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SI Units

Details

The International System of Units (SI) defines 7 base units: s
(second), m (meter), kg (kilogram), A (ampere), K
(kelvin), mol (mole) and cd (candela). In addition to base units,
there are 22 derived units, which can all be represented as products of
powers of these base units.

Derived unit

Base unit equivalent

rad

1

sr

1

Hz

s^-1

N

kg m s^-2

Pa

kg m^-1 s^-2

J

kg m^2 s^-2

Derived unit

Base unit equivalent

W

kg m^2 s^-3

C

A s

V

kg m^2 s^-3 A^-1

F

kg^-1 m^-2 s^4 A^2

Ω

kg m^2 s^-3 A^-2

S

kg^-1 m^-2 s^3 A^2

Derived unit

Base unit equivalent

Wb

kg m^2 s^-2 A^-1

T

kg s^-2 A^-1

H

kg m^2 s^-2 A^-2

°C

K

lm

cd

lx

cd m^-2

Derived unit

Base unit equivalent

Bq

s^-1

Gy

m^2 s^-2

Sv

m^2 s^-2

kat

mol s^-1

SI also defines 24 symbols known as prefixes, denoting powers of ten.

Symbol

Factor

Q

10^30

R

10^27

Y

10^24

Z

10^21

E

10^18

P

10^15

Symbol

Factor

T

10^12

G

10^9

M

10^6

k

10^3

h

10^2

da

10^1

Symbol

Factor

d

10^-1

c

10^-2

m

10^-3

μ

10^-6

n

10^-9

p

10^-12

Symbol

Factor

f

10^-15

a

10^-18

z

10^-21

y

10^-24

r

10^-27

q

10^-30

Each argument is an SI unit with a possible prefix. Print it as a product of a
power of ten and its base units. For example, GW (gigawatt) becomes
10^9 kg m^2 s^-3. Keep in mind the following exceptions:

The kilogram is a base unit with an inherent prefix. Other prefixes attach
to g (gram), and you should print their values relative to the
kilogram: g is 10^-3 kg and Mg
is 10^3 kg.

Instead of 10^1, print 10.

Instead of 10^0, print 1.

For rad and sr, only print a power of ten. (Example: for
Mrad, print 10^6, not 10^6 1.)

There is no universal order among the base units. For C, you must
output A s rather than s A. We follow the
conventions of NIST.

μ is U+03BC GREEK SMALL LETTER MU (UTF-8: ce bc).

Ω is U+03A9 GREEK CAPITAL LETTER OMEGA (UTF-8: ce a9).