SI coherent derived units with special names and symbols

Coherent derived units are products of powers of base units that include no numerical factor other than one. The base units and coherent derived units of the SI form a coherent set, designated the set of coherent SI units.

All SI coherent derived units can be defined directly from the SI defining constants.

To simplify their expression, 22 coherent derived units in the SI have been given special names.

SI coherent derived units with special names and symbols

Name	Symbol	Quantity	Base units
hertz	Hz	frequency	s^-1
$1 \mspace{4mu} \text{Hz} \mspace{6mu} = \dfrac{1}{9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770} \mspace{6mu} \Delta \nu _{Cs}\\ \\ \\ 1 \mspace{4mu} \text{Hz} \mspace{6mu} \approx 1.087 \mspace{4mu} 827 \mspace{4mu} 757 \mspace{4mu} 077 \mspace{4mu} 666 \mspace{4mu} 563 \times10^{-10} \mspace{6mu} \Delta \nu _{Cs}$
radian	rad	plane angle	m/m
$1 \mspace{4mu} \text{rad} \mspace{6mu} =$	$\text{the angle subtended at the}\\ \text{centre of a circle of radius} \mspace{6mu} r\\ \text{by an arc of length} \mspace{6mu} s = r$
steradian	sr	solid angle	m²/m²
$1 \mspace{4mu} \text{sr} \mspace{6mu} =$	$\text{the solid angle subtended at the}\\ \text{centre of a sphere of radius} \mspace{6mu} r\\ \text{by any portion of its surface}\\ \text{with area} \mspace{6mu} A = r^2$
newton	N	force	kg m s^-2
$1 \mspace{4mu} \text{N} \mspace{6mu} = \dfrac{299 \mspace{4mu} 792 \mspace{4mu} 458}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^2} \mspace{6mu} \dfrac{h \mspace{4mu} {\Delta \nu _{Cs}}^2}{c}\\ \\ \\ 1 \mspace{4mu} \text{N} \mspace{6mu} \approx 5.354 \mspace{4mu} 081 \mspace{4mu} 104 \mspace{4mu} 982 \mspace{4mu} 697 \mspace{4mu} 161 \times10^{21} \mspace{6mu} h \mspace{4mu} c^{-1} \mspace{4mu} {\Delta \nu _{Cs}}^2$
pascal	Pa	pressure	kg m⁻¹ s⁻²
$1 \mspace{4mu} \text{Pa} \mspace{6mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)^3}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^4} \mspace{6mu} \dfrac{h \mspace{4mu} {\Delta \nu _{Cs}}^4}{c^3}\\ \\ \\ 1 \mspace{4mu} \text{Pa} \mspace{6mu} \approx 5.694 \mspace{4mu} 382 \mspace{4mu} 339 \mspace{4mu} 804 \mspace{4mu} 557 \mspace{4mu} 242 \times10^{18} \mspace{6mu} h \mspace{4mu} c^{-3} \mspace{4mu} {\Delta \nu _{Cs}}^4$
joule	J	energy	kg m² s⁻²
$1 \mspace{4mu} \text{J} \mspace{6mu} = \dfrac{1}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)} \mspace{6mu} h \mspace{4mu} \Delta \nu _{Cs}\\ \\ \\ 1 \mspace{4mu} \text{J} \mspace{6mu} \approx 1.641 \mspace{4mu} 738 \mspace{4mu} 968 \mspace{4mu} 123 \mspace{4mu} 762 \mspace{4mu} 714 \times10^{23} \mspace{6mu} h \mspace{4mu} \Delta \nu _{Cs}$
watt	W	power	kg m² s^-3
$1 \mspace{4mu} \text{W} \mspace{6mu} = \dfrac{1}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^2} \mspace{6mu} h \mspace{4mu} {\Delta \nu _{Cs}}^2\\ \\ \\ 1 \mspace{4mu} \text{W} \mspace{6mu} \approx 1.785 \mspace{4mu} 929 \mspace{4mu} 219 \mspace{4mu} 401 \mspace{4mu} 075 \mspace{4mu} 514 \times10^{13} \mspace{6mu} h \mspace{4mu} {\Delta \nu _{Cs}}^2$
coulomb	C	electric charge	s A
