SI coherent derived units whose names include SI coherent derived units with special names

SI coherent derived units whose names and symbols include SI coherent derived units with special names and symbols

The names and symbols of many SI coherent derived units include SI coherent derived units with special names and symbols.

Some of these units, and their definitions, are listed below.

Examples of SI coherent derived units whose names and symbols include SI coherent derived units with special names and symbols
Name Symbol Quantity Base units
pascal second Pa s dynamic viscosity kg m−1 s−1
1 \mspace{4mu} \text{Pa} \mspace{4mu} \text{s} \mspace{6mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)^3}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^3} \mspace{6mu} \dfrac{h \mspace{4mu} {\Delta \nu _{Cs}}^3}{c^3}\\ \\ \\ 1 \mspace{4mu} \text{Pa} \mspace{4mu} \text{s} \mspace{6mu} \approx 5.234 \mspace{4mu} 636 \mspace{4mu} 000 \mspace{4mu} 741 \mspace{4mu} 430 \mspace{4mu} 849 \times10^{28} \mspace{6mu} h \mspace{4mu} c^{-3} \mspace{4mu} {\Delta \nu _{Cs}}^3
newton metre N m torque,
moment of force
kg m2 s−2
1 \mspace{4mu} \text{N} \mspace{4mu} \text{m} \mspace{6mu} = \dfrac{1}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)} \mspace{6mu} h \mspace{4mu} \Delta \nu _{Cs}\\ \\ \\ 1 \mspace{4mu} \text{N} \mspace{4mu} \text{m} \mspace{6mu} \approx 1.641 \mspace{4mu} 738 \mspace{4mu} 968 \mspace{4mu} 123 \mspace{4mu} 762 \mspace{4mu} 714 \times10^{23} \mspace{6mu} h \mspace{4mu} \Delta \nu _{Cs}
newton per metre N/m surface tension kg s−2
1 \mspace{4mu} \text{N} / \text{m} \mspace{6mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^3} \mspace{6mu} \dfrac{h \mspace{4mu} {\Delta \nu _{Cs}}^3}{c^2}\\ \\ \\ 1 \mspace{4mu} \text{N} / \text{m} \mspace{6mu} \approx 1.746 \mspace{4mu} 086 \mspace{4mu} 621 \mspace{4mu} 278 \mspace{4mu} 988 \mspace{4mu} 563 \times10^{20} \mspace{6mu} h \mspace{4mu} c^{-2} \mspace{4mu} {\Delta \nu _{Cs}}^3
joule second J s action,
angular momentum
kg m2 s−1
1 \mspace{4mu} \text{J} \mspace{4mu} \text{s} \mspace{6mu} = \dfrac{1}{6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34}} \mspace{6mu} h\\ \\ \\ 1 \mspace{4mu} \text{J} \mspace{4mu} \text{s} \mspace{6mu} \approx 1.509 \mspace{4mu} 190 \mspace{4mu} 179 \mspace{4mu} 642 \mspace{4mu} 151 \mspace{4mu} 842 \times10^{33} \mspace{6mu} h
radian per second rad/s angular velocity s−1
1 \mspace{4mu} \text{rad} / \text{s} \mspace{6mu} = \dfrac{1}{9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770} \mspace{6mu} \Delta \nu _{Cs}\\ \\ \\ 1 \mspace{4mu} \text{rad} / \text{s} \mspace{6mu} \approx 1.087 \mspace{4mu} 827 \mspace{4mu} 757 \mspace{4mu} 077 \mspace{4mu} 666 \mspace{4mu} 563 \times10^{-10} \mspace{6mu} \Delta \nu _{Cs}
