Units
of measure
Names and symbols
of SI units of measure
Basic units
Symbol of the magnitude1
Unit
Symbol of the unit
Dimension
Basic units
length
mass
time
electrical current
thermodynamic temperature 2
quantity of material
light intensity
l, (L)
m
t
I
T
n
I, (Iv)
metre
kilogramme
second
ampere
kelvin
mole
candela
m
kg
s
A
K
mol
cd
L
M
T
I
θ
N
J
Additional units
angle (plane angle)
solid angle
α, β, γ …
Ω, (ω)
radian
steradian
rad
sr
N/A
N/A
Magnitude
Common magnitudes and units
Name
Symbol
Dimension
SI Unit: name
(symbol)
Comments
and other units
Magnitude: space and time
length
l, (L)
L
metre (m)
area
A, (S)
L2
metre squared (m2)
centimetre (cm): 1 cm = 10-2 m
(microns must no monger be used,
instead the micrometre (µm))
are (a): 1 a = 102 m2
hectare (ha): 1 ha = 104 m2 (agricult. meas.)
volume
plane angle
V
α, β, γ …
L3
N/A
metre cubed (m3 )
radian (rad)
solid angle
time
Ω, (ω)
t
N/A
T
steradian (sr)
second (s)
speed
rad/s
acceleration
v
L T-1
metre per second (m/s)
a
L T-2
angular speed
angular acceleration
ω
α
T-1
T -2
metre per second squared
acceleration due to gravity:
(m/s2)
g = 9.80665 m/s2
radian per second (rad/s)
radian per second squared (rad/s 2)
Magnitude: mass
mass
m
M
kilogramme (kg)
linear mass
mass per surface area
mass per volume
volume per mass
concentration
ρ1
ρA' (ρs)
ρ
v
ρB
L-1 M
L-2 M
L-3 M
L3 M-1
M L-3
density
d
gradian (gr): 1 gr = 2π rad/400
revolution (rev): 1 tr = 2π rad
degree(°):1°= 2π rad/360 = 0.017 453 3 rad
minute ('): 1' = 2π rad/21 600
= 2,908 882 • 10-4 rad
second ("): 1" = 2π rad/1 296 000
= 4.848 137 • 10-6 rad
minute (mn)
hour (h)
day (d)
revolutions per second (rev/s): 1 tr/s = 2π
gramme (g) : 1 g = 10-3 kg
ton (t) : 1 t = 103 kg
N/A
kilogramme per metre (kg/m)
kilogramme per metre squared (kg/m2)
kilogramme per metre cubed (kg/m3)
metre cubed per kilogramme (m3/kg)
kilogramme per metre cubed
concentration by mass of component B
(kg/m3 )
(according to NF X 02-208)
N/A
Magnitude: periodic phenomena
period
T
frequency
f
phase shift
ϕ
wavelength
λ
T
T-1
N/A
L
second (s)
hertz (Hz)
radian (rad)
metre (m)
power level
N/A
decibel (dB)
Lp
1 Hz = 1s-1, f = 1/T
use of the angström (10-10 m) is forbidden.
