# What is a formula?

### What is a formula?

A formula is **a group of mathematical symbols and numbers that show how to work something out**.

Examples include formulae for calculating the perimeter and area of 2D shapes and how to work out the volume for 3D shapes.

Formulae are also used to convert measurements, for example from kilometres to miles or temperatures from ºC to ºF.

### How does a formula help children in maths?

A formula tells you which measurements or facts you need to solve a calculattion, and how to calculate the measurement or information you need. There are different formulae for different things.

For example, the formula to calculate the volume of a cuboid is W x H x D = V³ (the width multiplied by the height multiplied by the depth equals the volume, which we record in cubic units), where each symbol has a mathematical meaning.

- W means width
- H means height
- D means depth
- V means volume
- ³ means cubed
- = means equals

You can use the same formula to calculate the volume of any cuboid.

### How and when primary children are taught mathematical formulae

Children will be familiar with many of the symbols used in formulae (such as + x and =) from Year 1, but **it is not until Year 6 that children are formally introduced to the concept of a formula**.

Children will be expected to be able to **use a range of different formulae to calculate the perimeter and area of 2D shapes and volume of 3D shapes**.

For example:

Shape |
How to calculate the perimeter |
How to calculate the area |
How to calculate the volume |

Square |
4 x side | side² | Cube: w³ |

Rectangle |
2 x (L + W) | L x W | Cuboid: W x H x D |

Triangle |
Side + side + side (a x b x c) | (b x h) ÷ 2 | |

Circle |
2 x π x r | π x r² | |

Regular polygon |
n x l |

In the formulae the symbols represent the following:

L = Length W = Width H = Height D = Depth B = Base π = pi (3.14) r = radius n = number of sides

When learning to apply forumlae in calculations children will be given a diagram of a shape with the measurements needed marked on. Their task is to apply the measurements to the correct formula to calculate the required answer.

For example:

Using the formula W x H x D can you find out the volume of this cuboid?

The answer is 6 x 3 x 2 = 36cm³