Units & Dimensions

As already defined, Unit is a standard quantity. For each fundamental quantity a unit is defined. For example, for mass Kilogram (kg) is taken as unit.  Similarly, Dimension of any physical quantity can be expressed by fundamental dimensions. For example length can be used as dimension for length, area, volume etc.  The following are the Basic units and dimensions.

Fundamental dimensions are L for length, M for mass and T for time. There are other fundamental dimensions, but most of the physical quantities are represented by these dimensions

Basic Unit	Unit/Symbol	Dimension	Physical Quantity
Kilogram	kg	M	Mass
Meter	m	L	Length
Second	s	T	Time
Degree Kelvin	K	θ	Temperature
Ampere	A	I	Current
Candela	cd		Luminous intensity
Mole	mol		Amount of substance

Supplementary Unit	Unit/Symbol	Dimension	Physical Quantity
Radian	Rad	--	Plane angle
Steridian	Sr	--	Solid angle

Derived Unit	Unit / Symbol	Physical Quantity
Newton	N= kg m/s2	Force
Joule	J= N m = kg m2/s2	Energy, work, heat
Watt	W = J/s = N m/s = kg m2/s3	Power
Pascal	Pa = N/m2 = kg /m s2	Pressure, stress
Hertz	Hz = s-1	Frequency
Volt	V = W/A	Potential
Coulomb	C = A s	Charge
Ohm	Ω = V/A =W/A2	Resistance
Farad	F =A s/V =A2 s/W	Capacitance
Weber	Wb =V s =W s/A	Inductance
Henry	H = V s/A =W s/A2	Magnetic flux
Siemen	S =V/A =W/A2	Conductance
Tesla	T = Wb/m2 =V s/m2 =W s/A m2	Magnetic induction
Lumen	Lm =cd sr	Luminous flux
Lux	Lm/m2 =cd sr /m2	Luminance

There are many types of units. Some them are FPS (Foot, Pound and Second) units, MKS (Meter, Kilogram and Second) Units, CGS (Centimeter, Gram and Second) Units etc.  India and most of the countries follow SI units, International Standard or SI units.  Meter, Kilogram and Second are basic units.

RULES TO WRITE UNITS:

1. Leave at least one blank space between the number and units, e.g., 32 kg or 205 N/m² etc.
2. Do not use full stops, dots, dashes or plurals for units. Write Nm, not as N.m, N-m etc.  Write as 125 Nm not as 125 Nms
3. For numbers less than unity, Write 0 (zero) on the left of the decimal. E.g. 0.37 W
4. For numbers exceeding five digits, leave one blank space every three digits to show thousands or thousandth and millions or millionth as the case may be.  E.g. write 713 290 and 0.625 10

SOME BASIC CONVERSION FACTOR

To convert the following	Into SI units	Multiply by
Inches	Cm	2.54
Feet	m	0.3048
Miles	Km	1.6093
Gallons	m3	4.546 X 10-3
Pints	m3	0.5683 X 10-3
Liters	m3	1.0 X 10-3
Pounds	Kg	0.4536
Pound/sq.inch	kPa	6.895
Gallons/minute	m3/s	75.8 X 10-6
Cuses	m3/s	0.283
Poise	Ns/m2	0.1
Stoke	m2/s	0.1 X 10-3

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