Système International d'Unités

The International System of Units

The modern metric system is a coherent, rationalized meter-kilogram-second system of units.

Preferred SI prefixes are those which are powers of 1000:
prefix symbol value
yotta- Y 1024 1 000 000 000 000 000 000 000 000
zetta- Z 1021 1 000 000 000 000 000 000 000
exa- E 1018 1 000 000 000 000 000 000
peta- P 1015 1 000 000 000 000 000
tera- T 1012 1 000 000 000 000
giga- G 109 1 000 000 000
mega- M 106 1 000 000
kilo- k 103 1 000
[none]   100 1
milli- m 10-3 0.001
micro- µ 10-6 0.000 001
nano- n 10-9 0.000 000 001
pico- p 10-12 0.000 000 000 001
femto- f 10-15 0.000 000 000 000 001
atto- a 10-18 0.000 000 000 000 000 001
zepto- z 10-21 0.000 000 000 000 000 000 001
yocto- y 10-24 0.000 000 000 000 000 000 000 001

SI also includes four of the other prefixes to accomodate usage already established before the introduction of SI. The prefixes centi- (10-2), deci- (10-1), deka- (101), and hecto- (102) should generally be limited to areas and volumes, and nontechnical measurements of length such as centimeters for body measurements.

SI Base Units
quantity unit symbol
length metre m
mass kilogram kg
time second s
electric current ampere A
temperature kelvin K
luminous intensity candela cd
amount of substance mole mol

Derived SI units
quantity special name formula symbol
absorbed dose gray J kg-1 Gy
acceleration   m s-2  
activity becquerel s-1 Bq
area   m2  
capacitance farad A s V-1 F
catalytic activity katal mol s-1 kat
charge coulomb A s C
density   kg m-3  
dose equivalent sievert J kg-1 Sv
electric conductance siemens [Omega]-1 S
electric field strength   V m-1  
electric potential volt W A-1 V
energy, work, quantity of heat joule N m J
force newton kg m s-2 N
frequency hertz s-1 Hz
illumination lux lm m-2 lx
inductance henry V s A-1 H
luminance   cd m-2  
luminous flux lumen cd sr lm
magnetic field strength   A m-1
magnetic flux weber V s Wb
magnetic flux density tesla Wb m-2 T
momentum   kg m s-1  
plane angle radian m/m = 1 rad
power watt J s-1 W
pressure pascal N m-2 Pa
resistance ohm V A-1 [Omega]
solid angle steradian m2/m2 = 1 sr
stress   N m-2 or Pa  
temperature degree Celsius K (for interval) °C
velocity   m s-1  
viscosity, dynamic   Pa s  
viscosity, kinematic   m2 s-1  
volume   m3  

Click here for Relationships of the SI Derived Units with Special Names and the SI Base Units, a graphic from NIST, U.S. Department of Commerce.

Fundamental constants, CODATA 1998 values, see NIST link below for more:
constant symbol value
atomic mass constant mu 1.660 538 73(13) × 10-27 kg
Avogadro constant L, NA 6.022 141 99(47) × 1023 mol-1
Bohr magneton µB 9.274 008 99(37) × 10-24 J T-1
Boltzmann constant k 1.380 650 3(24) × 10-23 J K-1
electron charge e 1.602 176 462(63) × 10-19 C
electron mass me 9.109 381 88(72) × 10-31 kg
Faraday constant F 9.648 534 15(39) × 104 C mol-1
Loschmidt's constant NL 2.686 777 5(47) × 1025 m-3
molar gas constant R 8.314 472(15) J K-1 mol-1
molar volume (ideal gas, 101.325 kPa) Vm 2.241 399 6(39) × 10-2 m3 mol-1
neutron mass mn 1.674 927 16(13) × 10-27 kg
Newton's gravitational constant G 6.673(10) × 10-11 N m2 kg-2
permeability of vacuum µ0 4(pi) × 10-7 N A-2
1.256 637 061... × 10-6 N A-2
permittivity of vacuum epsilon0 8.854 187 817... × 10-12 F m-1
Planck constant h 6.626 068 76(52) × 10-34 J s
proton mass mp 1.672 621 58(13) × 10-27 kg
speed of light c 2.997 924 58 × 108 m s-1
Stefan-Boltzmann constant sigma 5.670 400(40) × 10-8 W m-2 K-4
NOTE: pi, epsilon, and sigma stand for lowercase Greek letters not available in Latin-1 character set

In the above table, the part in parentheses indicates uncertainty in the final digits given. For example, 6.672 59(85) × 10-11 means (6.672 59 ± 0.000 85) × 10-11. In other words, it is somewhere between 6.671 74 × 10-11 and 6.673 44× 10-11.

Elemental unit definitions

length: metre (m)
The metre is the length of the path travelled by light in vacuum during a time interval of 1/(299 792 458) second.
mass: kilogram (kg)
The kilogram is equal to the mass of the international platinum-iridium prototype kept by the International Bureau of Weights and Measures at Sèvres, near Paris. (This is the only base unit still defined by an artifact.)
time: second (s)
The second is 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 cesium-133 atom.
electric current: ampere (A)
The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible cross section, and placed one metre apart in vacuum, would produce a force between the conductors of 2 × 10-7 newton per metre of length.
temperature: kelvin (K)
The kelvin, SI unit of thermodynamic temperature, is equal to the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
The magnitude of the kelvin is equal to that of the degree Celsius, but a temperature expressed in degrees Celsius is numerically equal to the temperature in kelvins less 273.15. The former name 'degree Kelvin' (symbol °K) became obsolete by international agreement in 1967.
luminous intensity: candela (cd)
The candela is the luminous intensity in a given direction of a source which emits monochromatic radiation of frequency 540 terahertz and of which the radiant intensity in that direction is 1/683 watt per steradian.
amount of substance: mole (mol)
The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 12 grams of carbon-12. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles.

Links . . .

Metric Style Guide for the News Media The basics from NIST, U.S. Department of Commerce.

Interpretation of the SI for the United States and Metric Conversion Policy for Federal Agencies NIST Special Publication 814. The "official" metric system in U.S. law.

Metric Home Page, S I Jakub Assoc.

BIPM, the International Bureau of Weights and Measures, the organization with primary responsibility for keeping the international standards under the Metre Convention, or Treaty of the Meter, of 1875. Includes information on the history and use of SI, the activities of the BIPM, and links to web sites for national standards laboratories around the world.

SI Unit Rules and Style Conventions Checklist from NIST.

NIST Physics Laboratory's home page, The NIST Reference on Constants, Units, and Uncertainty. Three important publications on the SI and a helpful diagram concerning the SI derived units with specal names may be accessed from this page the Bibliography link on the International System of Units from NIST page:

Metrics the Right Way, by George Sudikatus, from the Authors Guide of Pacific Northwest National Laboratory.

Hectopascals: No, No, Never! Gene Nygaard looks at a crazy scheme to hang onto an obsolete unit by cloaking it in a pseudo-SI name.

Conversion Factors. From English or obsolete metric units to SI units. Here's where you find all the old pounds and gallons and tons and miles and calories and ergs and whatever.

Back to Gene's Measurements and Weather Page

Weight Force vs. Mass; What's the Difference