Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.
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.[clarification needed]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[1] 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.[2] 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[3] 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 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,[4]atomic massm is usually given in daltons, instead of kilograms, and chemical potentialμ is often given in Boltzmann constant times nanokelvin. The condensate's healing length is given by:
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 this gives
which 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 section needs additional citations for verification. Please help by adding citations to reliable sources. Unsourced material may be challenged and removed. Find sources: – ···scholar·JSTOR(January 2011) (Learn how and when to remove this template message)
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
Symbol
Definition
≡
exactly equal
≈
approximately equal to
≘
(exactly) corresponds to (different types of quantity describing the same phenomenon)
digits
indicates that digits repeat infinitely (e.g. 8.294369 corresponds to 8.294369369369369...)
The solid angle subtended at the center of a sphere of radius r by a portion of the surface of the sphere having an area r2. A sphere subtends 4π sr.[20]
= 1 sr
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 g0 is used to denote standard gravity in order to avoid confusion with the (upright) g symbol for gram.
≡ Time needed for the Earth to rotate once around its axis, determined from successive transits of a very distant astronomical object across an observer's meridian (International Celestial Reference Frame)
≡ Time of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom at 0 K[12] (but other seconds are sometimes used in astronomy). Also that time it takes for light to travel a distance of 299792458 metres.
Conceptually, the length of time it takes for the Sun to return to the same position in the cycle of seasons, [Converter 1] approximately 365.24219 d, each day being 86400 SI seconds[31]
≈ 31.556925 Ms
Year (sidereal)
a, y, or yr
≡ Time taken for Sun to return to the same position with respect to the stars of the celestial sphere, approximately 365.256363 d
^ Jump up to: abcThis is based on the average Gregorian year. See above for definition of year lengths.
^ Jump up to: abcdefghijklmnoWhere UTC is observed, the length of this unit may increase or decrease depending on the number of leap seconds which occur during the time interval in question.
^The length of ancient lustral cycles was not constant; see Lustrum for more details
Ratio of the speed to the speed of sound[note 1] in the medium (unitless).
≈ 340 m/s in air at sea level ≈ 295 m/s in air at jet altitudes
metre per second (SI unit)
m/s
≡ 1 m/s
= 1 m/s
mile per hour
mph
≡ 1 mi/h
= 0.44704 m/s
mile per minute
mpm
≡ 1 mi/min
= 26.8224 m/s
mile per second
mps
≡ 1 mi/s
= 1609.344 m/s
speed of light in vacuum
c
≡ 299792458 m/s
= 299792458 m/s
speed of sound in air
s
1225 to 1062 km/h (761–660 mph or 661–574 kn)[note 1]
≈ 340 to 295 m/s
Note
^ Jump up to: abThe speed of sound varies especially with temperature and pressure from about 340 m/s (1,225 km/h or 761 mph or 661 kn) in air at sea level to about 300 m/s (1,062 km/h or 660 mph or 573 kn) at jet altitudes (12200 m or 40000 ft).[33]
A velocity consists of a speed combined with a direction; the speed part of the velocity takes units of speed.
The difference in electric potential across two points along a conducting wire carrying one ampere of constant current when the power dissipated between the points equals one watt.[35]
= 1 V = 1 W/A = 1 kg⋅m2/(A⋅s3) = 1 J/C
Electrical resistance[]
Electrical resistance
Name of unit
Symbol
Definition
Relation to SI units
ohm (SI unit)
Ω
The resistance between two points in a conductor when one volt of electric potential difference, applied to these points, produces one ampere of current in the conductor.[35]
Magnetic flux which, linking a circuit of one turn, would produce in it an electromotive force of 1 volt if it were reduced to zero at a uniform rate in 1 second.[35]
= 1 Wb = 1 V⋅s = 1 kg⋅m2/(A⋅s2)
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.
The inductance of a closed circuit that produces one volt of electromotive force when the current in the circuit varies at a uniform rate of one ampere per second.[35]
= 1 H = 1 Wb/A = 1 kg⋅m2/(A⋅s)2
Temperature[]
Further information: Conversion of units of temperature
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.
