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Circle Calculator

Calculate a circle — enter radius, diameter, circumference or area and get the other three, step by step, with the formulas d=2r, C=2πr, A=πr².

Quick answer
How do you calculate a circle?
Every circle quantity comes from the radius r: the diameter is d = 2r, the circumference C = 2πr and the area A = πr². Know one and you get the rest. Example: r = 5 → d = 10, C ≈ 31.42, A ≈ 78.54.
The tool

Enter values — get full working

What do you know? — the radius
Comma or dot as decimal separator, negative values allowed.
Step-by-step
Press Calculate to see every step.
HowTo

Calculate a circle — 3 steps

Using r = 5
  1. 1
    Step 1 of 3

    Pick the known quantity

    Decide what you know: radius, diameter, circumference or area. Everything reduces to the radius.

  2. 2
    Step 2 of 3

    Find the radius

    From d: r = d/2. From C: r = C/(2π). From A: r = √(A/π). With r = 5 the radius is already given.

  3. 3
    Step 3 of 3

    Work out the rest

    With r = 5: d = 2·5 = 10, C = 2π·5 ≈ 31.42, A = π·5² ≈ 78.54.

Examples

Calculate a circle — worked examples

Typical inputs with the working
r = 5
d = 2·5
C = 2π·5
A = π·5²
d=10, C≈31.42, A≈78.54
d = 10
r = 10/2 = 5
r=5, C≈31.42, A≈78.54
C = 31.42
r = 31.42/(2π) ≈ 5
r≈5, d≈10, A≈78.54
A = 78.54
r = √(78.54/π) ≈ 5
r≈5, d≈10, C≈31.42
r = 1
C = 2π·1
A = π·1²
C≈6.28, A≈3.14
Theory

Radius, diameter, circumference and area

A circle is fully determined by a single quantity: the radius r, the distance from the centre to the edge. The diameter is the segment straight across through the centre, so twice as long: d = 2r. The circumference is the length of the circle’s edge and grows in proportion to the radius: C = 2πr — the constant π ≈ 3.14159 is the fixed ratio of circumference to diameter. The area, finally, grows with the square of the radius: A = πr². Because all four quantities are linked through r, one known value is enough to find the other three — the calculator rearranges the right formula for r (e.g. r = √(A/π) if you start from the area) and substitutes. These relations are standard geometry from grade 7 onward and show up everywhere, from wheels and pipes to pizzas and planetary orbits.

Pitfalls

Common mistakes

Mixing up radius and diameter

C = 2πr and A = πr² use the radius, not the diameter. If d is given, halve it first.

Using π as just 3

π ≈ 3.14159. Using 3 throws the result off by about 5%.

Forgetting to square in the area

A = πr² — the radius is squared. πr (no square) is wrong.

Swapping circumference and area

Circumference is a length (2πr), area is an amount of surface (πr²). Watch units: m vs m².
FAQ

Frequently asked questions

Glossary

Glossary — key terms explained simply

Radius (r)
Distance from the centre to the edge.
Diameter (d)
Segment through the centre, d = 2r.
Circumference (C)
Length of the circle’s edge, C = 2πr.
Area (A)
Amount of surface in the disc, A = πr².
Pi (π)
Ratio of circumference to diameter, ≈ 3.14159.
Centre
The point equidistant from every point on the edge.