radian per second squared rad/s2 angular acceleration s−2
1 \mspace{4mu} \text{rad} / \text{s}^2 \mspace{6mu} = \dfrac{1}{(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^2} \mspace{6mu} {\Delta \nu _{Cs}}^2\\ \\ \\ 1 \mspace{4mu} \text{rad} / \text{s}^2 \mspace{6mu} \approx 1.183 \mspace{4mu} 369 \mspace{4mu} 229 \mspace{4mu} 068 \mspace{4mu} 626 \mspace{4mu} 734 \times10^{-20} \mspace{6mu} {\Delta \nu _{Cs}}^2
watt per square metre W/m2 heat flux density,
irradiance
kg s−3
1 \mspace{4mu} \text{W} / \text{m}^2 \mspace{6mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^4} \mspace{6mu} \dfrac{h \mspace{4mu} {\Delta \nu _{Cs}}^4}{c^2}\\ \\ \\ 1 \mspace{4mu} \text{W} / \text{m}^2 \mspace{6mu} \approx 1.899 \mspace{4mu} 441 \mspace{4mu} 492 \mspace{4mu} 889 \mspace{4mu} 243 \mspace{4mu} 145 \times10^{10} \mspace{6mu} h \mspace{4mu} c^{-2} \mspace{4mu} {\Delta \nu _{Cs}}^4
joule per kelvin J/K heat capacity, entropy kg m2 s−2 K−1
1 \mspace{4mu} \text{J} / \text{K} \mspace{6mu} = \dfrac{1}{1.380 \mspace{4mu} 649 \times 10^{-23}} \mspace{6mu} k\\ \\ \\ 1 \mspace{4mu} \text{J} / \text{K} \mspace{6mu} \approx 7.242 \mspace{4mu} 970 \mspace{4mu} 516 \mspace{4mu} 039 \mspace{4mu} 920 \mspace{4mu} 356 \times10^{22} \mspace{6mu} k
joule per kilogram kelvin J/(kg K) specific heat capacity,
specific entropy
m2 s−2 K−1
1 \mspace{4mu} \text{J} / (\text{kg} \mspace{4mu} \text{K}) \mspace{6mu} = \dfrac{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)}{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2(1.380 \mspace{4mu} 649 \times 10^{-23})} \mspace{6mu} \dfrac{c^2 \mspace{4mu} k}{h \mspace{4mu} \Delta \nu _{Cs}}\\ \\ \\ 1 \mspace{4mu} \text{J} / (\text{kg} \mspace{4mu} \text{K}) \mspace{6mu} \approx 4.908 \mspace{4mu} 753 \mspace{4mu} 283 \mspace{4mu} 645 \mspace{4mu} 638 \mspace{4mu} 834 \times10^{-18} \mspace{6mu} h^{-1} \mspace{4mu} c^2 \mspace{4mu} {\Delta \nu _{Cs}}^{-1} \mspace{4mu} k
joule per kilogram J/kg specific energy m2 s−2
1 \mspace{4mu} \text{J} / \text{kg} \mspace{6mu} = \dfrac{1}{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2} \mspace{6mu} c^2\\ \\ \\ 1 \mspace{4mu} \text{J} / \text{kg} \mspace{6mu} \approx 1.112 \mspace{4mu} 650 \mspace{4mu} 056 \mspace{4mu} 053 \mspace{4mu} 618 \mspace{4mu} 432 \times10^{-17} \mspace{6mu} c^2
watt per metre kelvin W/(m K) thermal conductivity kg m s−3 K−1
1 \mspace{4mu} \text{W} / (\text{m} \mspace{4mu} \text{K}) \mspace{6mu} = \dfrac{299 \mspace{4mu} 792 \mspace{4mu} 458}{(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^2(1.380 \mspace{4mu} 649 \times 10^{-23})} \mspace{6mu} \dfrac{{\Delta \nu _{Cs}}^2 \mspace{4mu} k}{c}\\ \\ \\ 1 \mspace{4mu} \text{W} / (\text{m} \mspace{4mu} \text{K}) \mspace{6mu} \approx 2.569 \mspace{4mu} 553 \mspace{4mu} 665 \mspace{4mu} 732 \mspace{4mu} 917 \mspace{4mu} 340 \times10^{11} \mspace{6mu} c^{-1} \mspace{4mu} {\Delta \nu _{Cs}}^2 \mspace{4mu} k
