# 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)

Table 1. Base Units

## Derived Units

Multiplication of physical quantities creates new units. When you calculate the area, the unit becomes multiplied by itself to become, m2. 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 m2.kg.s-2
Watt W Power, Radiant flux J/s m2.kg.s-3
Pascal Pa Pressure, Stress N/m2 m-1.kg.s-2
Lumen lm Luminous flux cd.sr = 1/cd cd
lux lx Illuminance lm/m2 = 1/(m2.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 m2.kg.s-3.A-1
Ohm Ω Electric resistance, Impedance, Reactance V/A m2.kg.s-3.A-2
Farad F Electric capacitance C/V m-2.kg-1.s4.A2
Weber Wb Magnetic flux J/A m2.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 m2.kg.s-2.A-2
Siemens S Electrical conductance Ω-1 m-2.kg-1.s3.A2
Becquerel Bq Radioactivity (decays per unit time) s-1 s-1
Gray Gy Absorbed dose (of ionizing radiation) J/kg m2.s-2
Sievert Sv Equivalent dose (of ionizing radiation) J/kg m2.s-2
Katal kat Catalytic activity mol/s s-1.mol
Degree Celsius °C Thermodynamic temperature TC=TK-273.15

Table 2. Derived units and their special names.

## Other Derived Units

 Name Symbol Quantity Expression in terms of SI base units square metre m2 area m2 cubic metre m3 volume m3 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·m2·s−1 newton metre N·m torque, moment of force kg·m2·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·m3 specific volume kg−1·m3 mole per cubic metre m−3·mol amount (-of-substance) concentration m−3·mol cubic metre per mole m3·mol−1 molar volume m3·mol−1 joule per kelvin J·K−1 entropy kg·m2·s−2·K−1 joule per kelvin mole J·K−1·mol−1 molar heat capacity, molar entropy kg·m2·s−2·K−1·mol−1 joule per kilogram kelvin J·K−1·kg−1 specific entropy m2·s−2·K−1 joule per mole J·mol−1 molar energy kg·m2·s−2·mol−1 joule per kilogram J·kg−1 specific energy m2·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 m2·s−1 kinematic viscosity, diffusion coefficient m2·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·s3·A2 siemens square metre per mole S·m2·mol−1 molar conductivity kg-1·s3·mol−1·A2 farad per metre F·m−1 permittivity kg−1·m−3·s4·A2 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 m2·s−3

Table 3. Other derived units

## Suplementary Units

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

Name Unit