Why is pi special?

The same answer for every circle

Pick any circle. It could be a coin, a bike wheel or a pizza. Measure the distance straight across it, through the middle. That is the diameter. Now measure the distance all the way round the edge. That is the circumference. Divide the circumference by the diameter. You will always get a number close to 3.14. It does not matter how big the circle is. That number is pi, and it is written with the Greek letter π.

Why is it always the same? Every circle has exactly the same shape. A big circle is just a small circle that has been scaled up, so all of its measurements get bigger by the same number of times. If the diameter doubles, so does the distance round. This means the distance round a circle is always a little more than three times the distance across it. That gives us a rule: circumference = π × diameter. If you know how wide a circle is, you can work out how far it is round. The dish of Murriyang, CSIRO's Parkes radio telescope, is 64 metres across, so the distance round its rim is about 64 × 3.14, which is about 201 metres.

Pi also helps with the space inside a circle. The area of a circle is π × radius × radius, where the radius is half of the diameter.

A number that never ends

Pi starts 3.14159265358979… and keeps going. You might expect a number as important as pi to be neat, such as 3 or 3 and 1/7. It is not. Pi is an irrational number, which means it cannot be written as one whole number divided by another. When you write pi as a decimal, the digits go on for ever and never fall into a repeating pattern. The mathematician Johann Lambert proved in 1761 that pi is irrational, so nobody will ever find its last digit, because there is no last digit.

Fractions can come close, though. The fraction 22/7 is 3.142857…, which is right to two decimal places. The fraction 355/113 is 3.1415929…, which is right to six. But neither one is exactly pi.

Computers have worked out trillions of digits. In June 2026, Guinness World Records recognised a new record of 314 trillion digits, found by the team at StorageReview. One computer server ran for nearly 110 days to do it. There is no practical need for so many digits. Such records are a way of testing how good computers are.

Chasing pi through history

People have known about pi for almost 4,000 years. A Babylonian clay tablet from about 1900 to 1680 BC uses 3.125. The Egyptian Rhind Papyrus, from about 1650 BC, has a rule for the area of a circle that works out to about 3.16. These early values were found by measuring, not by proof. They were close, but they were not exact.

The first person to work out pi by careful reasoning, and not just by measuring, was Archimedes, a Greek mathematician who lived in Syracuse, on the island of Sicily, from about 287 to 212 BC. He drew a polygon with straight sides inside a circle and another polygon outside it. The distance around the circle must be longer than the distance around the inside polygon, and shorter than the distance around the outside one. As he gave the polygons more sides, they squeezed the circle tighter. With polygons that had 96 sides, he showed that pi is between 3 10/71 and 3 1/7, which is about 3.1408 and 3.1429. Archimedes knew that he had not found pi exactly, only trapped it between two numbers.

In China, about 1,500 years ago, the mathematician and astronomer Zu Chongzhi found the fraction 355/113. In the 1700s the Welsh mathematician William Jones began using the Greek letter π for the number, and the great Swiss mathematician Leonhard Euler made the symbol popular from 1737.

Pi Day, and a note about dates

Pi Day is on 14 March, because the date 3/14 looks like the start of pi, 3.14. It began in 1988 at the Exploratorium, a science museum in San Francisco, with a physicist named Larry Shaw. At the first Pi Day, he and his wife set up a table with fruit pies at 1:59 pm, to match the digits that come after 3.14. In 2009 the United States Congress officially recognised Pi Day. The date is also Albert Einstein's birthday, and UNESCO's International Day of Mathematics is on 14 March too.

Here is a catch for Australians. Pi Day works because Americans write the month first, so 14 March becomes 3/14. In Australia we write the day first, so 14 March is 14/3, which does not look like pi at all. That is no problem. Pi is the same everywhere, and anybody can celebrate it on any day. Some people who write the day first enjoy Pi Approximation Day on 22 July instead. Written day first, that date is 22/7, the fraction that Archimedes used as an upper limit for pi.

How many digits do we really need?

For its most accurate calculations, which are for steering spacecraft across the Solar System, NASA's Jet Propulsion Laboratory uses pi to just 15 decimal places: 3.141592653589793. Imagine a circle 64 billion kilometres across. Its circumference would be about 200 billion kilometres. If you used 15 decimal places of pi, your answer would be wrong by only about 1.5 centimetres.

Closer to home, a distance all the way round Earth is roughly 40,000 kilometres, and that is about pi times the distance through Earth's middle. Using the same 15 decimal places, the mistake in that distance would be as small as a molecule. NASA says that just 37 decimal places would work out the circumference of a circle as big as the known universe, to the width of a single hydrogen atom. So the pi that we really use fits on a sticky note. The rest of the digits are just for fun.

📚 Words to know

Circumference

The distance all the way around the edge of a circle.

Diameter

The distance straight across a circle, through its centre.

Radius

The distance from the centre of a circle to its edge. It is half of the diameter.

Pi

The number you get when you divide the circumference of any circle by its diameter. It is about 3.14, and it is written with the Greek letter π.

Irrational number

A number that cannot be written as one whole number divided by another. Its decimal digits never end and never repeat in a pattern.

🧪 Try this: measure pi with string

1. Collect five round things from around the house, such as a drinking glass, a tin, a roll of tape, a dinner plate and a bucket. You will also need a piece of string, a ruler or tape measure, a calculator, and a pair of scissors (ask an adult if you need help cutting). If you have a bike, you can use its wheel too.
2. Wrap the string once around the edge of one object, and cut it at exactly one circumference. Then stretch the string straight across the middle of the object, and cut off as many string diameters as you can. How many diameters can you cut? What is left over?
3. You should be able to cut three diameters, with a small piece left over. That piece should be about one-seventh of a diameter. It shows that the circumference is about 3 and 1/7 diameters, which is very close to pi.
4. Make a table with the headings 'object', 'circumference', 'diameter' and 'circumference ÷ diameter'. Measure each object with the ruler or tape measure and use the calculator to divide. Are your answers close to 3.14? Why might they not be exactly 3.14? Think about stretchy string, and things that are not perfectly round.
5. Challenge: use pi to make a prediction. Measure the diameter of a bike wheel and multiply by 3.14 to work out how far it will roll in one turn. Then mark the ground, roll the wheel one full turn, and measure the distance. How close was your prediction?