algebra.jpgA formula is a general rule or relation, written as an algebraic equation.

There are all types of formulae for calculating various quantities in many subject areas.


Substitution involves putting given values into a formula in place of the variables (written as letters).

Example 1
Example 2
Y11_Formulae_01.gif is the formula for the area of a trapezium.

If a = 5 cm, b = 7 cm and h = 10 cm


A = 60 cm2

V = IR is a formula used in physics, where V = voltage, I = current and R = resistance.

If I = 10 amps and R = 5 ohms

V = 10 × 5

V = 50 volts



Changing the Subject

The subject of a formula is the variable or letter that stands alone.



A is the subject

x + y + z = V

V is the subject


To make a different variable the subject of a formula, the usual algebraic techniques can be used.

Example 1
Example 2

To make b the subject ofY11_Formulae_03.gif


v2 = u2 − 2fs is a formula used in physics.

To make u the subject




Rearranging Rational Functions

Often rational expressions such as Y11_Formulae_06.gif have to be rearranged to make x the subject.


Rearranging formulae with Squares and Square roots

To rearrange formulae involving squares the square root often needs taking.

To rearrange formulae involving square roots both sides of the formulae need squaring.

Example involving square roots
Example involving squares