Reference for SI Base and Recognised Derived Units
Defining Constants and Corresponding Units
| Defining Constant | Symbol | Numerical Value | Unit |
|---|---|---|---|
| hyperfine transition frequency of Cs | \(\Delta \nu_{\text{Cs}}\) | \(9\ 192\ 631\ 770\) | \(\text{Hz}\) |
| speed of light in vacuum | \(c\) | \(299\ 792\ 458\) | \(\text{m}\ \text{s}^{−1}\) |
| Planck constant | \(h\) | \(6.626\ 070\ 15\ \times 10^{−34}\) | \(\text{J}\ \text{s}\) |
| elementary charge | \(e\) | \(1.602\ 176\ 634 × 10^{−19}\) | \(\text{C}\) |
| Boltzmann constant | \(k\) | \(1.380\ 649 \times 10^{−23}\) | \(\text{J}\ \text{K}^{−1}\) |
| Avogadro constant | \(N_A\) | \(6.022\ 140\ 76 \times 10^{23}\) | \(\text{mol}^{−1}\) |
| luminous efficacy | \(K_{cd}\) | \(683\) | \(\text{lm}\ \text{W}^{−1}\) |
SI Brochure: The International System of Units (SI) (2019). Bureau International des Poids et Mesures. Ninth Edition. Table 1 (The Seven Defining Constants of the SI and the Seven Corresponding Units They Define). pg. 128.
Base Quantities and Units
| Base quantity | Typical symbol | Base Unit | Symbol |
|---|---|---|---|
| time | \(t\) | second | s |
| length | \(l\), \(x\), \(r\), etc. | metre | m |
| mass | \(m\) | kilogram | kg |
| electric current | \(I\), \(i\) | ampere | A |
| thermodynamic temperature | \(T\) | kelvin | K |
| amount of substance | \(n\) | mole | mol |
| luminous intensity | \(I_v\) | candela | cd |
SI Brochure: The International System of Units (SI) (2019). Bureau International des Poids et Mesures. Ninth Edition. Table 2. (SI Base Units). pg. 130.
Note: The symbols for quantities are normally single letters of the Latin or Greek alphabets, printed in an italic font, and are recommendations. The symbols are mandatory, printed in an upright font (see How to Use Units and Quantities in Equations and Calculations).
Derived SI Units
Units With Reserved Names and Symbols
| Derived Quantity | Reserved Name of Unit | Unit Expressed in Terms of Base Units | Unit Expressed in Terms of Other SI Units |
|---|---|---|---|
| plane angle | radian | rad = \(\frac{\text{m}}{\text{m}}\) | |
| solid angle | steradian | sr = \(\frac{\text{m}^2}{\text{m}^2}\) | |
| frequency | hertz | Hz = \(\text{s}^{−1}\) | |
| force | newton | N = \(\text{kg}\ \text{m}\ \text{s}^{−2}\) | |
| pressure, stress | pascal | Pa = \(\text{kg}\ \text{m}^{-1}\ \text{s}^{−2}\) | \(\frac{\text{N}}{\text{m}^2}\) |
| energy, work, amount of heat | joule | J = \(\text{kg}\ \text{m}^{2}\ \text{s}^{−2}\) | \(\text{N}\ \text{m}\) |
| power, radiant flux | watt | W = \(\text{kg}\ \text{m}^2\ \text{s}^{−3}\) | \(\frac{\text{J}}{\text{s}}\) |
| electric charge | coulomb | C = \(\text{A}\ \text{s}\) | |
| electric potential difference | volt | V = \(\text{kg}\ \text{m}^2\ \text{s}^{−3}\ \text{A}^{−1}\) | \(\frac{\text{W}}{\text{A}}\) |
| capacitance | farad | F = \(\text{kg}^{−1}\ \text{m}^{−2}\ \text{s}^4\ \text{A}^2\) | \(\frac{\text{C}}{\text{V}}\) |
| electric resistance | ohm | Ω = \(\text{kg}\ \text{m}^2\ \text{s}^{−3}\ \text{A}^{−2}\) | \(\frac{\text{V}}{\text{A}}\) |
| electric conductance | siemens | S = \(\text{kg}^{−1}\ \text{m}^{−2}\ \text{s}^{3}\ \text{A}^2\) | \(\frac{\text{A}}{\text{V}}\) |
