The Metric System

A reference to the world's most widely used system of measurement

[The Metric System] [Values of Constants] [Conversion Factors]

The Metric System

The Fundamental Units

These are the fundamental units of the Metric System. All other units are derived from these. Each type of quantity is measured by one type of unit.

Unit Type Unit Name Symbol Definition
Length metre m 1/299,792,458 of the distance travelled by light in a vacuum in one second
Mass kilogram kg The mass of a Platinum-Iridium cylinder kept in Paris.
Time second s The duration of 9,192,631,770 periods of the radiation corresponding to the transition between two hyperfine levels of the ground state of the Caesium 133 atom.
ampere A The amount of current that if maintained in two parallel rectilinear conductors (of infinite length and negligible circular cross-section) placed 1 metre apart in a vacuum, would produce a force between these conductors equal to
2 × 10-7 newton per metre.
Temperature kelvin K The fraction 1/273.16 of the thermodynamic temperature at the triple point of water.
Amount of
mole mol The amount of substance which contains as many elementary units as there are atoms in 12 grams of pure Carbon 12.
candela cd The luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 x 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.
Angle radian rad The angle subtended at the centre of a circle by an arc of the circumference equal in length to the radius of the circle.
Solid Angle steradian sr The solid angle subtended at the centre of a sphere of radius r by a portion of the surface of the sphere having an area r2.


The Prefixes

All metric units can be used as fractions or multiples by using prefixes.

For example, kilo- means 1000 and can be used to denote 1000 of any unit (eg. 1000 metres is a kilometre, written as km). Also, milli- means 1/1000th and can be used to denote 1/1000th of any unit (1/1000th of a metre is a millimetre, written as mm).

Note that the case of the prefix is important. M is mega, while m is milli.

Prefix Name
tera T 1012
giga G 109
mega M 106
kilo k 103
centi c 10-2
milli m 10-3
micro µ 10-6
nano n 10-9
pico p 10-12
femto f 10-15
atto a 10-18


The Derived Units

The derived units in the Metric System are made up from various combinations of the fundamental units. Each type of quantity is measured by one type of unit.

The Fundamental Units are shown in red.

Note that the case of the unit is important. K is a degree Kelvin, k is kilo- (1000).

Unit Type Unit Name
Derivation from
Fundamental Units
Length metre m  
Area square metre   m2
Volume cubic metre   m3
Time second s  
Frequency hertz Hz s-1
Velocity metre per second   m s-1
Acceleration metre per second squared   m s-2
Kinematic Viscosity square metre per second   m2 s-1
Mass kilogram kg  
Density kilogram per cubic meter   kg m-3
Moment of Inertia kilogram square meter   kg m2
Force / Weight newton N kg m s-2
Momentum / Impulse newton second N s kg m s-1
Energy / Work / Torque joule J kg m2 s-2 (N m)
Power watt W kg m2 s-3 (J s-1)
Sound Intensity watt per square meter   W m-2
Surface Tension newton per meter   N m-1
Pressure pascal Pa N m-2
Compressibility square meter per newton   m2 N-1
Dynamic Viscosity newton second per square meter   N s m-2
Temperature kelvin K  
Thermal Conductivity watt per metre per kelvin   W m-1 K-1
Entropy / Heat Capacity joule per kelvin   J K-1
Specific Heat Capacity joule per kilogram per kelvin   J kg-1 K-1
Amount of Substance mole mol  
Ionic Strength mole per kilogram   mol kg-1
Molar Volume cubic metre per mole   m3 mol-1
Molar Mass kilogram per mole   kg mol-1
Luminous Intensity candela cd  
Luminance candela per square metre   cd m-2
Solid Angle steradian sr  
Luminous Flux lumen lm cd sr
Illumination lux lx cd sr m-2
Electric Current ampere A  
Magnetic Field Strength ampere per metre   A m-1
Electric Current Density ampere per square metre   A m-2
Magnetic Moment ampere square metre   A m2
Electric Charge coulomb C A s
Dipole Moment coulomb meter   C m
Surface Charge Density coulomb per square meter   C m-2
Volume Charge Density coulomb per cubic meter   C m-3
Potential Difference volt V kg m2 s-3 A-1
Electric Field Strength volt per meter   V m-1
Thermoelectric Power volt per kelvin   V K-1
Magnetic Flux weber Wb V s
Inductance henry H Wb A-1
Permeability henry per meter   H m-1
Flux Density tesla T kg s-2 A-1
Resistance / Impedance ohm W V A-1
Resistivity ohm meter   V A-1 m
Capacitance farad F A2 s4 kg-1 m-2
Permittivity farad per meter   F m-1
Conductance siemens S F s-1
Electrical Conductivity siemens per meter   S m-1
Molar Conductivity siemens square meter per mole   S m2 mol-1
Angle radian rad  
Power of Lens radian per meter   rad m-1
Angular Velocity radian per second   rad s-1
Angular Acceleration radian per second squared   rad s-2

Values of Constants

These are some of the fundamental constants in science. The case of the symbol is important.