Use of a factor of nanometre
(109 m) is recommended λ = c/f = cT
(c = celerity of light)
e1
2
Schneider Electric
the symbol in brackets can also be used
the temperature Celsius t is related to the themrodynamic temperature T by the relationship: t = T - 273.15 K
Merlin Gerin MV design Guide
67
Names and symbols
of SI units of measure
Units
of measure
Name
Symbol
Dimension
SI Unit:
name (symbol)
Comments
and other units
Magnitude: mechanical
force
weight
moment of the force
F
G, (P, W)
M, T
L M T-2
Newton
1 N = 1 m.kg/s2
L2 M T-2
Newton-metre (N.m)
surface tension
work
energy
γ, σ
W
E
M T-2
L2 M T-2
L2 M T-2
Newton per metre (N/m)
Joule (J)
Joule (J)
power
pressure
P
σ, τ
p
L2 M T-3
L-1 M T-2
Watt (W)
Pascal (Pa)
dynamic viscosity
kinetic viscosity
quantity of movement
η, µ
ν
p
L-1 M T-1
L2 T-1
L M T-1
Pascal-second (Pa.s)
metre squared per second (m2/s)
kilogramme-metre per second
(kg.m/s)
N.m and not m.N to avoid any confusion
with the millinewton
1 N/m = 1 J/m2
1 J : 1 N.m = 1 W.s
Watthour (Wh) : 1 Wh = 3.6 • 103 J
(used in determining electrical
consumption)
1 W = 1 J/s
1 Pa = 1 N/m2
(for the pressure in fluids we use bars
(bar): 1 bar = 105 Pa)
1 P = 10-1 Pa.s (P = poise, CGS unit)
1 St = 10-4 m2/s (St = stokes, CGS unit)
p = mv
Magnitude: electricity
current
electrical charge
electrical potential
electrical field
electrical resistance
electrical conductivity
electrical capacitance
electrical inductance
I
Q
V
E
R
G
C
L
I
TI
L2M T-3 I-1
L M T-3 I-1
L2 M T-3 I-2
L-2 M-1 T3 I2
L-2 M-1 T4 I2
L2 M T-2 I-2
Ampere (A)
Coulomb (C)
Volt (V)
Volt per metre (V/m)
Ohm (Ω)
Siemens (S)
Farad (F)
Henry (H)
M T -2 I-1
L2 M T-2 I-1
L-1 I
L-1 I
I
L3 M T-3 I-2
L-3 M-1 T3 I2
L-3 M-1 T4 I2
L2 M T-3
L2 M T-3
L2 M T-3
Tesla (T)
Weber (Wb)
Ampere per metre (A/m)
Ampere per metre (A/m)
Ampere (A)
Ohm-metre (Ω.m)
Siemens per metre (S/m)
Farad per metre (F/m)
Watt (W)
Voltampere (VA)
var (var)
1 T = 1 Wb/m2
1 Wb = 1 V.s
T
θ
Kelvin (K)
Kelvin and not degree Kelvin or °Kelvin
t, θ
E
C
S
c
θ
L2 M T-2
L2 M T-2 θ-1
L2 M T-2 θ-1
L2 T-2 θ-1
t = T - 273.15 K
λ
Q
Φ
P
hr
L M T-3 θ-1
L2 M T-2
L2 M T-3
L2 M T-3
M T-3 θ-1
degree Celsius (°C)
Joule (J)
Joule per Kelvin (J/K)
Joule per Kelvin (J/K)
Watt per kilogramme-Kelvin
(J/(kg.K))
Watt per metre-Kelvin (W/(m.K))
Joule (J)
Watt (W)
Watt (W)
Watt per metre squared-Kelvin
(W/(m2.K))
Magnitude: electricity, magnetism
magnetic induction
B
magnetic induction flux
Φ
magnetisation
Hi, M
magnetic field
H
magneto-motive force
F, Fm
resistivity
ρ
conductivity
γ
permittivity
ε
active
P
apparent power
S
reactive power
Q
Magnitude: thermal
thermodynamic
temperature
temperature Celsius
energy
heat capacity
entropy
specific heat
capacity
thermal conductivity
quantity of heat
thermal flux
thermal power
coefficient of thermal
radiation
68
Merlin Gerin MV design guide
1 C = 1 A.s
1 V = 1 W/A
1 Ω = 1 V/A
1 S = 1 A/V = 1Ω-1
1 F = 1 C/V
1 H = 1 Wb/A
1 µΩ.cm2/cm = 10-8 Ω.m
1 W = 1 J/s
1 var = 1 W
1 W = 1 J/s
Schneider Electric
Units
of measure
Names and symbols