| magnetic flux | weber | Wb = \(\text{kg}\ \text{m}^2\ \text{s}^{−2}\ \text{A}^{−1}\) | \(\text{V}\ \text{s}\) |
| magnetic flux density | tesla | T = \(\text{kg}\ \text{s}^{−2}\ \text{A}^{−1}\) | \(\frac{\text{Wb}}{\text{m}^2}\) |
| inductance | henry | H = \(\text{kg}\ \text{m}^2\ \text{s}^{−2}\ \text{A}^{−2}\) | \(\frac{\text{Wb}}{\text{A}}\) |
| Celsius temperature | degree Celsius | °C = \(\text{K}\) | |
| luminous flux | lumen | lm = \(\text{cd}\ \text{sr}\) | \(\text{cd}\ \text{sr}\) |
| illuminance | lux | lx = \(\text{cd}\ \text{sr}\ \text{m}^{−2}\) | \(\frac{\text{lm}}{\text{m}^2}\) |
| activity referred to a radionuclide | becquerel | Bq = \(\text{s}^{−1}\) | |
| absorbed dose, kerma | gray | Gy = \(\text{m}^2\ \text{s}^{−2}\) | \(\frac{\text{J}}{\text{kg}}\) |
| dose equivalent | sievert | Sv = \(\text{m}^2\ \text{s}^{−2}\) | \(\frac{\text{J}}{\text{kg}}\) |
| catalytic activity | katal | kat = \(\text{mol}\ \text{s}^{−1}\) |
SI Brochure: The International System of Units (SI) (2019). Bureau International des Poids et Mesures. Ninth Edition. Table 4 (The 22 SI Units with Special Names and Symbols). (SI base units). pg. 138.
Non-SI Units Accepted for Use
| Quantity | Name of Unit | Symbol for Unit | Value in SI units |
|---|---|---|---|
| time | minute | min | 1 min = \(60\ \text{s}\) |
| hour | h | 1 h = \(60\ \text{min}\) = \(3600\ \text{s}\) | |
| day | d | 1 d = \(\text{24}\ \text{h}\) = \(86\ 400\ \text{s}\) | |
| length | astronomical unit | au | 1 au = \(149\ 597\ 870\ 700\ \text{m}\) |
| plane and | degree | ° | 1° = \(\left( \frac{\pi}{180} \right)\ \text{rad}\) |
| phase angle | minute | ′ | 1′ = \(\left( \frac{1}{60} \right)\)° = \(\left( \frac{\pi}{10\ 800} \right)\ \text{rad}\) |
| second | ″ | 1″ = \(\left( \frac{1}{60} \right)\)′ = \(\left( \frac{\pi}{648\ 000} \right)\ \text{rad}\) | |
| area | hectare | ha | ha = \(1\ \text{hm}^2\) = \(10^4\ \text{m}^2\) |
| volume | litre | l, L | 1 l = 1 L = \(1\ \text{dm}^3\) = \(10^3\ \text{cm}^3\) = \(10^{−3}\ \text{m}^3\) |
| mass | tonne | t | 1 t = \(10^3\ \text{kg}\) |
| dalton | Da | 1 Da = \(1.660\ 539\ 066\ 60(50) \times 10^{−27}\ \text{kg}\) | |
| energy | electronvolt | eV | 1 eV = \(1.602\ 176\ 634 \times 10^{−19}\ \text{J}\) |
| logarithmic | neper | Np | |
| ratio quantities | bel | B | |
| decibel | dB |
SI Brochure: The International System of Units (SI) (2019). Bureau International des Poids et Mesures. Ninth Edition. Table 8 (Non-SI Units Accepted for use With The SI Units). pg. 138.
Note: Use the units of logarithmic ratio quantities, the neper, bel and decibel, to convey information on the nature of the logarithmic ratio quantity concerned. For natural logarithms the neper, Np, expresses values of quantities based on the neperian (or natural) logarithm, \(\ln = \log_e\) . Similarly, the bel, B, and the decibel, dB, expresses the values of logarithmic ratio quantities whose numerical values of the decadic logarithm, \(\lg = \log_{10}\). The units of decibel and bel relate as follows
\[L_x = m\ \text{dB} = \left( \frac{m}{10} \right)\ \text{B}\]