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
is10^-3 kg
andMg
is10^3 kg
. - Instead of
10^1
, print10
. - Instead of
10^0
, print1
. - For rad and sr, only print a power of ten. (Example: for
Mrad
, print10^6
, not10^6 1
.) - There is no universal order among the base units. For C, you must
output
A s
rather thans 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
).°
is U+00B0 DEGREE SIGN (UTF-8:c2 b0
).
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