Difference between revisions of "Systems of units"
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Revision as of 00:26, 8 December 2017
Contents
Systems of units
The International System of Units (SI, from the French Système international (d'unités)) is the most widely used system of measurement. It has now been adopted accross the world, except in Liberia, Myanmar and the United States. The US is the only industrialized nation that does not mainly use the SI in its commercial and standards activities^{Wikipedia, International System of Units}. The SI is available here, free of charge. (The English version follows the French version.)
In the SI, units are classified as follows (with reference to the table in the SI):
- Base units (Table 1)
- Coherent derived units (Table 2)
- Coherent derived units with special names and symbols (Table 3)
Note that coherent derived units can include coherent derived units with special names and symbols (Table 4)
- Non-SI units accepted for use with the SI (Table 6)
- Non-SI units whose values in SI units must be obtained experimentally (Table 7)
- Other non-SI units (Table 8)
- Non-SI units associated with the CGS and the CGS-Gaussian system of units (Table 9)
- Other non-SI units not recommended of use (including the British imperial system and the United States customary system of units)
Conversion factors for the later units are available from the US National Institute of Standards and Technology (NIST):
SI base units
There are seven base units in the SI:
Name | Symbol | Formulas question input |
---|---|---|
metre | m | m |
kilogram | kg | kg |
second | s | s |
ampere | A | A |
kelvin | K | K |
mole | mol | mol |
candela | cd | cd |
Coherent derived units
Coherent derived units are products of powers of base units, without a numerical factor. Some examples of coherent derived units are as follows:
Name | Symbol | Formulas question Input from either column is acceptable | |
---|---|---|---|
square meter | m^{2} | m^2 | |
cubic meter | m^{3} | m^2 | |
meter per second | m/s | m/s | m s^(-1) |
meter per second squared | m/s^{2} | m/s^2 | m s^(-2) |
reciprocal metre | m^{-1} | m^(-1) | |
kilogram per cubic metre | kg/m^{3} | kg/m^3 | kg m^(-3) |
kilogram per square metre | kg/m^{2} | kg/m^2 | kg m^(-2) |
cubic metre per kilogram | m^{3}/kg | m^3/kg | m^3 kg^(-1) |
ampere per square metre | A/m^{2} | A/m^2 | A m^(-2) |
etc. |
Coherent derived units with special names and symbols
Some coherent derived units have special names and symbols:
Name | Symbol | Formulas question Input from either column is acceptable | ||
---|---|---|---|---|
radian | rad | rad | ||
steradian | sr | sr | ||
hertz | Hz | Hz | s^(-1) | |
newton | N | N | m kg s^(-2) | |
pascal | Pa | Pa | N/m^2 | m^(-1) kg s^(-2) |
joule | J | J | N m | m^2 kg s^(-2) |
watt | W | W | J/s | m^2 kg s^(-3) |
coulomb | C | C | s A | |
volt | V | V | W/A | m^2 kg s^(-3) A^(-1) |
farad | F | F | ||
ohm | Ω | |||
siemens | S | S | ||
weber | Wb | Wb | ||
tesla | T | T | ||
henry | H | H | ||
degree Celcius | ℃ | ℃ | ||
lumen | lm | lm | ||
lux | lx | lx | ||
becquerel | Bq | |||
gray | Gy | |||
sievert | Sv | |||
katal | kat |
The base and coherent derived units of the SI form a coherent set, designated the set of coherent SI units. There are also units outside the SI.
Non-SI units accepted for use with the SI
Non-SI units accepted for use with the SI are:
Name | Symbol | Formulas question input |
---|---|---|
minute | min | min |
hour | h | h |
day | d | d |
degree (plan angle) | ° | |
minute (plan angle) | ′ | |
second (plan angle) | ″ | |
hectare | ha | ha |
litre | L, l | L or l |
tonne | t | t |
SI Prefixes
The SI and Formulas question prefixes are given in the table below. The only difference between the two systems is that the prefix micro is written μ in the SI but entered as u in the Formulas question.
Factor | Name | SI symbol | Formulas question input |
Factor | Name | SI symbol | Formulas question input | |
---|---|---|---|---|---|---|---|---|
10^{1} | deca | da | da | 10^{-1} | deci | d | d | |
10^{2} | hecto | h | h | 10^{-2} | centi | c | c | |
10^{3} | kilo | k | k | 10^{-3} | milli | m | m | |
10^{6} | mega | M | M | 10^{-6} | micro | μ | u | |
10^{9} | giga | G | G | 10^{-9} | nano | n | n | |
10^{12} | tera | T | T | 10^{-12} | pico | p | p | |
10^{15} | peta | P | P | 10^{-15} | femto | f | f | |
10^{18} | exa | E | E | 10^{-18} | atto | a | a | |
10^{21} | zetta | Z | Z | 10^{-21} | zepto | z | z | |
10^{24} | yotta | Y | Y | 10^{-24} | yocto | y | y |
Formulas question system of units
The system of units of the Formulas question type complies with the SI. Formulas question units can be any of all the units mentioned above, i.e. SI units and non-SI units.
Formulas question unit |
Type | Examples
| ||
---|---|---|---|---|
Name of unit | SI symbol | Formulas question input | ||
Single (i.e. individual) unit | SI base unit | meter | m | m |
kilogram | kg | kg | ||
second | s | s | ||
Coherent derived SI units with special names and symbols | hertz | Hz | Hz | |
newton | N | N | ||
pascal | Pa | Pa | ||
Non-SI units accepted for use with the SI | minute | min | min | |
hour | h | h | ||
day | d | d | ||
Non-SI units whose values in SI units must be obtained experimentally | electronvolt | eV | eV | |
dalton | Da | Da | ||
unified atomic mass unit | u | u | ||
Other non-SI units | bar | bar | bar | |
millimetre of mercury | mmHg | mmHg | ||
ångström | Å | Å (Ascii 143) | ||
Non-SI units associated with the CGS and the CGS-Gaussian system of units | erg | erg | erg | |
dyne | dyn | dyn | ||
poise | P | P | ||
Other non-SI units not recommended for use | barrel of oil | bbl | bbl | |
inch | inch | in | ||
foot | ft | ft | ||
Combined unit (any combination of single units) | All types | square meter | m^{2} | m^2 |
meter per second | m/s | m/s | ||
meter per second squared | m/s^{2} | m/s^2 | ||
hertz expressed in terms of SI base units | s^{-1} | s^(-1) | ||
newton expressed in terms of SI base units | m kg s^{-2} | m kg s^(-2) | ||
pascal expressed in terms of SI base units | m^{-1} kg s^{-2} | m^(-1) kg s^(-2) | ||
pascal second | Pa s | Pa s | ||
radian per second squared | rad/s^{2} | rad/s^2 | ||
watt per square metre steradian | W/(m^{2} sr) | W/(m^2 sr) | ||
poise expressed in terms of CGS units | dyn s cm^{-2} | dyn s cm^(-2) | ||
foot pound | ft lb | ft lb | ||
pound per inch squared | lb/in^{2} | lb/in^2 | ||
Btu per hour | Btu/h | Btu/h |