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