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 Math Help > Physics > Physics Units

# The SI System

SI stands for Syst�me International, which consists of the base units of length, mass, temperature, time, and charge.

### Base Units:

Length: meter, m.  Originally defined as one ten-millionth of the great-circle distance from the North Pole through Paris, France and Barcelona, Spain to the equator.  Now defined as length of the path traveled by light in vacuum during a time interval of 1/299,792,458 of second.

Mass: kilogram, kg.  Originally defined as the mass of water at its densest filling 1000 cm³.

Temperature: kelvin, K. Originally defined as one one-hundredth of the difference between the freezing and boiling temperatures of water under an atmospheric pressure that balances a 760-mm (29.92-inch) column of mercury.  Now defined as the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.

Time: second, s.  Originally defined as one 86,400th of a mean sidereal day.  Now defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom.

Ampere: ampere, A.  Defined as the current (a number of electrons per second that pass by a point) on either of two, parallel conductive wires of indefinite length that are spaced one meter apart such that a magnetic force of 2 � 10-7 newton, N, is applied between interfacing, one-meter lengths of the two wires. An ampere is one coulomb per second, and a coulomb contains about 6.2 � 1018 electrons.

Amount of substance: mole, mol; number, Avogadro's N, 6.0221 x 1023, defined as the amount of substance of a system which contains as many elementary entities as there are atoms in 12 grams of carbon 12.

Light Intensity: candela, cd; Luminous intensity; before 1982 it was defined from 1/60 of the emitted luminous intensity from the integral radiator (black body) to the temperature of solidification of the platinum (2045 K�), in perpendicular direction to the hole of outlet of the radiation from the radiator, being the hole area of equal to 1 cm2; after 1982, the candela is defined as 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.

(A steradian is a solid angle whose vertex is at the center of a unit sphere that is subtended by an area of one square unit; A complete sphere is 4 pi steradians.)

### Prefixes

The following table lists the SI prefix names and codes for the positive and negative powers of ten:

 Power of 10 Prefix Name Prefix Code English Meaning Original Language +18 exa E outside Greek +15 peta P spread Greek +12 tera T monster Greek +9 giga G giant Greek +6 mega M large Greek +3 kilo k thousand Greek +2 hecto h hundred Greek +1 deka D ten Greek - 1 deci d ten Latin - 2 centi c hundred Latin - 3 milli m thousand Latin - 6 micro � small Latin - 9 nano n dwarf Greek - 12 pico p tiny Italian - 15 femto f fifteen Old Norse - 18 atto a eighteen Old Norse

Notes:

1)   These prefix codes are valid only when they are followed by a basic-unit code. Examples are: meter, m, versus millimeter, mm, and tesla, T, the SI unit of magnetic induction, versus terawatt, TW, a trillion watts (U.S.) or a billion watts (British).

2)   This coding scheme respects the original metric conventions except for the following deviations: The Greek kilo- and hecto-prefix codes are in lowercase letters. The Latin micro-prefix code is the Greek-letter, �, because the milli-prefix code uses the Latin-letter, m.

3)   Niels Bohr, a Dane, is responsible for the addition of the femto- and atto-prefix names to the lexicon of the metric system.

### Derived Units:

(non SI units and conversions in parentheses)

Volume: length x length x length, m³ (liter, L = dm³ = 1000 cm³)

Force: mass x acceleration, kg�m/s², newton, N

Energy (work): force x distance, N�m, joule, J

N�m = kg�m/s²�m = kg�m²/s², (1 kcal = 4.184 kJ)

Power (work rate): J�s-1, watt, W

Pressure: force per unit area, N/m², pascal, Pa (760 mm of Hg or torr, T = 1 atm = 101.325 kPa)