The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.[40]
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.[47]
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.[50]
^ Jump up to: abcdefghijklmnLide, D. (Ed.). (1990). Handbook of Chemistry and Physics (71st ed). Boca Raton, FL: CRC Press. Section 1.
^ Jump up to: abNational Bureau of Standards. (June 30, 1959). Refinement of values for the yard and the pound. Federal Register, viewed September 20, 2006 at National Geodetic Survey web site.
^International System of Units,Archived August 21, 2008, at the Wayback Machine 8th ed. (2006), Bureau International des Poids et Mesures, Section 4.1 Table 8.
^Cox, Arthur N., ed. (2000). Allen's Astrophysical Quantities (4th ed.). New York: AIP Press / Springer. Bibcode:2000asqu.book.....C. ISBN0387987460.
^Binney, James; Tremaine, Scott (2008). Galactic Dynamics (2nd ed.). Princeton, NJ: Princeton University Press. Bibcode:2008gady.book.....B. ISBN978-0-691-13026-2.
^P. Kenneth Seidelmann, Ed. (1992). Explanatory Supplement to the Astronomical Almanac. Sausalito, CA: University Science Books. p. 716 and s.v. parsec in Glossary.
^Thompson, A. and Taylor, B.N. (2008). Guide for the Use of the International System of Units (SI). National Institute of Standards and Technology Special Publication 811. p. 57.
^Barry N. Taylor, Ed.,NIST Special Publication 330: The International System of Units (SI) (2001 Edition), Washington: US Government Printing Office, 43,"The 12th Conference Generale des Poids et Mesures (CGPM)...declares that the word "litre" may be employed as a special name for the cubic decimetre".
^The Swiss Federal Office for Metrology gives Zentner on a German language web page "Archived copy". Archived from the original on 2006-09-28. Retrieved 2006-10-09.CS1 maint: archived copy as title (link) and quintal on the English translation of that page "Archived copy". Archived from the original on 2001-03-09. Retrieved 2006-10-09.CS1 maint: archived copy as title (link); the unit is marked "spécifiquement suisse !"
^ Jump up to: abPedersen O. (1983). "Glossary" in Coyne, G., Hoskin, M., and Pedersen, O. Gregorian Reform of the Calendar: Proceedings of the Vatican Conference to Commemorate its 400th Anniversary. Vatican Observatory. Available from Astrophysics Data System.
^Richards, E.G. (1998), Mapping Time, Oxford University Press, pp. 94–95, ISBN0-19-850413-6
^Steel, Duncan (2000), Marking Time, John Wiley & Sons, p. 46, ISBN0-471-29827-1
^ Jump up to: abRichards, E. G. (2013). "Calendars" in S. E. Urban & P. K. Seidelmann, eds. Explanatory Supplement to the Astronomical Almanac. Mill Valley, CA: University Science Books.
^Richards, E. G. (2013). "Calendars" in S. E. Urban & P. K. Seidelmann, eds. Explanatory Supplement to the Astronomical Almanac. Mill Valley, CA: University Science Books. p. 587.
^Until 1970 the UK Admiralty (and until 1954 the US) used other definitions of the nautical mile and hence the knot. See also #Length
^Tom Benson. (2010.) "Mach Number"Archived 2006-04-10 at the Wayback Machine in Beginner's Guide to Aeronautics. NASA.
^Barry N. Taylor, (April 1995), Guide for the Use of the International System of Units (SI) (NIST Special Publication 811), Washington, DC: US Government Printing Office, p. 5.
^International System of Units,Archived July 16, 2012, at the Wayback Machine 8th ed. (2006), Bureau International des Poids et Mesures, Section 4.1 Table 7.
^Robert G. Mortimer Physical chemistry,Academic Press, 2000 ISBN0-12-508345-9, page 677
^Standard for the Use of the International System of Units (SI): The Modern Metric System IEEE/ASTM SI 10-1997. (1997). New York and West Conshohocken, PA: Institute of Electrical and Electronics Engineers and American Society for Testing and Materials. Tables A.1 through A.5.
^The technical definition of tropical year is the period of time for the ecliptic longitude of the Sun to increase 360 degrees. (Urban & Seidelmann 2013, Glossary, s.v. year, tropical)