nK, the calculation of healing length can be done in two steps:
Calculate the pre-factor
Assume that this giveswhich is our pre-factor.
Calculate the numbers
Now, make use of the fact that. With,.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.
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 are shown and expressed in terms of the corresponding SI unit. Conversions between units in the metric system are defined by their prefixes and are thus not listed in this article. Exceptions are made if the unit is commonly known by another name. Within each table, the units are listed alphabetically, and the SI units are highlighted.| Symbol | Definition |
| ≡ | exactly equal |
| ≈ | approximately equal to |
| indicates that digits repeat infinitely | |
| of chiefly historical interest |
Length
Area
Volume
Plane 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 unit gee is used to denote standard gravity in order to avoid confusion with the "g" symbol for grams.
| Name of unit | Symbol | Definition | Relation to SI units |
| atomic mass unit, unified | u; AMU | Same as dalton | ≈ |
| atomic unit of mass, electron rest mass | me | ≈ | |
| bag | ≡ 60 kg | = 60 kg | |
| bag | ≡ 94 lb av | = | |
| barge | ≡ short ton | = | |
| carat | kt | ≡ gr | = mg |
| carat | ct | ≡ 200 mg | = 200 mg |
| clove | ≡ 8 lb av | = | |
| crith | ≡ mass of 1 L of hydrogen gas at STP | ≈ 89.9349 mg | |
| dalton | Da | 1/12 the mass of an unbound neutral atom of carbon-12 in its nuclear and electronic ground state and at rest | ≈ |
| dram | dr t | ≡ 60 gr | = |
| dram | dr av | ≡ gr | = |
| electronvolt | eV | ≡ 1 eV / c2 | = |
| gamma | γ | ≡ 1 μg | = 1 μg |
| grain | gr | ≡ lb av | ≡ |
| grave | gv. | grave was the original name of the kilogram | ≡ 1 kg |
| hundredweight | long cwt or cwt | ≡ 112 lb av | = |
| hundredweight ; cental | sh cwt | ≡ 100 lb av | = |
| kilogram | kg | ≡ mass of the prototype near Paris ≈ mass of 1 litre of water | ≡ 1 kg |
| kip | kip | ≡ av | = |
| mark | ≡ 8 oz t | = | |
| mite | ≡ gr | = | |
| mite | ≡ g | = 50 mg | |
| ounce | oz t | ≡ lb t | = |
| ounce | oz av | ≡ lb | = |
| ounce | oz | ≡ 28 g | = 28 g |
| pennyweight | dwt; pwt | ≡ oz t | = |
| point | ≡ ct | = 2 mg | |
| pound | lb av | ≡ = grains | ≡ |
| pound | ≡ 500 g | = 500 g | |
| pound | lb t | ≡ grains | = |
| quarter | ≡ long cwt = 2 st = 28 lb av | = | |
| quarter | ≡ short ton | = | |
| quarter, long | ≡ long ton | = | |
| quintal | q | ≡ 100 kg | = 100 kg |
| scruple | s ap | ≡ 20 gr | = |
| sheet | ≡ lb av | = 647.9891 mg | |
| slug; geepound; hyl | slug | ≡ 1 standard gravity| × 1 lb av × 1 s2/ft | ≈ |
| stone | st | ≡ 14 lb av | = |
| ton, assay | AT | ≡ 1 mg × 1 long ton ÷ 1 oz t | = 32. g |
| ton, assay | AT | ≡ 1 mg × 1 short ton ÷ 1 oz t | = 29.1 g |
| ton, long | long tn or ton | ≡ | = |
| ton, short | sh tn | ≡ | = |
| tonne | t | ≡ | = |
| wey | ≡ 252 lb = 18 st | = | |
| Zentner | Ztr. | Definitions vary. |
Density
Time
Frequency
Speed or velocity
A velocity consists of a speed combined with a direction; the speed part of the velocity takes units of speed.Flow (volume)
Acceleration
Force
See also: Conversion between weight and massPressure or mechanical stress
Torque or moment of force
Energy
Power or heat flow rate
Action
Dynamic viscosity
Kinematic viscosity
Electric current
Electric charge
Electric dipole
Electromotive force, electric potential difference
Electrical resistance
Capacitance
Magnetic flux
Magnetic flux density
Inductance
Temperature
| Name of unit | Symbol | Definition | Relation to SI units |
| degree Celsius | °C | ≡ − 273.15 | ≡ + 273.15 |
| degree Delisle | °De | = 373.15 − × | |
| degree Fahrenheit | °F | ≡ × + 32 | ≡ × |
| degree Newton | °N | = × + 273.15 | |
| degree Rankine | °R; | ≡ × | ≡ × 5/9 |
| degree Réaumur | °Ré | = × + 273.15 | |
| degree Rømer | °Rø | = × + 273.15 | |
| Regulo Gas Mark | GM | ≡ × 25 + 300 | ≡ × + 422.038 |
| kelvin | K | ≡ of the thermodynamic temperature of the triple point of water. | ≡ 1 K |
Information entropy
| Name of unit | Symbol | Definition | Relation to SI units | Relation to bits |
| natural unit of information; nip; nepit | nat | |||
| shannon; bit | Sh; bit; b | ≡ ln × nat | ≈ | = 1 bit |
| hartley; ban | Hart; ban | ≡ ln × nat | ≈ | |
| nibble | ≡ 4 bits | = 22 bit | ||
| byte | B | ≡ 8 bits | = 23 bit | |
| kilobyte | kB | ≡ | = bit | |
| kilobyte | KB; KiB | ≡ | = 213 bit = bit |
Modern standards prefer the shannon to the bit as a unit for a quantity of information entropy, whereas the 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.| Name of unit | Symbol | Definition | Relation to SI units |
| candela ; candle | cd | The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian. | = 1 cd |
| candlepower | cp | ≡ cd The use of candlepower as a unit is discouraged due to its ambiguity. | = 1 cd |
| candlepower | cp | Varies and is poorly reproducible. Approximately 0.981 cd. | ≈ 0.981 cd |
Luminance
Luminous flux
Illuminance
Radiation – source activity
Although becquerel and hertz both ultimately refer to the same SI base unit, Hz is used only for periodic phenomena, and Bq is only used for stochastic processes associated with radioactivity.Radiation – exposure
The roentgen is not an SI unit and the NIST strongly discourages its continued use.Radiation – absorbed dose
Radiation – equivalent dose
Although the definitions for sievert and gray would seem to indicate that they measure the same quantities, this is not the case. The effect of receiving a certain dose of radiation 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 aswhere 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.