$1 \mspace{4mu} \text{C} \mspace{6mu} = \dfrac{1}{1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19}} \mspace{6mu} e\\ \\ \\ 1 \mspace{4mu} \text{C} \mspace{6mu} \approx 6.241 \mspace{4mu} 509 \mspace{4mu} 074 \mspace{4mu} 460 \mspace{4mu} 762 \mspace{4mu} 608 \times10^{18} \mspace{6mu} e$
volt	V	potential difference	kg m² s⁻³ A^-1
$1 \mspace{4mu} \text{V} \mspace{6mu} = \dfrac{1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19}}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)} \mspace{6mu} \dfrac{h \mspace{4mu} \Delta \nu _{Cs}}{e}\\ \\ \\ 1 \mspace{4mu} \text{V} \mspace{6mu} \approx 2.630 \mspace{4mu} 355 \mspace{4mu} 813 \mspace{4mu} 855 \mspace{4mu} 163 \mspace{4mu} 441 \times10^{4} \mspace{6mu} h \mspace{4mu} \Delta \nu _{Cs} \mspace{4mu} e^{-1}$
farad	F	capacitance	kg^-1 m^-2 s⁴ A²
$1 \mspace{4mu} \text{F} \mspace{6mu} = \dfrac{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)}{(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})^2} \mspace{6mu} \dfrac{e^2}{h \mspace{4mu} \Delta \nu _{Cs}}\\ \\ \\ 1 \mspace{4mu} \text{F} \mspace{6mu} \approx 2.372 \mspace{4mu} 876 \mspace{4mu} 339 \mspace{4mu} 232 \mspace{4mu} 955 \mspace{4mu} 900 \times10^{14} \mspace{6mu} h^{-1} \mspace{4mu} {\Delta \nu _{Cs}}^{-1} \mspace{4mu} e^2$
ohm	Ω	electrical resistance	kg m² s⁻³ A^-2
$1 \mspace{4mu} \Omega \mspace{6mu} = \dfrac{(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})^2}{6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34}} \mspace{6mu} \dfrac{h}{e^2}\\ \\ \\ 1 \mspace{4mu} \Omega \mspace{6mu} \approx 3.874 \mspace{4mu} 045 \mspace{4mu} 864 \mspace{4mu} 931 \mspace{4mu} 825 \mspace{4mu} 323 \times10^{-5} \mspace{6mu} h \mspace{4mu} e^{-2}$
siemens	S	electrical conductance	kg^-1 m^-2 s³ A²
$1 \mspace{4mu} \text{S} \mspace{6mu} = \dfrac{6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34}}{(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})^2} \mspace{6mu} \dfrac{e^2}{h}\\ \\ \\ 1 \mspace{4mu} \text{S} \mspace{6mu} \approx 2.581 \mspace{4mu} 280 \mspace{4mu} 745 \mspace{4mu} 930 \mspace{4mu} 450 \mspace{4mu} 666 \times10^{4} \mspace{6mu} h^{-1} \mspace{4mu} e^2$
weber	Wb	magnetic flux	kg m² s⁻² A^-1
$1 \mspace{4mu} \text{Wb} \mspace{6mu} = \dfrac{1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19}}{6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34}} \mspace{6mu} \dfrac{h}{e}\\ \\ \\ 1 \mspace{4mu} \text{Wb} \mspace{6mu} \approx 2.417 \mspace{4mu} 989 \mspace{4mu} 242 \mspace{4mu} 084 \mspace{4mu} 918 \mspace{4mu} 162 \times10^{14} \mspace{6mu} h \mspace{4mu} e^{-1}$
tesla	T	magnetic flux density	kg s⁻² A^-1
$1 \mspace{4mu} \text{T} \mspace{6mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^2} \mspace{6mu} \dfrac{h \mspace{4mu} {\Delta \nu _{Cs}}^2}{c^2 \mspace{4mu} e}\\ \\ \\ 1 \mspace{4mu} \text{T} \mspace{6mu} \approx 2.571 \mspace{4mu} 674 \mspace{4mu} 759 \mspace{4mu} 493 \mspace{4mu} 629 \mspace{4mu} 589 \times10^{11} \mspace{6mu} h \mspace{4mu} c^{-2} \mspace{4mu} {\Delta \nu _{Cs}}^2 \mspace{4mu} e^{-1}$
henry	H	inductance	kg m² s⁻² A^-2
$1 \mspace{4mu} \text{H} \mspace{6mu} = \dfrac{(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)(1.602 \mspace{4mu} 176 \mspace{4mu} 634 \times 10^{-19})^2}{6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34}} \mspace{6mu} \dfrac{h}{\Delta \nu _{Cs} \mspace{4mu} e^2}\\ \\ \\ 1 \mspace{4mu} \text{H} \mspace{6mu} \approx 3.561 \mspace{4mu} 267 \mspace{4mu} 709 \mspace{4mu} 640 \mspace{4mu} 942 \mspace{4mu} 635 \times10^{5} \mspace{6mu} h \mspace{4mu} {\Delta \nu _{Cs}}^{-1} \mspace{4mu} e^{-2}$