Frequency: s-1, hertz, Hz

Electric Flux: coulomb, C, A�s

Quantity Unit Name Unit Symbol Expression in Terms of Other SI Units
Absorbed dose, specific energy imparted, kerma, absorbed dose index gray Gy J/kg
Activity (of a radionuclide) becquerel Bq 1/s
Celsius temperature degree Celsius degree C K
Dose equivalent sievert Sv J/kg
Electric charge, quantity of electricity coulomb C A�s
Electric conductance siemens S A/V
Electric inductance henry H Wb/A
Electric potential, potential difference, electromotive force volt V W/A
Electric resistance ohm Omega V/A
Energy, work, quantity of heat joule J N�m
Force newton N kg�m/s2
Frequency (of a periodic phenomenon) hertz Hz 1/s
Illuminance lux lx lm/m2
Luminous flux lumen lm cd�sr
Magnetic flux weber Wb V�s
Magnetic flux density tesla T Wb/m2
Power, radiant flux watt W J/s
Pressure, stress pascal Pa N/m2

```                                  x  y  z
SYMBOL :      HAS DIMENSIONS  M  L  T  :      WITH VALUES :   x     y     z
===============================================================================
(a )= Acceleration                 (meter/second)/(second)         1    -2
(A )= Area                                  (square meter)         2
(aa)= Fine structure constant                                -------------
(a0)= Radius of first orbit in Bohr atom           (meter)         1
(A0)= Area of sphere with radius (a0)       (square meter)         2
(aD)= Absorbed dose              (gray)=(joule)/(kilogram)         2    -2
(aR)= Absorbed dose rate                   (gray)/(second)         2    -3
(b )= Mass frequency                   (kilogram)/(second)   1          -1
(B )= Magnetic induction    (tesla)=(weber)/(square meter)  1/2  -3/2
(Bm)= Bohr Magneton                 (ampere)(square meter)  1/2   7/2   -2
(c )= Light velocity in vacuum            (meter)/(second)         1    -1
(Cm)= Compressibility   (volume per [volume per pressure])  -1     1     2
(Cn)= Conductance                (siemens)=(ampere)/(volt)         1    -1
(Ct)= Conductivity                       (siemens)/(meter)              -1
(Cw)= Compton's wavelength                         (meter)         1
(d )= Permeability                         (henry)/(meter)        -2     2
(D )= Density                     (kilogram)/(cubic meter)   1    -3
(De)= Dose equivalent         (sievert)=(joule)/(kilogram)         2    -2
(e )= Energy                       (joule)=(newton)(meter)   1     2    -2
(E )= Electric field strength               (volt)/(meter)  1/2  -1/2   -1
(eD)= Energy density                 (joule)/(cubic meter)   1    -1    -2
(Ed)= Electric flux density       (coulomb)/(square meter)  1/2  -1/2   -1
(Ef)= Electric flux                              (coulomb)  1/2   3/2   -1
(el)= Base of natural logarithm                               -------------
(Ep)= Electric polarization                 (volt)/(meter)  1/2  -1/2   -1
(Ex)= Radiation exposure              (coulomb)/(kilogram) -1/2   3/2   -1
(Eu)= Expansion of universe  (redshift per distance ratio)   -------------
(eS)= Specific energy                   (joule)/(kilogram)         2    -2
(f )= Frequency                         (hertz)=(1/second)              -1
(F )= Force     (newton)=(kilogram)(meter)/(square second)   1     1    -2
(f0)= Bohr atom electron orbital frequency         (hertz)              -1
(Fe)= Force of electrical interaction             (newton)   1     1    -2
(Fg)= Force of gravitational interaction          (newton)   1     1    -2
(g )= Gravitational field strength     (newton)/(kilogram)         1    -2
(G )= Gravity constant (newton)/([(kilogram/meter]squared)  -1     3    -2
(h )= Planck constant                      (joule)/(hertz)   1     2    -1
(h-Bar)= Planck constant)/[2(Pi)]          (joule)/(hertz)   1     2    -1
(H )= Magnetic field strength             (ampere)/(meter)  1/2   1/2   -2
(Hc)= Hubble constant       (velocity change per distance)              -1