joule per cubic metre J/m3 energy density kg m−1 s−2
1 \mspace{4mu} \text{J} / \text{m}^3 \mspace{6mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)^3}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^4} \mspace{6mu} \dfrac{h \mspace{4mu} {\Delta \nu _{Cs}}^4}{c^3}\\ \\ \\ 1 \mspace{4mu} \text{J} / \text{m}^3 \mspace{6mu} \approx 5.694 \mspace{4mu} 382 \mspace{4mu} 339 \mspace{4mu} 804 \mspace{4mu} 557 \mspace{4mu} 242 \times10^{18} \mspace{6mu} h \mspace{4mu} c^{-3} \mspace{4mu} {\Delta \nu _{Cs}}^4
volt per metre V/m electric field strength kg m s−3 A−1
1 \mspace{4mu} \text{V} / \text{m} \mspace{6mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^2} \mspace{6mu} \dfrac{h \mspace{4mu} {\Delta \nu _{Cs}}^2}{c \mspace{4mu} e}\\ \\ \\ 1 \mspace{4mu} \text{V} / \text{m} \mspace{6mu} \approx 8.578 \mspace{4mu} 183 \mspace{4mu} 642 \mspace{4mu} 944 \mspace{4mu} 178 \mspace{4mu} 366 \times10^{2} \mspace{6mu} h \mspace{4mu} c^{-1} \mspace{4mu} {\Delta \nu _{Cs}}^2 \mspace{4mu} e^{-1}
coulomb per cubic metre C/m3 electric charge density m−3 s A
1 \mspace{4mu} \text{C} / \text{m}^3 \mspace{6mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)^3}{(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^3(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})} \mspace{6mu} \dfrac{{\Delta \nu _{Cs}}^3 \mspace{4mu} e}{c^3}\\ \\ \\ 1 \mspace{4mu} \text{C} / \text{m}^3 \mspace{6mu} \approx 2.164 \mspace{4mu} 871 \mspace{4mu} 501 \mspace{4mu} 342 \mspace{4mu} 103 \mspace{4mu} 134 \times10^{14} \mspace{6mu} c^{-3} \mspace{4mu} {\Delta \nu _{Cs}}^3 \mspace{4mu} e
coulomb per square metre C/m2 surface charge density,
electric flux density,
electric displacement
m−2 s A
1 \mspace{4mu} \text{C} / \text{m}^2 \mspace{6mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2}{(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^2(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})} \mspace{6mu} \dfrac{{\Delta \nu _{Cs}}^2 \mspace{4mu} e}{c^2}\\ \\ \\ 1 \mspace{4mu} \text{C} / \text{m}^2 \mspace{6mu} \approx 6.638 \mspace{4mu} 214 \mspace{4mu} 541 \mspace{4mu} 476 \mspace{4mu} 228 \mspace{4mu} 501 \times10^{15} \mspace{6mu} c^{-2} \mspace{4mu} {\Delta \nu _{Cs}}^2 \mspace{4mu} e
farad per metre F/m permittivity kg−1 m−3 s4 A2
