Circle area, circumference, arc and sector calculator
Enter any one measurement of a circle — radius, diameter, circumference or area — and this calculator returns the other three, in terms of π as well as decimals. Add a sector angle and it also gives the arc length and sector area, which is where most GCSE circle marks sit.
Enter one measurement of the circle
Area = 25π ≈ 78.5398
Circumference: 10π ≈ 31.4159
Radius: 5 · Diameter: 10
Working
- C = 2πr = 2 × π × 5 = 31.4159
- A = πr² = π × 5² = 78.5398
The method behind it
- Circumference C = 2πr = πd; area A = πr².
- Working backwards: r = C ÷ 2π and r = √(A ÷ π).
- Sector: arc = (θ/360) × 2πr, sector area = (θ/360) × πr².
How to use this tool
1. Choose what you know
Pick radius, diameter, circumference or area from the selector and type your value in.
2. Read all four measurements
The calculator converts your value to the radius first, then applies C = 2πr and A = πr², so the working matches the mark scheme.
3. Add a sector angle if needed
Enter the angle at the centre in degrees to get the arc length and sector area as a fraction of the full circle.
Frequently asked questions
What are the formulas for the area and circumference of a circle?
Area = πr² and circumference = 2πr = πd, where r is the radius and d is the diameter. Mixing up the two is the single most common circle error in exams — area uses the square.
How do you find the radius from the area?
Divide the area by π, then square root: r = √(A ÷ π). From the circumference, divide by 2π instead: r = C ÷ 2π.
How do you calculate arc length and sector area?
Both are fractions of the whole circle: arc length = (θ ÷ 360) × 2πr and sector area = (θ ÷ 360) × πr², where θ is the angle at the centre in degrees.
When should I leave the answer in terms of π?
Whenever the question says 'give your answer in terms of π' — an answer such as 25π cm² is exact and earns the mark, while 78.5 cm² may lose accuracy marks on non-calculator papers.
Practise this properly, not just once
A solver gives you the answer; exam marks come from the working. MathsGradeUp pairs exam-board questions with step-by-step feedback and revision notes on the exact topics you keep dropping marks on.