The International System of Units (SI Units)
28th Mar 2019 @ 20 min read
The International System of Units or in short SI (in French Le Systeme International d’Unités) is the currently accepted system of measurement. It originated from France. The SI was established in 1960 by the 11th CGPM (General Conference on Weights and Measures or Conférence Générale des Poids et Mesures in French). The SI system is the updated version of the metric system. It is presently accepted worldwide; though, certain countries like the USA still follows traditional English units. The SI system includes the seven base units, names of 22 derived units, and a set of prefixes.
The SI units comprise of the base units and derived units.
SI base units
There are seven fundamental or base units. According to Inter International System of Units, they are metre, kilogram, second, ampere, kelvin, mole and candela. From these base units, we can derive any other SI units; in other words, all rest SI Units are the combination of these seven base units.
Each SI base unit is associated with a basic physical quantity. Physical quantities with its respective SI units are length with metre, mass with kilogram, time with second, current with ampere, temperature with kelvin, amount of substance with mole, and luminous intensity with candela. The table below explains the same.
| Physical Quantity | Quantity Symbol | SI Unit | SI Unit Symbol |
|---|---|---|---|
| Length | l | metre | m |
| Mass | m | kilogram | kg |
| Time | t | second | s |
| Current | I | ampere | A |
| Temperature | T | kelvin | K |
| Amount of substance | n | mole | mol |
| Luminous intensity | Iv | candela | cd |
The General Conference on Weights and Measures (CGPM) is responsible for the maintenance and improvisation of SI units. The CGPM keeps improving the SI system, including definitions of the SI units, for better accuracy and precision. The base SI units are defined from constants of nature like the speed of light in vacuum, the triple point of water. Their definitions keep modifying with time. Thus, the SI system is an evolving system. The table below lists the definitions as of 2019.
| SI Unit | Symbol | Definition |
|---|---|---|
| metre | m | A metre is distance travelled by light in vacuum in 1⁄299 792 458 of a second. |
| kilogram | kg | The definition of kilogram is based on three parameters: the Planck constant (6.626 070 15 × 10−34 J·s), the speed of light and the natural microwave radiation of the caesium atom. |
| second | s | The duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom. |
| ampere | A | An ampere is the flow of 1⁄1.602 176 634 × 10−19 times the elementary charge per second. |
| kelvin | K | The kelvin is defined by fixing the value of the Boltzmann constant to 1.380 649 × 10−23 J·K−1. |
| mole | mol | A mole represents 6.022 140 76 × 1023 elementary entities. This number is also called the Avogadro constant, NA |
| candela | cd | It is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 5.40 × 1014 hertz and that has a radiant intensity in that direction of 1⁄683 watt per steradian. |
Note: Earlier the base SI unit of temperature was °K or Kelvin (with “K” capital), but now it is revised to K or kelvin.
SI derived units
SI derived units are units derived from various combinations (product, power, and quotient) of 7 SI base units. They may be dimensionless or express in terms of the above SI base units or other SI derived units. Consider an example of pressure; pressure is force per unit area. The unit of pressure is pascal or Pa; The pascal can be expressed in another SI derived unit, N·m−2 or in the base unit, kg·m−1·s−2.
There is no limit to SI derived units; they are unlimited. The below table mentions various SI derived units in the form of the SI base units.
| Physical Quantity | Quantity Symbol | SI Unit | SI Unit Symbol |
|---|---|---|---|
| Area | A | square metre | m2 |
| Volume | V | cubic metre | m3 |
| Density | ρ | kilogram per cubic metre | kg⋅m−3 |
| Specific volume | Vsp | cubic metre per kilogram | m3⋅kg−1 |
| Concentration | C | mole per cubic metre | mol⋅m−3 |
| Velocity | v | metre per second | m⋅s−1 |
| Acceleration | a | metre per second squared | m⋅s−2 |
| Magnetic field strength | H | ampere per metre | A⋅m−1 |
| Luminance | Lv | candela per square metre | cd⋅m−2 |
| Refractive index | n | one | 1 |
In the International System of Units, there are special names and symbols of 22 SI derived units. They are listed in the below table.