(i )= Current                  (ampere)=(coulomb)/(second)  1/2   3/2   -2
(I )= Inductance                  (henry)=(weber)/(ampere)        -1     2
(Ir)= Irradiance                     (watt)/(square meter)   1          -3
(j )= Current density              (ampere)/(square meter)  1/2  -1/2   -2
(k )= Permittivity                         (farad)/(meter)   0     0     0
(k0)= Boltzmann's constant         (joule)/(degree Kelvin)   1     2    -2
(Ke)= Electrical interaction constant         1/[4(k)(Pi)]   0     0     0
(L )= Length                                       (meter)         1
(m )= Magnetic field strength             (ampere)/(meter)  1/2   1/2   -2
(M )= Mass                                      (kilogram)   1
(mI)= Moment of inertia           (kilogram)(square meter)   1     2
(Me)= Rest mass of electron                     (kilogram)   1
(Mn)= Rest mass of neutron                      (kilogram)   1
(Mp)= Rest mass of proton                       (kilogram)   1
(Mx)= Magnetic flux quantum                        (weber)  1/2   1/2
(O )= Origin                                                 0     0     0
(p )= Momentum                    [kilogram](meter/second)   1     1    -1
(p0)= Bohr atom electron momentum [kilogram](meter/second)   1     1    -1
(P )= Power                        (watt)=(joule)/(second)   1     1    -3
(phi)=Sacred cut; Constant of proportion; Golden section     -------------
(Pi)= Ratio of circumference to diameter of circle           -------------
(PL)= Planck's length                              (meter)         1
(PM)= Planck's mass                             (kilogram)   1
(Pr)= Pressure            (pascal)=(newton)/(square meter)   1    -1    -2
(PT)= Planck's time                               (second)               1
(q )= Electric dipole moment              (coulomb)(meter)  1/2   5/2   -1
(Q )= Charge                    (coulomb)=(ampere)(second)  1/2   3/2   -1
(Q0)= Electron charge                            (coulomb)  1/2   3/2   -1
(r )= Resistivity            [(ohm)(square meter)]/(meter)               1
(R )= Resistance                     (ohm)=(volt)/(ampere)        -1     1
(Rc)= Rydberg's constant                         (1/meter)        -1
(S )= Poynting vector    [(joule)/(second)]/(square meter)   1          -3
(St)= Surface tension               (joule)/(square meter)   1          -2
(T )= Time                                        (second)               1
(Tr)= Torque                               (newton)(meter)   1     2    -2
(u )= Magnetic dipole moment        (ampere)(square meter)  1/2   7/2   -2
(U )= Voltage                       (volt)=(watt)/(ampere)  1/2   1/2   -1
(v )= Velocity                            (meter)/(second)         1    -1
(V )= Volume                                 (cubic meter)         3
(v0)= Bohr atom electron velocity         (meter)/(second)         1    -1
(V0)= Volume of sphere with radius (a0)      (cubic meter)         3
(Vi)= Dynamic viscosity                   (pascal)(second)   1    -1    -1
(V/M)=Specific volume             (cubic meter)/(kilogram)  -1     3
(w )= Magnetic flux                 (weber)=(volt)(second)  1/2   1/2
(w0)= Magnetic flux quantum                        (weber)  1/2   1/2
(Wn)= Wave number                                (1/meter)        -1
(X )= The vector product: (B) x (E)  [tesla](volt)/(meter)   1    -2    -1
(Y )= Angular momentum   (kilogram)(square meter)/[second]   1     2    -1
(Z )= Impedance                                      (ohm)        -1     1
(z0)= Intrinsic impedance of vacuum                  (ohm)        -1     1
(!!)= (Q)/(M) = Specfic Charge        (coulomb)/(kilogram) -1/2   3/2   -1
(# )= Gyromagnetic ratio                   (hertz)/(tesla)  1/2  -3/2    1
(\$ )= Charge density               (coulomb)/(cubic meter)  1/2  -3/2   -1
(& )= Kinematic viscosity          (viscosity per density)         2    -1
```

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