Mathématiques

Pi: The Ratio Every Circle in the World Shares

Pi is circumference divided by diameter, the same for every circle. Where 3.14159 and 22/7 come from, and which one an exam actually wants from you.

Pi (π)

Pi is the ratio of a circle's circumference to its diameter — approximately 3.14159, and identical for every circle regardless of size.

Aussi appelé: π
Où les élèves le rencontrent: Grade 6 mathematics, when circumference and area of a circle are introduced, and in every circle question from that point onwards.

La réponse en bref
Pi is the number obtained when any circle's circumference is divided by its diameter. It is the same for every circle, large or small, and equals approximately 3.14159. Pi is irrational, so its decimal expansion never ends and never repeats, and 22/7 is only an approximation to it.

Un exemple

C = πd = π × 7 ≈ 21.99 cm, or exactly 22 cm taking π as 22/7

A circle of diameter 7 cm has a circumference of about 21.99 cm using the calculator's π. Take π as 22/7 instead and the sevens cancel, leaving precisely 22 cm. This is why questions that instruct you to use 22/7 almost always choose a radius or diameter that is a multiple of 7 — the fraction is there to make the arithmetic clean, not to make the answer more accurate.

A ratio, not a length

Wrap a string around any circular object, then measure straight across it. Divide the first measurement by the second and the answer is a little over three, whether the object is a coin or a stadium. That constant answer is pi.

This is the whole reason one number turns up in every circle formula. Circumference is πd because the circumference is always pi times the width; area is πr² for a related reason that takes a little more work to see. Pi has no units, because it is one length divided by another.

3.14, 22/7, and the button on the calculator

Pi is irrational: its decimal expansion runs forever without falling into a repeating pattern, a fact proved by Johann Heinrich Lambert in 1761. Every written value of pi is therefore a rounding, including the 3.14159265 stored in a calculator.

The fraction 22/7 comes out as 3.142857..., which agrees with pi to two decimal places and is about 0.04% too large. It was useful when calculations were done by hand and remains common in South Asian textbooks. It is not more accurate than the calculator value, and treating it as the true value of pi is a genuine misunderstanding rather than a harmless habit.

Which one an exam actually wants

Use the π button unless told otherwise. It carries more digits than you will ever need, and rounding once at the end keeps the answer inside the accepted range in a mark scheme.

Use 22/7 only when the question says to. Some papers, particularly older or hand-computed ones, specify it, and in those questions the numbers are chosen so the sevens cancel.

On a non-calculator paper, leave the answer in terms of π. A circle of radius 5 cm has an area of 25π cm², and that is a complete, exact answer — converting it to 78.5 cm² without a calculator introduces error and wins nothing.

Pi to eight decimal places; the expansion continues without ending or repeating: 3.14159265Pi to eight decimal places; the expansion continues without ending or repeating
A common approximation, correct to two decimal places and about 0.04% above pi: 22/7A common approximation, correct to two decimal places and about 0.04% above pi

Questions fréquentes

Is pi equal to 22/7?

No. 22/7 is 3.142857..., which is close to pi but about 0.04% too big and disagrees from the third decimal place onwards. Pi is irrational and cannot equal any fraction at all. Use 22/7 only when a question explicitly instructs you to, and never treat it as the exact value.

Why is pi the same for every circle?

Because all circles are similar shapes — enlarge one and you get another. When every length in a shape is multiplied by the same scale factor, the ratio between any two of those lengths is unchanged. Circumference divided by diameter is such a ratio, so it stays fixed however big the circle grows.

How many decimal places of pi do I need?

For school work, none of them by hand — use the calculator's π and round the final answer as the question asks, usually to three significant figures. Knowing 3.14 as a rough check is useful for spotting a wrong answer, but memorising further digits has no effect on marks.

What does it mean that pi is irrational?

It means pi cannot be written exactly as one whole number divided by another, so its decimal form never terminates and never settles into a repeating block. This was proved in 1761. It is why an answer written as 25π is exact while 78.54 is only close.

Dernière mise à jour 21 août 2026