| Physical Quantity | Name | Symbol | SI Units | Equivalent Units |
|---|---|---|---|---|
| Frequency | hertz | Hz | s−1 | 1/s |
| Angle | radian | rad | 1 | m/m |
| Solid angle | steradian | sr | 1 | m2/m2 |
| Force, weight | newton | N | kg⋅m⋅s−2 | kg⋅m/s2 |
| Pressure, stress | pascal | Pa | kg⋅m−1⋅s−2 | N/m2 |
| Work, energy | joule | J | kg⋅m2⋅s−2 | N⋅m, W⋅s, C⋅V |
| Power | watt | W | kg⋅m2⋅s−3 | J/s, V⋅A |
| Electric charge | coulomb | C | s⋅A | s⋅A, F⋅V |
| Voltage, e.m.f | volt | V | kg⋅m2⋅s−3⋅A−1 | W/A, J/C |
| Capacitance | farad | F | kg−1⋅m−2⋅s4⋅A2 | s/Ω, C/V |
| Electrical resistance, impedance | ohm | Ω | kg⋅m2⋅s−3⋅A−2 | V/A, 1/S |
| Electrical conductance | siemens | S | kg−1⋅m−2⋅s3⋅A2 | 1/Ω, A/V |
| Magnetic flux | weber | Wb | kg⋅m2⋅s−2⋅A−1 | J/A, T⋅m2 |
| Magnetic induction, magnetic flux density | tesla | T | kg⋅s−2⋅A−1 | Wb/m2, V⋅s/m2 N/(A⋅m) |
| Electrical inductance | henry | H | kg⋅m2⋅s−2⋅A−2 | Ω⋅s, Wb/A, V⋅s/A |
| Temperature | degree Celsius | ℃ | K | K |
| Luminous flux | lumen | lm | cd | cd⋅sr |
| Illuminance | lux | lx | cd⋅sr⋅m−2 | lm/m2 |
| Radioactivity | becquerel | Bq | s−1 | 1/s |
| Absorbed dose | gray | Gy | m2⋅s−2 | J/kg |
| Equivalent dose | sievert | Sv | m2⋅s−2 | J/kg |
| Catalytic activity | katal | kat | s−1⋅mol | mol/s |
Note: Angle and steradian are the only dimensionless SI derived units in the above table. They are together known as supplementary units. Relation between the SI base units and SI derived units
[Image source: NIST]
SI Prefixes
Prefixes precede the original unit. They are used to create the multiple or fraction of the original units. These prefixes are all decadic. The SI prefixes are adopted by the International System of Quantities. The table below lists them.
| Prefixes | Symbol | Factor (Base 10) | English Word | Example |
|---|---|---|---|---|
| yotta | Y | 1024 | Septillion | Earth’s mass is 5972.6 Yg |
| zetta | Z | 1021 | Sextillion | Atmosphere’s mass is 2 Zg |
| exa | E | 1018 | Quintillion | 1 EeV is 0.1602 J |
| peta | P | 1015 | Quadrillion | 9.461 Pm is 1 light-year |
| tera | T | 1012 | Trillion | 1 TB of storage |
| giga | G | 109 | Billion | 4 GHz of clock rate (CPU) |
| mega | M | 106 | Million | 50 MW of electricity |
| kilo | k | 103 | Thousand | 5 kg of sugar |
| hecto | h | 102 | Hundred | 2 hm2 farm area |
| deca | da | 101 | Ten | 1 dam wide road |
| 100 | One | One dollar | ||
| deci | d | 10−1 | Tenth | 1 dm is one-tenth metre |
| centi | c | 10−2 | Hundredth | A typical ruler is 15 cm long. |
| milli | m | 10−3 | Thousandth | 10 mg of salt |
| micro | μ | 10−6 | Millionth | 2.5 μm of bacteria |
| nano | n | 10−9 | Billionth | wavelengths of visible light range from 380 nm to 740 nm |
| pico | p | 10−12 | Trillionth | 25 pm is the radius of a Hydrogen atom |
| femto | f | 10−15 | Quadrillionth | Proton’s diameter is 1.6 fm |
| atto | a | 10−18 | Quintillionth | Mass of the virus is 1510 ag |
| zepto | z | 10−21 | Sextillionth | 160.21 zC is charge on an electron |
| yocto | y | 10−24 | Septillionth | 1.674 yg is the rest mass of a neutron |
Accepted non-SI units
Many traditional units are still in practice and are difficult to replace with their respective SI alternatives. This is because of the long history of usage of these non-SI units. The international committee does recognise these traditional units. These units are mentioned below.
| Quantity | Unit | Symbol | Value in SI |
|---|---|---|---|
| Plane angle | degree | ° | 1° = (π⁄180) rad |
| Plane angle | minute | ′ | 1′ = (1⁄60)° |
| Plane angle | second | ″ | 1″ = (1⁄60)′ |
| Time | minute | min | 1 min = 60 s |
| Time | hour | h | 1 h = 60 min |
| Time | day | d | 1 d = 24 h |
| Volume | litre | L, l | 1 L = 10−3 m3 |
| Mass | gram | g | 1 g = 10−3 kg |
| Mass | ton | t | 1 t = 103 kg |
| Area | hectare | ha | 1 ha = 104 m2 |
| Ratio | Neper | Np | 1 Np = 1 |
| Ratio | Bel | B | 1 B = 1⁄2 ln(10) Np |
| Electronvolt | energy | eV | 1 eV = 1.602 176 53(14) × 10−19 J |
| Astronomical unit | length | au | 1 au = 1.495 978 707 00 × 1011 m |
| Atomic mass unit | mass | u | 1 u = 1.660 538 86(28) × 10−27 kg |
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