# Units of Measurement

## Introduction

Physics is about the study of energy and forces. In order to test and measure physical quantities we need to define some standard measures which we everyone can agree on. These standards can never perfectly accurate because they are rooted in the physical world but every endevour is made to make them as precise as possible. The internationally recognised authority for the definition of these standards is the Conference Generale des Poids et Measures (CGPM).

## Units

We must ensure that the result we use in our calculations are in the correct units. The consequence of getting it wrong can be very expensive as with the loss of the NASA Mars Climate Orbiter spacecraft in 1999. It spun out of control because part of the software assumed Imperial units and another part assumed metric units.

The units by which we now measure physical quantities is called the S.I. (System International) system established in 1960. Within this system, the most commonly used set of units in physics are M.K.S (Metres, Kilograms, Seconds) system

## Base Units

The basic units are shown in Table. 1.

Quantity | Unit |
---|---|

Length | Metre (m) |

Mass | Kilogram (kg) |

Time | Second (s) |

Electric Charge | Ampere (A) |

Temperature | Kelvin (K) |

Luminenscent Intensity | Candela (Cd) |

## Derived Units

Multiplication of physical quantities creates new units. When you calculate the area, the unit becomes multiplied by itself to become, m^{2}. The unit of area is an example of a derived unit. Other derived units occur so often they are named after illustrious scientists, in honour of their work. Table 2, list derived units and their special names.

Name | Symbol | Quantity | Expression in terms of other units | Expression in terms of SI base units |
---|---|---|---|---|

Hertz | Hz | Frequency | 1/s | s^{-1} |

Newton | N | Force, Weight | m.kg.s^{-2} |
m.kg.s^{-2} |

Joule | J | Work, Heat | N.m | m^{2}.kg.s^{-2} |

Watt | W | Power, Radiant flux | J/s | m^{2}.kg.s^{-3} |

Pascal | Pa | Pressure, Stress | N/m^{2} |
m^{-1}.kg.s^{-2} |

Lumen | lm | Luminous flux | cd.sr = 1/cd | cd |

lux | lx | Illuminance | lm/m^{2} = 1/(m^{2}.cd) |
m^{-2}.cd |

Coulomb | C | Electric charge or flux | A.s | A.s |

Volt | V | Electrical potential difference, Electromotive force | W/A = J/C | m^{2}.kg.s^{-3}.A^{-1} |

Ohm | Ω | Electric resistance, Impedance, Reactance | V/A | m^{2}.kg.s^{-3}.A^{-2} |

Farad | F | Electric capacitance | C/V | m^{-2}.kg^{-1}.s^{4}.A^{2} |

Weber | Wb | Magnetic flux | J/A | m^{2}.kg.s^{-2}.A^{-1} |

Tesla | T | Magnetic flux density, magnetic induction | V.s.m^{-2} = Wbm^{-2} |
kg.s^{-2}.A^{-1} |

Henry | H | Inductance | V.s/A=Wb/A | m^{2}.kg.s^{-2}.A^{-2} |

Siemens | S | Electrical conductance | Ω^{-1} |
m^{-2}.kg^{-1}.s^{3}.A^{2} |

Becquerel | Bq | Radioactivity (decays per unit time) | s^{-1} |
s^{-1} |

Gray | Gy | Absorbed dose (of ionizing radiation) | J/kg | m^{2}.s^{-2} |

Sievert | Sv | Equivalent dose (of ionizing radiation) | J/kg | m^{2}.s^{-2} |

Katal | kat | Catalytic activity | mol/s | s^{-1}.mol |

Degree Celsius | °C | Thermodynamic temperature | T_{C}=T_{K}-273.15 |

## Other Derived Units

Name |
Symbol | Quantity | Expression in terms of SI base units |

square metre | m^{2} |
area | m^{2} |

cubic metre | m^{3} |
volume | m^{3} |

metre per second | m·s^{−1} |
speed, velocity | m·s^{−1} |

metre per second squared | m·s^{−2} |
acceleration | m·s^{−2} |

metre per second cubed | m·s^{−3} |
jerk | m·s^{−3} |

radian per second | rad·s^{−1} |
angular velocity | s^{−1} |

Newton second | N·s | momentum | kg·m·s^{−1} |

newton metre second | N·m·s | angular momentum | kg·m^{2}·s^{−1} |

newton metre | N·m | torque, moment of force | kg·m^{2}·s^{−2} |

reciprocal metre | m^{−1} |
wavenumber | m^{−1} |

kilogram per cubic metre | kg·m^{−3} |
density, mass density | kg·m^{−3} |

cubic metre per kilogram | kg^{−1}·m^{3} |
specific volume | kg^{−1}·m^{3} |

mole per cubic metre | m^{−3}·mol |
amount (-of-substance) concentration | m^{−3}·mol |

cubic metre per mole | m^{3}·mol^{−1} |
molar volume | m^{3}·mol^{−1} |

joule per kelvin | J·K^{−1} |
entropy | kg·m^{2}·s^{−2}·K^{−1} |

joule per kelvin mole | J·K^{−1}·mol^{−1} |
molar heat capacity, molar entropy | kg·m^{2}·s^{−2}·K^{−1}·mol^{−1} |

joule per kilogram kelvin | J·K^{−1}·kg^{−1} |
specific entropy | m^{2}·s^{−2}·K^{−1} |

joule per mole | J·mol^{−1} |
molar energy | kg·m^{2}·s^{−2}·mol^{−1} |

joule per kilogram | J·kg^{−1} |
specific energy | m^{2}·s^{−2} |

joule per cubic metre | J·m^{−3} |
energy density | kg·m^{−1}·s^{−2} |

newton per metre | N·m^{−1} = J·m^{−2} |
surface tension | kg·s^{−2} |

watt per square metre | W·m^{−2} |
heat flux density, irradiance | kg·s^{−3} |

watt per metre kelvin | W·m^{−1}·K^{−1} |
thermal conductivity | kg·m·s^{−3}·K^{−1} |

square metre per second | m^{2}·s^{−1} |
kinematic viscosity, diffusion coefficient | m^{2}·s^{−1} |

pascal second | Pa·s = N·s·m^{−2} |
dynamic viscosity | kg·m^{−1}·s^{−1} |

coulomb per cubic metre | C·m^{−3} |
electric charge density | m^{−3}·s·A |

ampere per square metre | A·m^{−2} |
electric current density | A·m^{−2} |

siemens per metre | S·m^{−1} |
conductivity | kg^{−1}·m^{−3}·s^{3}·A^{2} |

siemens square metre per mole | S·m^{2}·mol^{−1} |
molar conductivity | kg^{-1}·s^{3}·mol^{−1}·A^{2} |

farad per metre | F·m^{−1} |
permittivity | kg^{−1}·m^{−3}·s^{4}·A^{2} |

henry per metre | H·m^{−1} |
permeability | kg·m·s^{−2}·A^{−2} |

volt per metre | V·m^{−1} |
electric field strength | kg·m·s^{−3}·A^{−1} |

ampere per metre | A·m^{−1} |
magnetic field strength | A·m^{−1} |

candela per square metre | cd·m^{−2} |
luminance | cd·m^{−2} |

coulomb per kilogram | C·kg^{−1} |
exposure (X and gamma rays) | kg^{−1}·s·A |

gray per second | Gy·s^{−1} |
absorbed dose rate | m^{2}·s^{−3} |

## Suplementary Units

These angular units and solid-angle unit are often used but are actually dimensionless.

Name | Unit |
---|---|

radian | rad |

steridan | rad^{2} |