Circumference of a circle and area of a disc

The number pi

The number pi (pi ≈ 3.14) is a very special mathematical constant: it is the ratio of a circle’s circumference to its diameter, and this ratio is the same for all circles, regardless of their size.

For calculations at secondary school level, the approximation pi ~ 3.14 is often used.

Circumference of a circle

The circumference P (the length of the outline) of a circle with radius r is calculated as follows:

P = 2 × pi × r

or, using the diameter d: P = pi × d

Example

For a circle with radius r = 3 cm: P = 2 × π × 3 = 6 × π ~ 6 × 3.14 = 18.84 cm

Area of a disc

The area A (the surface area) of a disc of radius r is calculated as follows:

A = π × r²

Please note: this is r squared, not 2 × r! This is the most common pitfall.

Example

For a disc with a radius of r = 3 cm: A = pi x 3^2 = pi x 9 ~ 3.14 x 9 = 28.26 cm^2

Summary table

Quantity	Formula	Unit
Circumference of a circle	P = 2 × π × r	cm, m... (length)
Area of a disc	A = π × r²	cm², m²... (area)

Pitfalls to avoid

• Do not confuse the circumference (length, one dimension) with the area (surface area, two dimensions): the units are different (cm versus cm²).
• Always check whether the question specifies the radius or the diameter before calculating.
• Don’t forget the square in the area formula.

These two formulas are essential and feature in many real-world problems: wheels, plates, roundabouts, etc.