Circle formulas
Area = π × r². Circumference = 2 × π × r. Here r is the radius, the distance from the centre to the edge, and π is about 3.14159.
The diameter is twice the radius, so r = d ÷ 2. In terms of the diameter, area = π × (d ÷ 2)² and circumference = π × d.
Common mistakes
- Using the diameter where the formula needs the radius. If a problem says a circle is 12 cm across, the radius is 6 cm.
- Forgetting to square the radius. Area uses r², not 2r.
- Mixing up units. Area is in square units (cm², m²), while circumference is a length (cm, m).
Which value of π does it use?
This calculator uses the full value of π that your browser provides, then rounds the result to four decimal places. If your homework says to use 3.14, your answer will differ slightly in the later decimals.
Worked examples
Radius 5
= Area 78.5398, circumference 31.4159
Area = π × 5² = π × 25 ≈ 78.5398. Circumference = 2 × π × 5 ≈ 31.4159.
Radius 2.5
= Area 19.6350, circumference 15.7080
Area = π × 2.5² = π × 6.25 ≈ 19.6350. Circumference = 2 × π × 2.5 ≈ 15.7080.
Diameter 12 (radius 6)
= Area 113.0973, circumference 37.6991
The radius is 12 ÷ 2 = 6. Area = π × 36 ≈ 113.0973. Circumference = 2 × π × 6 ≈ 37.6991.
Frequently asked questions
How do I find the area of a circle?
Square the radius and multiply by π. A circle with radius 5 has area π × 25 ≈ 78.54.
How do I find the area from the diameter?
Halve the diameter to get the radius, then use the same formula. Diameter 12 gives radius 6 and area π × 36 ≈ 113.10.
What is the difference between area and circumference?
Area is the space inside the circle, measured in square units. Circumference is the distance around the edge, measured in ordinary units of length.
What if I only know the circumference?
Divide the circumference by 2π to get the radius, then use the area formula. This calculator starts from the radius or diameter, so do that first step by hand.