A formula is a mathematical rule or relationship that uses letters to represent amounts which can be changed – these are called variables. For example, the formula to work out the area of a triangle.

Scalene triangle with b (base) and height (h) labelled

\(\text{Triangle area} = \frac{bh}{2}\) (where \(b\) represents the base of the triangle and \(h\) represents the height of the triangle). \(b\) and \(h\) are variables because we can use different values, depending on the size of the triangle.

The plural of formula is formulae or formulas. Formulae contain equals signs, as do equations, so it can sometimes be difficult to tell the difference between an equation and a formula.

  • A formula is a calculation for a specific purpose, for example converting Fahrenheit to Celsius or vice versa. A formula is also always true, no matter what values are put in.
  • An equation will only work for certain values, and is not always true. For example, the equation \(2x + 5 = 13\) will only be true if \(x\) is equal to 4. If any other value is put in, then the equation will no longer be correct.