A formula is a rule or equation used to calculate the value of a quantity.
The plural of formula is formulae or formulas.
There are all types of formulae for calculating various quantities in many areas of life.
Examples of Formulae
Quantity being found

Formula

Variables

Perimeter of a rectangle 
P = 2l + 2w

P = perimeter of rectangle 
Cost of plumber 
C = 55x + m +1.5k

C = total cost of plumber ($) 
Volume of a packing boxes 
V = l w h

V = volume of box 
Area of a circular design 
A = π r^{2}

A = area of circle r = radius of circle π = pi ( 3.14 to 3 sig.fig.) 
Substitution into a Formula
To find the value of a quantity in a formula we put given values into a formula in place of the variables (written as letters).
e.g. Find the area of a 5 m discus circle at an athletics track
A = π r^{2} is the formula for finding the area of a circle
If r = 5 m and π = 3.14
A = 3.14 × 5^{2 }cm^{2}
A = 78.5 cm^{2}
Constructing a Formula
Sometimes formulae have to be constructed from information given.
e.g. Construct a formula for the perimeter and the area of the rectangle below :
Perimeter formula
P = 2x + 4y + 2x + 4y
P = 4x + 8y
P = 4(x + 2y)
Area formula
A = 2x . 4y
A = 8xy
The perimeter and area can now be found if values of x and y are given.
Sequences and Formulae
In mathematics, numbers are often arranged in a sequence. These sequences can be shown be a formula or function.
Often a sequence follows a rule or pattern.
Some sequences are obvious: 1, 3, 5, 7, 9...
This is the sequence of ODD numbers.
The formula for this sequence is 2n − 1 where n stands for a counting number.
To find the next number in this sequence, calculate 2 × 6 − 1 = 11
The sequence 1, 8, 27, 64, ... is the sequence of cube numbers.
Comparing this sequence to the set of counting numbers {1, 2, 3, 4...}
1 2 3 4 ... 1 8 27 64 ...
The next number in this sequence is 5^{3} = 125