The science and technology world still uses a number of different measure systems, like the CGS system, mainly used in scientific publications, the technical system (or MKS), the BritishAmerican system, etc. The following tables show the base and derived units of measure of the International System (IS), together with the conversion factors of the most frequently used ones.
Base units  Derived units  

Quantity  Unit  Symbol  Quantity  Unit  Symbol 
Length

metre

m

Plane angle

radian

Rad

Mass

kilogram

kg

Solid angle

steradian

Sr

Time

second

s



Electric current

ampere

A

Notes:


Temperature

Kelvin

K

centigrades [°C] = degrees [K] – 273.15


Luminous intensity

Candela

Cd

Degrees Fahrenheit [°F] = + 32


Amount of substance

Mole

Mol

Quantity  Unit  Symbol  Formula 

Frequency (of a periodical event)

hertz

Hz

1/s

Force

newton

N

(kg×m)/s^{2}

Pressure

pascal

Pa

N/m^{2}

Energy, work, quantity of heat

joule

J

N×m

Power

watt

W

J/s

Quantity of electricity, electric charge

coulomb

C

A×s

Electric potential, electromotive force, potential difference

volt

V

W/A

Capacitance

farad

F

C/V

Electric resistance

ohm

W

V/A

Conductance

siemens

S

A/V

Magnetic flux

weber

Wb

V×s

Magnetic flux density

tesla

T

Wb/m^{2}

Inductance

henry

H

Wb/A

Luminous flux

lumen

Lm

cd×sr

Illuminance

lux

Lx

lm/m^{2}

Activity (of radioactive substances)

becquerel

Bq

1/s

Absorbed dose

gray

Gy

J/kg

Note: 1 calorie = 4.184 joule
Multiplying factor (= scientific note)  Prefix  Symbol  