Velocity of light in a vacuum c 2.997 925 × 108 m s-1
Boltzmann Constant k 1.380 54 × 10-23 J K-1
Planck Constant h 6.625 59 × 10-34 J s
Gravitational Constant G 6.673 × 10-11 N m2 kg-2
Acceleration of gravity
on the Earth's surface
g 9.806 65 m s-2
Stefan Constant s 5.670 3 × 10-8J K-4 m-2 s-1
Faraday Constant F 9.648 70 × 104 C mol-1
Avogadro Constant L 6.022 52 × 1023 mol-1
Charge on an electron e 1.602 10 × 10-19 C
Rest mass of electron me 9.109 08 × 10-31 kg
Hubble Constant H 2.5 × 10-18 m s-1 m-1
Gas Constant R 8.314 34 J K-1 mol-1

Conversion Factors

This table lists some of the more common units used by certain countries (USA and UK being the most important). It also lists other non-metric units in general use.

Note that many of these units differ by country. This makes them of little use in a global environment, like the WORLD Wide Web or trans-national business.

Unit Description Value
Ångström Length (Atomic) 1.000 × 10-10 m
acre Area of Land 4.047 × 103 m2
astronomical unit Distance Between Earth and Sun 1.496 × 1011 m
atmosphere Atmospheric Pressure on the surface
of the Earth at Sea Level
1.013 × 105 N m-2
atomic mass unit Mass of Hydrogen Atom 1.660 × 10-27 kg
barrel Volume of Oil 0.1636 m3
British thermal unit Energy 1.055 × 103 J
bushel (UK) Volume (Dry Substances) 3.637 × 10-2 m3
bushel (USA) Volume (Dry Substances) 3.531 × 10-2 m3
calorie Energy 4.184 J
carat Weight 2 × 10-4 kg
chain Length 20.12 m
cubic foot Volume 2.832 × 10-2 m3
cubic yard Volume 0.7646 m3
curie Radioactivity 3.7 × 1010 s-1
day Time 8.6400 × 104 s
degree Angle 1.745 × 10-2 rad
degree Celsius Temperature 1.000 K
degree Fahrenheit Temperature 0.5556 K
dyne Force 1.000 × 10-5 N
electron volt Energy (Atoms and Sub-Atomic Particles) 1.602 × 10-19 J
erg Energy 1.000 × 10-7 J
fathom Distance (Depth) 1.8288 m
fluid ounce (UK) Volume (Liquid) 2.841 × 10-5 m3
foot Length 0.3048 m
foot pound force Energy 1.356 × 105 J
gallon (UK) Volume (Liquid) 4.546 × 10-3 m3
gallon (USA) Volume (Liquid) 3.785 × 10-3 m3
gill (UK) Volume (Liquid) 1.4205 × 10-4 m3
gill (USA) Volume (Liquid) 2.841 × 10-4 m3
hectare Area of Land 1.000 × 104 m2
hour Time 3.600 × 103 s
horsepower Power 7.457 × 102 W
hundredweight (UK) Weight 50.80 kg
inch Length 2.54 × 10-2 m
kilowatt hour Energy 3.600 × 106 J
knot Velocity (at Sea / Flight) 0.5114 m s-1
league Distance 9.0885 km
light year Distance (Stars / Galaxies) 9.461 × 1012 km
litre Volume (Liquid) 1.000 × 10-3 m3
mile Distance 1.609 km
mile (nautical) Distance (Sea / Air) 1.852 km
mile per hour Velocity 0.4704 m s-1
minute Angle 2.909 × 10-4 rad
minute Time 60 s
ounce Weight 2.835 × 10-2 kg
parsec Distance (Stars / Galaxies) 3.084 × 1013 km
peck (UK) Volume (Dry) 9.092 × 10-3 m3
peck (USA) Volume (Dry) 8.810 × 10-3 m3
pint (UK) Volume (Liquid) 5.682 × 10-4 m3
pint (USA) Volume (Dry) 5.517 × 10-4 m3
pint (USA) Volume (Liquid) 4.735 × 10-4 m3
pound Weight 0.4536 kg
pound-force Force 4.448 N
rad / röntgen Radiation Dosage 1.00 × 10-2 J kg-1
second Angle 4.848 × 10-6 rad
square foot Area 9.290 × 10-2 m2
square inch Area 6.452 × 10-4 m2
square mile Area 2.590 × 106 m2
square yard Area 0.8361 m2
therm Energy 1.055 × 108 J
ton (UK) Weight 1.016 × 103 kg
tonne (metric ton) Weight 1000 kg
tropical year Time 3.156 × 107 s
yard Length 0.9144 m

Not everyone realizes that there is a difference between metric tools and standard tools. A mechanic in the United States can use the same tool bench as a mechanic in the UK, but he will use a 1-inch wrench rather than a 10mm wrench.

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