How Many? A Dictionary of Units of Measurement
© Russ Rowlett and the University of North Carolina at Chapel Hill

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About the Dictionary
Using the Dictionary

Derived Units of the International System (SI)

In addition to the seven base units, the General Conference on Weights and Measures has approved 22 names for SI units defined as combinations of the base units. Within the SI, these units are the named derived units.

Following are links to the definitions of these 22 units. The third column shows how each unit is derived from the preceding units, and the fourth column gives the formal equivalence of the unit in terms of the base units.

Derived Unit Measures Derivation Formal Definition
hertz (Hz) frequency /s s-1
newton (N) force kg·(m/s2) kg·m·s-2
pascal (Pa) pressure N/m2 kg·m-1·s-2
joule (J) energy or work N·m kg·m2·s-2
watt (W) power J/s kg·m2·s-3
coulomb (C) electric charge A·s A·s
volt (V) electric potential W/A kg·m2·s-3·A-1
farad (F) electric capacitance C/V kg-1·m-2·s4·A2
ohm (omega) electric resistance V/A kg·m2·s-3·A-2
siemens (S) electric conductance A/V kg-1·m-2·s3·A2
weber (Wb) magnetic flux V·s kg·m2·s-2·A-1
tesla (T) magnetic flux density Wb/m2 kg·s-2·A-1
henry (H) inductance Wb/A kg·m2·s-2·A-2
degree Celsius (°C) temperature K - 273.15 K
radian (rad) plane angle m·m-1
steradian (sr) solid angle m2·m-2
lumen (lm) luminous flux cd·sr cd·sr
lux (lx) illuminance lm/m2 cd·sr·m-2
becquerel (Bq) activity /s s-1
gray (Gy) absorbed dose J/kg m2·s-2
sievert (Sv) dose equivalent Gy·(multiplier) m2·s-2
katal (kat) catalytic activity mol/s mol·s-1

The term derived unit covers any algebraic combination of the base units, but it is only the 22 combinations listed above that have approved special names. For example, the SI derived unit of momentum (mass times velocity) has no special name; momentum is stated in kilogram meters per second (kg·m/s) or in newton seconds (N·s). A few SI derived units do have special names that have been defined but not approved. Here are some examples:

Derived Unit Measures Derivation
stere (st) volume m3
diopter (dpt) refractive power m-1
thermal ohm thermal resistance K/W
poiseuille (Pl) dynamic viscosity Pa·s
rayl sound impedance Pa·s/m
acoustic ohm sound resistance Pa·s/m3
daraf electric elastance F-1
talbot luminous energy lm·s
nit (nt) luminance cd/m2
molal chemical concentration mol/kg

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All material in this folder is copyright © 2004 by Russ Rowlett and the University of North Carolina at Chapel Hill. Permission is granted for personal use and for use by individual teachers in conducting their own classes. All other rights reserved. You are welcome to make links to this page, but please do not copy the contents of any page in this folder to another site. The material at this site will be updated from time to time.

Latest update July 14, 2004