1 \mspace{4mu} \text{F} / \text{m} \mspace{6mu} = \dfrac{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(299 \mspace{4mu} 792 \mspace{4mu} 458)}{(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})^2} \mspace{6mu} \dfrac{e^2}{h \mspace{4mu} c}\\ \\ \\ 1 \mspace{4mu} \text{F} / \text{m} \mspace{6mu} \approx 7.738 \mspace{4mu} 484 \mspace{4mu} 996 \mspace{4mu} 105 \mspace{4mu} 633 \mspace{4mu} 022 \times10^{12} \mspace{6mu} h^{-1} \mspace{4mu} c^{-1} \mspace{4mu} e^2
henry per metre H/m permeability kg m s−2 A−2
1 \mspace{4mu} \text{H} / \text{m} \mspace{6mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})^2}{6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34}} \mspace{6mu} \dfrac{h}{c \mspace{4mu} e^2}\\ \\ \\ 1 \mspace{4mu} \text{H} / \text{m} \mspace{6mu} \approx 1.161 \mspace{4mu} 409 \mspace{4mu} 732 \mspace{4mu} 252 \mspace{4mu} 647 \mspace{4mu} 916 \times10^{4} \mspace{6mu} h \mspace{4mu} c^{-1} \mspace{4mu} e^{-2}
joule per mole J/mol molar energy kg m2 s−2 mol−1
1 \mspace{4mu} \text{J} / \text{mol} \mspace{6mu} = \dfrac{1}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)(6.022 \mspace{4mu} 140 \mspace{4mu} 76 \times 10^{23})} \mspace{6mu} h \mspace{4mu} \Delta \nu _{Cs} \mspace{4mu} N_A\\ \\ \\ 1 \mspace{4mu} \text{J} / \text{mol} \mspace{6mu} \approx 2.726 \mspace{4mu} 171 \mspace{4mu} 694 \mspace{4mu} 671 \mspace{4mu} 186 \mspace{4mu} 520 \times10^{-1} \mspace{6mu} h \mspace{4mu} \Delta \nu _{Cs} \mspace{4mu} N_A
joule per mole kelvin J/(mol K) molar heat capacity,
molar entropy
kg m2 s−2 K−1 mol−1
1 \mspace{4mu} \text{J} / (\text{mol} \mspace{4mu} \text{K}) \mspace{6mu} = \dfrac{1}{(1.380 \mspace{4mu} 649 \times 10^{-23})(6.022 \mspace{4mu} 140 \mspace{4mu} 76 \times 10^{23})} \mspace{6mu} k \mspace{4mu} N_A\\ \\ \\ 1 \mspace{4mu} \text{J} / (\text{mol} \mspace{4mu} \text{K}) \mspace{6mu} \approx 1.202 \mspace{4mu} 723 \mspace{4mu} 550 \mspace{4mu} 427 \mspace{4mu} 260 \mspace{4mu} 414 \times10^{-1} \mspace{6mu} k \mspace{4mu} N_A
coulomb per kilogram C/kg exposure (x- and γ-rays) kg−1 s A
1 \mspace{4mu} \text{C} / \text{kg} \mspace{6mu} = \dfrac{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)}{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})} \mspace{6mu} \dfrac{c^2 \mspace{4mu} e}{h \mspace{4mu} \Delta \nu _{Cs}}\\ \\ \\ 1 \mspace{4mu} \text{C} / \text{kg} \mspace{6mu} \approx 4.230 \mspace{4mu} 036 \mspace{4mu} 294 \mspace{4mu} 682 \mspace{4mu} 392 \mspace{4mu} 435 \times10^{-22} \mspace{6mu} h^{-1} \mspace{4mu} c^2 \mspace{4mu} {\Delta \nu _{Cs}}^{-1} \mspace{4mu} e
gray per second Gy/s absorbed dose rate m2 s−3
1 \mspace{4mu} \text{Gy} / \text{s} \mspace{6mu} = \dfrac{1}{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)} \mspace{6mu} c^2 \mspace{4mu} \Delta \nu _{Cs}\\ \\ \\ 1 \mspace{4mu} \text{Gy} / \text{s} \mspace{6mu} \approx 1.210 \mspace{4mu} 371 \mspace{4mu} 614 \mspace{4mu} 889 \mspace{4mu} 147 \mspace{4mu} 716 \times10^{-27} \mspace{6mu} c^2 \mspace{4mu} \Delta \nu _{Cs}
