🔢 Math

The circle and the number π

A circle showing its center, radius and diameter, and the number π, which is about 3.14

📖 In short

Take any circle: a plate, a wheel or a lid. Measure the distance around it, then measure its width from edge to edge. You'll find the distance around is always a bit more than three times the width! This amazing number is called π, read “pi”, and is about 3.14.

🤩 Did you know?

  • π is about 3.14, a little more than three.
  • Math fans celebrate π Day on March 14, because its first digits are 3 then 14.
  • Al-Kashi worked out π to 16 decimal places in 1424.
  • Computers have worked out more than 100000 billion digits of π.

🔎 Find out more

🌟 Center and radius

Every point on a circle is the same distance from a point in the middle called the “center”. That distance is called the “radius”. The “diameter” is a line through the center from edge to edge, and it's twice as long as the radius.

🔍 Compass

We draw a circle with a compass: fix its sharp point at the center, open it to the length of the radius, then turn the pencil all the way round. You can also draw one with string, a pencil and a nail.

💡 The number π

The circumference of any circle equals its diameter × π. If a wheel's diameter is 50 cm, its circumference is about 50 × 3.14 = 157 cm. That's why when the wheel turns once, the bike moves forward about 157 cm.

🎯 A never-ending number

The digits of π after the point never end and never repeat: 3.14159265… The Muslim scholar Ghiyath al-Din al-Kashi worked out 16 of them in 1424, and today computers work out thousands of billions.

📊 See it in a picture

The parts of a circle: the center, radius and diameter, and the circumference is a little more than three diameters
The parts of a circle; its circumference is a little longer than three diameters.

🧮 Worked examples

  1. Diameter = 2 × radiusThe radius is 5 cm, so the diameter is 10 cm.
  2. Circumference ≈ 3.14 × diameterA diameter of 10 cm, so the circumference is about 31.4 cm.

📚 Key words

center
The point in the middle of a circle
diameter
A line through the center joining two sides of the circle
Perimeter
The length of the line around a shape

🧪 Try it at home

Take three round things (a cup, a plate, a lid). Wrap a string around each one and measure it, then measure the diameter. Divide the string's length by the diameter on a calculator. Do you always get a number close to 3.14?

🧩 Test yourself

1 About how much is π?

2 If the radius is 4 cm, what is the diameter?

3 What tool do we draw a circle with?

📚 Read next

🎮 Try it yourself