International System of Units (SI)
The International System of Units (SI) was adopted by the 11th General conference on Weights and Measures (CGPM) in 1960. It is a coherent system of units built from seven SI base units, one for each of the seven dimensionally independent base quantities. These are as follows.
SI base units
|
Quantity |
Unit |
Symbol |
|
length |
Meter |
m |
|
mass |
Kilogram |
kg |
|
time |
Second |
s |
|
electric current |
Ampere |
A |
|
thermodynamic temperature |
Kelvin |
K |
|
amount of substance |
Mole |
mol |
|
luminous intensity |
Candela |
cd |
The definitions of the SI base units are given in appropriate alphabetic list. The SI derived units are expressed as products of powers of the base units, analogous to the corresponding relations between physical quantities, but with numerical factors equal to unity. Some derived units are given special names which are given in the table below,
Derived Units with Special Names and Symbols
|
Physical quantity |
Name of SI unit |
Symbol for SI unit |
Expression in terms of SI base units |
|
frequency |
hertz |
Hz |
s-1 |
|
force |
newton |
N |
m kg s-2 |
|
pressure, stress |
pascal |
Pa |
N m-2 = m-1 kg s-2 |
|
energy, work, heat |
joule |
J |
N m = m2 kg s-2 |
|
power, radiant flux |
watt |
W |
J s-1 = m2 kg s-3 |
|
electric charge |
coulomb |
C |
A s |
|
electric potential, electromotive force |
volt |
V |
J C-1 = m2 kg s-3 A-1 |
|
electric resistance |
ohm |
W |
V A-1 = m2 kg s-3 A-2 |
|
electric conductance |
siemens |
S |
W -1 = m-2 kg-1 s3 A2 |
|
electric capacitance |
farad |
F |
C V-1 = m-2 kg-1 s4 A2 |
|
magnetic flux density |
tesla |
T |
V s m-2 = kg s-2 A-1 |
|
magnetic flux |
weber |
Wb |
V s = m2 kg s-2 A-1 |
|
inductance |
henry |
H |
V A-1 s = m2 kg s-2 A-2 |
|
Celsius temperature |
degree Celsius |
o C |
K |
|
luminous flux |
lumen |
Lm |
cd sr |
|
illuminance |
lux |
Lx |
cd sr m-2 |
|
activity (radioactive) |
becqeurel |
Bq |
s-1 |
|
absorbed dose of radiation |
gray |
Gy |
J kg-1 = m2 s-2 |
|
dose equivalent |
sievert |
Sv |
J kg-1 |
|
plane angle |
radian |
Rad |
m m-1 |
|
solid angle |
steradian |
Sr |
m-2 m-2 |
(1) For radial (circular) frequency and for angular velocity the unit rad s-1 should be used, and this may not be simplified to Hz. The unit Hz should be used only for frequency in the sense of cycles per second.
(2) The SI unit of Celsius temperature interval is the degree Celsius, oC which is equal to kelvin, K. oC should be treated as a single symbol, with no space between the sign o and letter C. ( the symbol oK, and o should no longer be used)
(3)The units gray and sievert are admitted for reasons of safeguarding human health.
(4) The units radians and steradians are described as ‘SI supplementary units’.
Units in Use Together with the SI
These units are not part of SI, but it is recognized that they will be used in appropriate context. SI prefixes may be attached to some of these units, such as milliliter, ml; megaelectronvolt, MeV.
|
Physical quantity |
Name of unit |
Symbol |
Value in SI unit |
|
time |
minute |
min |
60 s |
|
time |
hour |
h |
3600 s |
|
time |
day |
d |
86 400 s |
|
plane angle |
degree |
o |
( p /180) rad |
|
plane angle |
minute |
, |
( p /10 800) rad |
|
plane angle |
second |
,, |
( p /648 000) rad |
|
length |
angstrom |
A |
10-10 m |
|
area |
barn |
b |
10-28 m2 |
|
volume |
liter |
l, L |
10-3 m3 |
|
mass |
tonne |
t |
103 kg |
|
pressure |
bar |
bar |
105 Pa |
|
energy |
electronvolt |
eV |
@ 1.60218 ´ 10-19 J |
|
mass |
unified atomic mass unit |
u |
@ 1.66054´ 10-27 kg |
Prefixes used with SI units
|
Factor |
Name of prefix |
Symbol |
|
1018 |
E |
exa |
|
1015 |
P |
peta |
|
1012 |
T |
tera |
|
109 |
G |
giga |
|
106 |
M |
mega |
|
103 |
K |
kilo |
|
102 |
H |
hecto |
|
10 |
Da |
deca |
|
10-1 |
D |
deci |
|
10-2 |
C |
centi |
|
10-3 |
M |
milli |
|
10-6 |
m |
micro |
|
10-9 |
N |
nano |
|
10-12 |
P |
pico |
|
10-15 |
F |
femto |
|
10-18 |
A |
atto |
Conventions to be followed while using SI units
(1) Symbols for units of physical quantities should be printed in roman (upright) type.
(2) Symbols for units should not contain a full stop and should remain unaltered in the plural e.g. 7 cm and 7 not cms.
(3) Symbols should be in lower case roman letter except for units which have been derived from proper names, when it should start from capital roman letter; e.g. m (meter), A (ampere), Wb (weber), Hz (hertz). Note when full unit is used , the lower case is used always.
(4) The prefixes which should be used to indicate decimal multiples and submultiples of a unit are given in table "Prefixes used with SI units".
(5) Compound prefixes, formed by juxtaposition of two or more prefixes are not permissible, e.g. m
m s: wrong; ns: right.(6) When the symbol prefix is placed before the symbol of a unit, the combination of two symbols should be considered a new symbol, which can be raised to positive or negative power without using brackets. e.g. cm3, mA2,
m s-1.cm3 means (0.01m)3 but not 0.01m3
m
s-1 means (10-6s)-1 but not 10-6 s-1(7) Multiplication of two units may be indicated in one of the following way:
N m (leaving space), N.m or N-m.
(8) Division of one unit by another may be indicated in one of the following way:
m/s or m s-1 or m.s-1 or m-s-1
More than one slash (/) should not be used.
e.g. W/m/K : wrong ; W/m K : right
(9) To facilitate reading, digits may be grouped in groups of three; no comma sign should be used in between the digits.
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