The dimension of any physical quantity can be written as,               La Mb Tc Qd Ce Kf

Where a, b, c, d, e and f are integers numbers such as -4, -3, -2, -1, 0, 1, 2, 3, 4 and 

L is size, K is temperature, Q is charge, T is time, C is luminous intensity and M is volume 

mass. An exponent (power) of zero seems the dimension does not apply to the physical 

quantity. 

The simple functions of algebra for exponents apply for combining dimensions are as follows.

Rule 1: In order to sum or subtract two physical quantities the quantities must have the same 

dimension. The final physical quantity has the same dimensions. Physical quantities with the 

similar dimension in different systems of units can be added or subtracted by multiplying one 

of the quantities by a unit conversion factor to obtain compatible units.

Rule 2: The product of two physical quantities results in a new physical quantity that has the 

sum of the exponents of the dimensions of the initial two quantities.

Rule 3: The division of single physical quantity by another results in a new physical quantity 

that has the dimension of the exponents of the first quantity minus the exponents of the 

second quantity.

Rule 4: Calculating the square root of a physical quantity results in a new physical quantity

 having a dimension with exponents half of the initial dimension.

Rule 5: The derivative of a physical quantity with respect to another physical quantity 

results in a new physical quantity with the exponents of the first dimension minus the 

exponents of the other dimension. 

Example:         Speed v has dimension L/T, length l has dimension L, time t has 

dimension T, then dv/dt has dimension L/T2 of acceleration.

Rule 6: The integral part of a physical quantity over the range of another physical 

quantity results in a new physical quantity that has a dimension with the sum of the 

exponents of the two quantities. 

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