of SI units of measure
Correspondence between
Imperial units and
international system units (SI)
Magnitude
Unit
Symbol
Conversion
acceleration
calory capacity
foot per second squared
British thermal unit per pound
ft/s2
Btu/Ib
1 ft/s2 = 0.304 8 m/s2
1 Btu/Ib = 2.326 • 103 J/kg
heat capacity
magnetic field
British thermal unit per cubit foot.degree Fahrenheit
British thermal unit per (pound.degree Fahrenheit)
oersted
Btu/ft3.°F
Btu/Ib°F
Oe
1 Btu/ft3.°F = 67.066 1 • 103 J/m3.°C
1 Btu/Ib.°F = 4.186 8 • 103 J(Kg.°C)
1 Oe = 79.577 47 A/m
thermal conductivity
energy
British thermal unit per square foot.hour.degree Fahrenheit
British thermal unit
Btu/ft2.h.°F
Btu
1 Btu/ft2.h.°F = 5.678 26 W/(m2.°C)
1 Btu = 1.055 056 • 103 J
energy (couple)
thermal flux
pound force-foot
pound force-inch
British thermal unit per square foot.hour
Ibf/ft
Ibf.in
Btu/ft2.h
1 Ibf.ft = 1.355 818 J
1 Ibf.in = 0.112 985 J
1 Btu/ft2.h = 3.154 6 W/m2
force
length
British thermal unit per second
pound-force
foot
Btu/s
Ibf
ft, '
1 Btu/s = 1.055 06 • 103 W
1 Ibf = 4.448 222 N
1 ft = 0.304 8 m
inch (1)
mile (UK)
in, "
mile
1 in = 25.4 mm
1 mile = 1.609 344 km
knot
yard (2)
once (ounce)
pound (livre)
pound per foot
pound per inch
yd
oz
Ib
Ib/ft
Ib/in
1 852 m
1 yd = 0.914 4 m
1 oz = 28.349 5 g (6)
1 Ib = 0.453 592 37 kg
1 Ib/ft = 1.488 16 kg/m
1 Ib/in = 17.858 kg/m
mass per surface area
pound per square foot
pound per square inch
Ib/ft2
Ib/in2
1 Ib/ft2 = 4.882 43 kg/m2
1 Ib/in2 = 703,069 6 kg/m2
mass per volume
pressure - strain
pound per cubic foot
pound per cubic inch
pound square foot
foot of water
inch of water
pound force per square foot
Ib/ft3
Ib/in3
Ib.ft2
ft H2O
in H2O
Ibf/ft2
1 Ib/ft3 = 16.018 46 kg/m3
1 Ib/in3 = 27.679 9 • 103 kg/m3
1 Ib.ft2 = 42.140 g.m2
1 ft H2O = 2.989 07 • 103 Pa
1 in H2O = 2,490 89 • 102 Pa
1 Ibf/ft2 = 47.880 26 Pa
calorific power
pound force per square inch (3)
British thermal unit per hour
Ibf/in2 (psi)
Btu/h
1 Ibf/in2 = 6.894 76 • 103 Pa
1 Btu/h = 0.293 071 W
square foot
square inch
degree Fahrenheit (4)
degree Rankine (5)
pound force-second per square foot
pound per foot-second
sq.ft, ft2
sq.in, in2
°F
°R
Ibf.s/ft2
Ib/ft.s
1 sq.ft = 9.290 3 • 10-2 m2
1 sq.in = 6.451 6 • 10-4 m2
TK = 5/9 (q °F + 459.67)
TK = 5/9 q °R
1 Ibf.s/ft2 = 47.880 26 Pa.s
1 Ib/ft.s = 1.488 164 Pa.s
cubic foot
cubic inch
cu.ft
cu.in, in3
1 cu.ft = 1 ft3 = 28.316 dm3
1 in3 = 1.638 71 • 10-5 m3
fluid ounce (UK)
fluid ounce (US)
gallon (UK)
fl oz (UK)
fl oz (US)
gal (UK)
fl oz (UK) = 28.413 0 cm3
fl oz (US) = 29.573 5 cm3
1 gaz (UK) = 4.546 09 dm3
gallon (US)
gal (US)
1 gaz (US) = 3.785 41 dm3
mass
linear mass
moment of inertia
pressure
surface area
temperature
viscosity
volume
(1)
12 in = 1 ft
1 yd = 36 in = 3 ft
Or p.s.i.: pound force per square inch
(4)
T K = temperature kelvin with q°C = 5/9 (q°F - 32)
(5)
°R = 5/9 °K
(6)
Apart from mass of precious metals (silver, gold, for example) where the carat is used (1 carat = 3.110 35 10-2 kg)
(2)
(3)
Schneider Electric
Merlin Gerin MV design guide
69