1 000 000 000 000 000 000 000 000

= 10^{24}

Yotta

Y

1 000 000 000 000 000 000 000

= 10^{21}

Zetta

Z

1 000 000 000 000 000 000

= 10^{18}

Exa

E

1 000 000 000 000 000

= 10^{15}

Peta

P

1 000 000 000 000

= 10^{12}

Tera

T

1 000 000 000

= 10^{9}

Giga

G

1 000 000

= 10^{6}

Mega

M

1 000

= 10^{3}

Kilo

K

100

= 10^{2}

Hecto

H

10

= 10^{1}

Deka

Da

0.1

= 10^{1}

Deci

D

0.01

= 10^{2}

Centi

C

0.001

= 10^{3}

Milli

M

0.000 001

= 10^{6}

Micro

m

0.000 000 001

= 10^{9}

Nano

N

0.000 000 000 001

= 10^{12}

Pico

P

0.000 000 000 000 001

= 10^{15}

Femto

F

0.000 000 000 000 000 001

= 10^{18}

Atto

A

0.000 000 000 000 000 000 001

= 10^{21}

Zepto

Z

0.000 000 000 000 000 000 000 001

= 10^{24}

Yocto

Y

The 11^{th} Conférence Générale des Poids et Mésures (CGPM) in 1960 adopted the first series of prefixes and symbols for the decimal multiples and submultiples of the International System units.
The 10^{15} and 10^{18} prefixes were introduced in 1964 by the 12^{th} CGPM.
The 10^{15} and 10^{18} prefixes were introduced in 1975 by the 15^{th} CGPM.
The 10^{21}, 10^{24}, 10^{21} and 10^{24} prefixes, proposed in 1990 by the CIPM, were approved in 1991 by the 19^{th} CGPM.
The IS has laid down the rules for writing names and symbols of physical quantities. We report herebelow the most important ones:
Example: ampere, not Ampère.
Example: 3 ampere, not 3 amperes.
Example: mol for mole, K for Kelvin.
Example: 1 kg , not kg 1.
Example: N·m or N m.
Example.: J/s or J×s^{1}).
We give herebelow the definitions for the units of measure of a few base quantities.
For each unit is indicated the Conférence Générale des Poids et Mésures (GCPM) that introduced it.
Second is the duration of 9 192 631 770 periods of the radiation emitted by a Caesium 133 atom during the transition between the hyperfine (F=4, M=0) and (F=3, M=0) levels of its ^{2}S(1/2) fundamental state.
(13^{th} GCPM, 1967)
The primary reference sample is a caesium clock. A caesium clock can make a maximum relative error of 1×10^{12}, equivalent to 1 ms every 12 days.
Metre is the distance covered by light in a vacuum during a time interval equal to 1/299 792 458 of a second.
(17^{th} CGPM, 1983)
The propagation speed of electromagnetic waves in a vacuum (speed of light) is one of physics fundamental constants. Following the definition of metre introduced in 1983, its value is taken to be an exact and non modifiable value:
299 792 458 m/s.
The recommended way to make a metre reference sample is to use the monochromatic radiation emitted by a heliumneon laser in the visible red region (633 nm wavelength).
Kilogram is the international prototype mass kept at the Pavillon de Breteuil (Sevres, France).
(3^{rd} CGPM, 1901)
It is the only IS base unit represented by an artificial sample. This is a platinumiridium cylinder, 38 mm in diameter and height, kept under a triple glass case, in a vacuum, together with 6 other control samples, in the conditions set up by the 1^{st} CGPM in 1889.
The sample relative precision is in the order of 10^{9}.
The introduction of natural mass sample based on atomic properties is currently under study.
Kelvin is 1/273.16 of the thermodynamic temperature of water’s triple point.
(13^{th} CGPM, 1967)
A substance triple point is the thermodynamic state where the three phases (liquid, solid and gas are at equilibrium). Water’s triple point occurs at a pressure of 610 Pa and (by definition) a temperature of 273.16 K, corresponding to 0.01 °C.
The precision in measuring the temperature of water’s triple point is c. 1×10^{6}.
Mole is the quantity of a substance containing as many elementary entities as the atoms contained in 0.012 kg carbon 12. When using the mole as unit of measure, we must specify the nature of the elementary entities, which can be atoms, molecules, ions, electrons, other particles or specific groups of such particles.
(14^{th }CGPM, 1971)
(17^{th} CGPM, 1983)
^{12}C (carbon 12) is the most abundant carbon isotope: its atomic nucleus is made up of 6 protons and 6 neutrons.
When we use the mole as unit of measure we must specify the nature of the elementary entities we are referring to: number of moles of atoms, molecules, ions, etc.
The number of elementary entities making up 1 mole is called Avogadro number; its approximate value is
N_{A}= 6.022×10^{23}.
One ampere is the current that, flowing in two parallel, indefinitely long conductors (the crosssection value is irrelevant) placed at 1 metre distance from each other in a vacuum, produces a force equal to 2×10^{7} newton per metre length.
(9^{th} CGPM, 1948)
We define the ampere by referring to the law describing the interaction force F between two parallel conductors of length s and distance d, carrying respectively current I_{1} and I_{2}: F = 2 k_{m}×I_{1}×I_{2}×s/d, where the k_{m} constant is assigned the value 10^{7} (in general, k_{m} is expressed as a function of the magnetic permeability in a vacuum m0: k_{m} = m_{0}/4p).
According to the IS definition, ampere values can be obtained with an electrodynamometer, an instrument measuring the force between two conductors run through by a current. The common practice, however, is to refer to Ohm’s law (I=V/R) and obtain the current (I expressed in ampère) as the ratio between potential difference (V expressed in volts) and resistance (R expressed in ohm). The reference sample for potential difference (volt) and resistance (ohm) are currently obtained by referring to two quantum phenomena, the Josephson and Hall quantum effect respectively.
Candela is the light intensity, in one assigned direction, of a source emitting a monochromatic radiation with frequency 540×10^{12} Hz and whose energy intensity in such direction is 1/683 W/sr.
(16^{th }GCPM, 1979)
Photometry measures the properties of electromagnetic radiations in the range perceived by the human eye (the so called visible light). The average human eye is sensitive to electromagnetic radiations in a wavelength range of 400nm  750nm (corresponding respectively to violet and red). Maximum sensitivity is registered for a wavelength of about 556 nm, corresponding to a frequency of 540×10^{12} Hz.
Light intensity is photometry main quantity; it corresponds to the energy emitted by a light source in the time unit and solid angle unit, weighed according to the human eye average sensitivity curve.
Unit  cm  m (*)  In  ft  

1 cm

=

1

0.01

0.3937

0.032808

1 m (*)

