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.

Unit
Type Unit
Name Symbol Definition

Length metre m 1,650,763.73 wavelengths in vacuum of radiation corresponding to the transition 2p₁₀-5d₃ of the Krypton 86 atom.

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.

Electric
Current 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
Substance mole mol The amount of substance which contains as many elementary units as there are atoms in 12 grams of pure Carbon 12.

Luminous
Intensity candela cd The luminous intensity, in the perpendicular direction, of a surface of 1/60 square centimetre of a black body at the freezing temperature of Platinum under a pressure of 101,325 pascal (1 atmosphere).

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 1000 metres is a kilometre (written as km); 1/1000th of a metre is a millimetre (written as mm).

Prefix Name	Symbol	Multiple
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. Fundamental units in red.

Unit Type Unit Name Symbol 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.

Quantity	Symbol	Value
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	m_e	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.

Unit	Description	Value
acre	Land Area	4.047 × 10³ m²
astronomical unit	Distance Between Earth and Sun	1.496 × 10¹¹ m
atmosphere	Atmospheric Pressure	1.013 × 10⁵ N m^-2
atomic mass unit	Mass of Hydrogen Atom	1.660 × 10^-27 kg
barrel	Oil Volume	0.1636 m³
British thermal unit	Energy	1.055 × 10³ J
bushel	Volume	3.637 × 10^-2 m³
calorie	Energy	4.184 J
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	Atomic Energy	1.602 × 10^-19 J
erg	Energy	1.000 × 10^-7 J
fluid ounce (UK)	Volume	2.841 × 10^-5 m³
foot	Length	0.3048 m
foot pound force	Energy	1.356 × 10⁵ J
gallon (UK)	Volume	4.546 × 10^-3 m³
gallon (USA)	Volume	3.785 × 10^-3 m³
hectare	Land Area	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	0.5114 m s^-1
light year	Stellar Distance	9.461 × 10¹² km
litre	Volume	1.000 × 10^-3 m³
mile	Distance	1.609 km
mile (nautical)	Distance	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	Stellar Distance	3.084 × 10¹³ km
pint (UK)	Volume	5.682 × 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

Metric Links

UK Metrication
United Kingdom metric site.
US Metric Association
The USA is the largest country not using the metric system. This site has a lot of useful information.
Metric Units and Conversions
Another site containing metric units and conversions.
Freedom2Measure
Not everybody likes the metric system. This is a US anti-metric site.
Non-Metric Units
The most commonly used non-metric units (used in USA and UK) can be found here.

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Comments, suggestions, or corrections to Kryss at webmaster@krysstal.com

Unit Type	Unit Name	Symbol	Definition
Length	metre	m	1,650,763.73 wavelengths in vacuum of radiation corresponding to the transition 2p₁₀-5d₃ of the Krypton 86 atom.
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.
Electric Current	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 Substance	mole	mol	The amount of substance which contains as many elementary units as there are atoms in 12 grams of pure Carbon 12.
Luminous Intensity	candela	cd	The luminous intensity, in the perpendicular direction, of a surface of 1/60 square centimetre of a black body at the freezing temperature of Platinum under a pressure of 101,325 pascal (1 atmosphere).
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.

Unit Type	Unit Name	Symbol	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