watt per steradian W/sr radiant intensity kg m2 s−3
1 \mspace{4mu} \text{W} / \text{sr} \mspace{6mu} = \dfrac{1}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^2} \mspace{6mu} h \mspace{4mu} {\Delta \nu _{Cs}}^2\\ \\ \\ 1 \mspace{4mu} \text{W} / \text{sr} \mspace{6mu} \approx 1.785 \mspace{4mu} 929 \mspace{4mu} 219 \mspace{4mu} 401 \mspace{4mu} 075 \mspace{4mu} 514 \times10^{13} \mspace{6mu} h \mspace{4mu} {\Delta \nu _{Cs}}^2
watt per square metre steradian W/(m2 sr) radiance kg s−3
1 \mspace{4mu} \text{W} / (\text{m}^2 \mspace{4mu} \text{sr}) \mspace{6mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^4} \mspace{6mu} \dfrac{h \mspace{4mu} {\Delta \nu _{Cs}}^4}{c^2}\\ \\ \\ 1 \mspace{4mu} \text{W} / (\text{m}^2 \mspace{4mu} \text{sr}) \mspace{6mu} \approx 1.899 \mspace{4mu} 441 \mspace{4mu} 492 \mspace{4mu} 889 \mspace{4mu} 243 \mspace{4mu} 145 \times10^{10} \mspace{6mu} h \mspace{4mu} c^{-2} \mspace{4mu} {\Delta \nu _{Cs}}^4
katal per cubic metre kat/m3 catalytic activity m−3 s−1 mol
1 \mspace{4mu} \text{kat} / \text{m}^3 \mspace{6mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)^3(6.022 \mspace{4mu} 140 \mspace{4mu} 76 \times 10^{23})}{(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^4} \mspace{6mu} \dfrac{{\Delta \nu _{Cs}}^4}{c^3 \mspace{4mu} N_A}\\ \\ \\ 1 \mspace{4mu} \text{kat} / \text{m}^3 \mspace{6mu} \approx 2.272 \mspace{4mu} 236 \mspace{4mu} 624 \mspace{4mu} 259 \mspace{4mu} 796 \mspace{4mu} 834 \times10^{9} \mspace{6mu} c^{-3} \mspace{4mu} {\Delta \nu _{Cs}}^4 \mspace{4mu} {N_A}^{-1}
lumen second lm s luminous energy s cd
1 \mspace{4mu} \text{lm} \mspace{4mu} \text{s} \mspace{6mu} = \dfrac{1}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)(683)} \mspace{6mu} h \mspace{4mu} \Delta \nu _{Cs} \mspace{4mu} K_{cd}\\ \\ \\ 1 \mspace{4mu} \text{lm} \mspace{4mu} \text{s} \mspace{6mu} \approx 2.403 \mspace{4mu} 717 \mspace{4mu} 376 \mspace{4mu} 462 \mspace{4mu} 317 \mspace{4mu} 297 \times10^{20} \mspace{6mu} h \mspace{4mu} \Delta \nu _{Cs} \mspace{4mu} K_{cd}
lumen per watt lm W-1 luminous efficacy kg-1 m-2 s3 cd
1 \mspace{4mu} \text{lm} \mspace{4mu} \text{W}^{-1} \mspace{6mu} = \dfrac{1}{683} \mspace{6mu} K_{cd}\\ \\ \\ 1 \mspace{4mu} \text{lm} \mspace{4mu} \text{W}^{-1} \mspace{6mu} \approx 1.464 \mspace{4mu} 128 \mspace{4mu} 843 \mspace{4mu} 338 \mspace{4mu} 213 \mspace{4mu} 763 \times10^{-3} \mspace{6mu} K_{cd}

All SI coherent derived units can be defined in terms of products of powers of the seven SI base units, or more directly in terms of products of powers of the seven SI defining constants and a dimensionless scaling factor.