=

100

1

39.37

3.28083

1 in

=

2.540

0.0254

1

0.08333

1 ft

=

30.480

0.3048

12

1

^{(1)} In this and the following tables, International System units are indicated in (*).
Note: in = inches
ft = feet
Example
To convert length values from inches to centimetres, just multiply the inch values by the conversion factor seen in the box where the row containing the starting unit of measure (in this case inches) meets the column containing the final unit of measure (in this case centimetres):
2.5 in = 2.5×2.540 cm = 6.35 cm
Units  cm^{2}  M^{2} (*)  sq.in (= in^{2})  sq.ft (= ft^{2})  

1 cm^{2}

=

1

10^{4}

0.155

1.0764×10^{3}

1 m^{2} (*)

=

10^{4}

1

1550

10.764

1 sq.in (= 1 in^{2})

=

6.4516

6.4516×10^{4}

1

6.944×10^{3}

1 sq.ft (= 1 ft^{2})

=

929.034

0.0929

144

1

Units  g  Kg (*)  Lb  

1 g

=

1

10^{3}

2.2046×10^{3}

1 kg (*)

=

10^{3}

1

2.2046

1 lb

=

453.59

0.45359

1

Note: lb = pounds
Units  cm^{3}  litre  cubic in (= in^{3})  cubic ft (= ft^{3})  Gal  m^{3} (*)  

1 cm^{3}

=

1

0.99997×10^{3}

0.061023

3.5314×10^{5}

2.6417×10^{4}

10^{6}

1 litre

=

1000.028

1

61.025

0.0353

0.264

10^{3}

1 cubic in (= in^{3})

=

16.387

1.63867×10^{2}

1

5.7870×10^{4}

4.3290×10^{3}

1.639×10^{5}

1 cubic ft (= ft^{3})

=

28317.017

28.316

1728

1

7.4805

0.0283

1 US gal

=

3785.4345

3.7853

231.0000

0.13368

1

3.785×10^{5}

1 m^{3} (*)

=

10^{4}

999.97

6.1×10^{4}

35.315

264.18

1

Definition: 1 litre is defined as the volume occupied by 1 kg water at 4°C temperature and 760 torr pressure. It exceeds by about 28 mm^{3} the volume of 1 dm^{3}; therefore:
1 litre » 1 dm^{3} = 1000 cm^{3} (cc)
1 ml (millilitre) » 1 cm^{3}
Note: US gal = United States gallon
UK gal = United Kingdom gallon
1 UK gal = 4.5460 litres
thus N = kg×m/s^{2}.
thus dyne = g×cm/s^{2}
Note: 1 kg_{p} » 9.8067 N
1 N = 10^{5} dyne
psi = pounds per squared inches
Unit  g/cm^{3} = kg/litre  Kg/m^{3} = g/litre (*)  lb/cubic ft  

1 g/cm^{3} = 1 kg/litre  =  1  1000  62.6 
1 kg/m^{3} = 1 g/litre (*)  =  0.001  1  0.0625 
1 lb/cubic ft  =  0.016  16  1 
Unit  Poise  CP  lb/(ft×h)  N×s/m^{2} (*)= Pa×s  

1 Poise =
= 1 g/(cm×s) = 1 dyne×s/cm^{2}

=

1

100

242

0.1

1 cP

=

0.01

1

2.42

10^{3}

1 lb/(ft×h)

=

0.00413

0.413

1

4.13×10^{4}

1 N×s/m^{2} (*)= Pa×s

=

10

10^{3}

2.42×10^{3}

1

Note: 1 mPa×s = 1 Poise (cP)
Definition: kinematic viscosity (n) º ratio between viscosity (m) and density (r) of the fluid at hand; thus n = m/r .
IS Unit of measure: m^{2}/s
CGS Unit of measure: stoke (St), equal to cm^{2}/s
Let’s suppose we want to convert a compression strength value from MPa to kg_{p}/cm^{2}; what is the conversion factor?
1 MPa = 106 Pa = 106(N/m²) We must now convert N into kg_{p} and m^{2} into cm^{2} =
=
The conversion factor from MPa to kg_{p}/cm^{2} is 10.2. The conversion factor between Pa and kg_{p}/cm^{2} quoted on the “Pressure Units” table is 1.02×10^{5}; multiplying it by 10^{6} (to go from Pa to MPa) we obtain the same result.