Roll the wheel
The C/D ratio, π
Circle against square
For a square, perimeter : side is always 4 : 1. A circle has a perimeter too. It is called the circumference (C), and the distance across the circle through its centre is the diameter (D).
Is the ratio of C to D the same for big circles and small circles?
What this lesson covers
The idea
The ratio of the circumference (C) of a circle to its diameter (D) does not change with the size of the circle; this constant C/D ratio is denoted by π.
Circle against square
For a square, perimeter : side is always 4 : 1. A circle has a perimeter too. It is called the circumference (C), and the distance across the circle through its centre is the diameter (D).
Is the ratio of C to D the same for big circles and small circles?
- Bigger circles have a bigger ratio
- It is the same for every circle
- Smaller circles have a bigger ratio
One turn of the wheel
Roll the wheel once. The red dot on the rim marks out the circumference C on the ground. Then see how many diameters D fit into it. Do this for each size.
The same for every circle
The ratio of the circumference (C) of a circle to its diameter (D) does not change with the size of the circle. This constant C/D ratio is denoted by π.
Every wheel rolled out 3 diameters and a bit more. The bit more is about 0.14 of a diameter, so C/D is about 3.14. We read π as "pi", as in "pie". In 1706 William Jones chose π because it is the first letter of *perimetros*, the Greek word for perimeter.
Notes
The ratio of the circumference (C) to the diameter (D) is the same for every circle. This constant C/D ratio is π, about 3.14.
Check yourself
Which statement about the C/D ratio is true?
A circle has diameter 5 cm. Using C/D = 3.14, what is its circumference?
Answer: 15.7 cm
C = 3.14 × 5 = 15.7 cm.
A wheel has circumference 31.4 cm. Using C/D = 3.14, what is its diameter?
Answer: 10 cm
D = 31.4 ÷ 3.14 = 10 cm.
The wheel rolled out 3 diameters and a bit more. What does the bit more tell us?
- Bigger circles have a bigger C/D ratio. The ratio does not change with the size of the circle.
- It is the same for every circle, big or small — correct. Yes. A bigger circle has a bigger C, but also a bigger D. The ratio stays the same.
- The C/D ratio of a circle is exactly 3. The wheel rolled out 3 diameters and a bit more: about 3.14, not exactly 3.
- C/D is exactly 3. If it were exactly 3, there would be no bit more left over.
- C/D is less than 3. The circumference is more than 3 diameters, so C/D is more than 3.
- C/D is a little more than 3 — correct. Yes. About 3.14.