Units and Measurement


Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit. The result of a measurement of a physical quantity is expressed by a number (or numerical measure) accompanied by a unit. Although the number of physical quantities appears to be very large, we need only a limited number of units for expressing all the physical quantities, since they are interrelated with one another. The units for the fundamental or base quantities are called fundamental or base units. The units of all other physical quantities can be expressed as combinations of the base units. Such units obtained for the
derived quantities are called derived units. A complete set of these units, both the base units and derived units, is
known as the system of units.


In earlier time scientists of different countries were using different systems of units for measurement. Three such systems, the CGS, the FPS (or British) system and the MKS system were in use extensively till recently. The base units for length, mass and time in these systems were as follows :

• In CGS system they were centimeter, gram and second respectively.
• In FPS system they were foot, pound and second respectively.
• In MKS system they were meter, kilogram and second respectively.
The system of units which is at present internationally accepted for measurement is the Système Internationale d’ Unites (French for International System of Units), abbreviated as SI. The SI, with standard scheme of symbols, units and abbreviations, was developed and recommended by General Conference on Weights and Measures in 1971 for international usage in scientific, technical, industrial and commercial work. Because SI units used decimal system, conversions within the system are quite simple and convenient. We shall follow the SI units in this book. In SI, there are seven base units as given in Table1. Besides the seven base units, there are two more units that are defined for (a) plane angle dθ as the ratio of length of arc ds to the radius r and (b) solid angle dΩ as the ratio of the intercepted area dA of the spherical surface, described about the apex O as the center, to the square of its radius r, as shown in Fig. 2.1(a) and (b) respectively. The unit for plane angle is radian with the symbol rad and the unit for the solid angle is steradian with the symbol sr. Both these are dimensionless quantities.


Table 1.  SI base units

SI base unit

Base quantity Name 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

Table 2. Examples of SI derived units expressed in terms of SI base units

SI derived unit

Derived quantity Name Symbol

area square meter m2
volume cubic meter m3
speed, velocity meter per second m/s
acceleration meter per second squared m/s2
wavenumber reciprocal meter m-1
density, mass density kilogram per cubic meter kg/m3
specific volume cubic meter per kilogram m3/kg
current density ampere per square meter A/m2
magnetic field strength ampere per meter A/m
luminance candela per square meter cd/m2
amount-of-substance concentration
amount concentration , concentration mole per cubic meter mol/m3

Table 3. The 22 SI coherent derived units with special names and symbols.

SI coherent derived unit (a)

Special Name Special
Expression in
terms of other
SI units
Expression in
terms of SI
base units

plane angle radian(b) rad 1(b) m/m
solid angle steradian(b) sr(c) 1(b) m2/m2
frequency hertz(d) Hz s-1
force newton N m · kg · s-2
pressure, stress pascal Pa N/m2 m-1 · kg · s-2
energy, work,
amount of heat
joule J N · m m2 · kg · s-2
power, radiant flux watt W J/s m2 · kg · s-3
electric charge,
amount of electricity
coulomb C s · A
electric potential difference(e),
electromotive force
volt V W/A m2 · kg · s-3 · A-1
capacitance farad F C/V m-2 · kg-1 · s4 · A2
electric resistance ohm V/A m2 · kg · s-3 · A-2
electric conductance siemens S A/V m-2 · kg-1 · s3 · A2
magnetic flux weber Wb V · s m2 · kg · s-2 · A-1
magnetic flux density tesla T Wb/m2 kg · s-2 · A-1
inductance henry H Wb/A m2 · kg· s-2 · A-2
Celsius temperature degree Celsius (f) °C K
luminous flux lumen lm cd · sr(c) Cd
illuminance lux lx lm/m2 m-2· cd
activity referred to
a radionuclide(g)
becquerel(d) Bq s-1
absorbed dose,
specific energy (imparted),
gray Gy J/kg m2· s-2
dose equivalent,
ambient dose equivalent,
directional dose equivalent,
personal dose equivalent
sievert (h) Sv J/kg m2· s-2
catalytic activity katal kat s-1· mol

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