degree Celsius	°C	Celsius temperature	K
$1 \mspace{4mu} ^\circ \text{C} \mspace{6mu} = \dfrac{1.380 \mspace{4mu} 649 \times 10^{-23}}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)} \mspace{6mu} \dfrac{h \mspace{4mu} \Delta \nu _{Cs}}{k}\\ \\ \\ 1 \mspace{4mu} ^\circ \text{C} \mspace{6mu} \approx 2.266 \mspace{4mu} 665 \mspace{4mu} 264 \mspace{4mu} 601 \mspace{4mu} 104 \mspace{4mu} 867 \mspace{6mu} h \mspace{4mu} \Delta \nu _{Cs} \mspace{4mu} k^{-1}$
lumen	lm	luminous flux	cd
$1 \mspace{4mu} \text{lm} \mspace{6mu} = \dfrac{1}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^2(683)} \mspace{6mu} h \mspace{4mu} {\Delta \nu _{Cs}}^2 \mspace{4mu} K_{cd}\\ \\ \\ 1 \mspace{4mu} \text{lm} \mspace{6mu} \approx 2.614 \mspace{4mu} 830 \mspace{4mu} 482 \mspace{4mu} 285 \mspace{4mu} 615 \mspace{4mu} 686 \times10^{10} \mspace{6mu} h \mspace{4mu} {\Delta \nu _{Cs}}^2 \mspace{4mu} K_{cd}$
lux	lx	illuminance	m^-2 cd
$1 \mspace{4mu} \text{lx} \mspace{6mu} = \dfrac{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2}{(6.626 \mspace{4mu} 070 \mspace{4mu} 15 \times 10^{-34})(9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770)^4(683)} \mspace{6mu} \dfrac{h \mspace{4mu} {\Delta \nu _{Cs}}^4 \mspace{4mu} K_{cd}}{c^2}\\ \\ \\ 1 \mspace{4mu} \text{lx} \mspace{6mu} \approx 2.781 \mspace{4mu} 027 \mspace{4mu} 075 \mspace{4mu} 972 \mspace{4mu} 537 \mspace{4mu} 548 \times10^{7} \mspace{6mu} h \mspace{4mu} c^{-2} \mspace{4mu} {\Delta \nu _{Cs}}^4 \mspace{4mu} K_{cd}$
becquerel	Bq	radionuclide activity	s^-1
$1 \mspace{4mu} \text{Bq} \mspace{6mu} = \dfrac{1}{9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770} \mspace{6mu} \Delta \nu _{Cs}\\ \\ \\ 1 \mspace{4mu} \text{Bq} \mspace{6mu} \approx 1.087 \mspace{4mu} 827 \mspace{4mu} 757 \mspace{4mu} 077 \mspace{4mu} 666 \mspace{4mu} 563 \times10^{-10} \mspace{6mu} \Delta \nu _{Cs}$
gray	Gy	absorbed dose	m² s⁻²
$1 \mspace{4mu} \text{Gy} \mspace{6mu} = \dfrac{1}{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2} \mspace{6mu} c^2\\ \\ \\ 1 \mspace{4mu} \text{Gy} \mspace{6mu} \approx 1.112 \mspace{4mu} 650 \mspace{4mu} 056 \mspace{4mu} 053 \mspace{4mu} 618 \mspace{4mu} 432 \times10^{-17} \mspace{6mu} c^2$
sievert	Sv	dose equivalent	m² s⁻²
$1 \mspace{4mu} \text{Sv} \mspace{6mu} = \dfrac{1}{(299 \mspace{4mu} 792 \mspace{4mu} 458)^2} \mspace{6mu} c^2\\ \\ \\ 1 \mspace{4mu} \text{Sv} \mspace{6mu} \approx 1.112 \mspace{4mu} 650 \mspace{4mu} 056 \mspace{4mu} 053 \mspace{4mu} 618 \mspace{4mu} 432 \times10^{-17} \mspace{6mu} c^2$
katal	kat	catalytic activity	s⁻¹ mol
$1 \mspace{4mu} \text{kat} \mspace{6mu} = \dfrac{6.022 \mspace{4mu} 140 \mspace{4mu} 76 \times 10^{23}}{9 \mspace{4mu} 192 \mspace{4mu} 631 \mspace{4mu} 770} \mspace{6mu} \dfrac{\Delta \nu _{Cs}}{N_A}\\ \\ \\ 1 \mspace{4mu} \text{kat} \mspace{6mu} \approx 6.551 \mspace{4mu} 051 \mspace{4mu} 875 \mspace{4mu} 756 \mspace{4mu} 794 \mspace{4mu} 292 \times10^{13} \mspace{6mu} \Delta \nu _{Cs} \mspace{4mu} {N_A}^{-1}$

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.