What is pi?

Circle to show Pi

For any circle, circumference \div diameter = 3.141592...

Portrait of mathematician Sir William Jones, by the artist William Hogarth, 1740
Credit: © NPG
Portrait of Welsh mathematician, Sir William Jones (1675 - 1749) by the artist William Hogarth

This number is so special that it is given its own symbol \pi (the Greek letter pi).

The value \pi is a constant, but is called an irrational number as an exact value for \pi does not exist. In non-calculator working out, approximate values are used, of which 3.14 and 3.142 are probably the most common. Other, less accurate approximations are \frac{22}{7} and 3.

All scientific calculators have a \pi button. You can use this to make your calculations more accurate.

The earliest known use of the Greek letter \pi, to represent the ratio of a circle's circumference to its diameter, was by the Welsh mathematician William Jones in his 1706 work ‘Synopsis Palmariorum Matheseos’ or, ‘A New Introduction to the Mathematics’.