How this circle calculator works
A circle is defined entirely by a single measurement: its radius (r), the distance from the centre to the edge. Once you know the radius, every other property follows. The diameter is twice the radius (d = 2r), the circumference — the distance all the way around — is C = 2πr = πd, and the area enclosed is A = πr².
This tool lets you start from any of the four values. If you enter the circumference, it works backwards to the radius using r = C / (2π); if you enter the area, it uses r = √(A / π); if you enter the diameter, it halves it. From that recovered radius it then computes the remaining three values, so you never have to rearrange the formulas yourself.
Reference note: results use π ≈ 3.141592653589793 and are rounded for display. The same unit applies throughout — if the radius is in centimetres, the circumference is in centimetres and the area is in square centimetres. Values must be positive.
Frequently asked questions
- How do I find the area of a circle?
- Use A = πr², where r is the radius. Square the radius and multiply by pi (about 3.14159). A circle with radius 5 has an area of π × 25 ≈ 78.54 square units.
- How do I find the circumference of a circle?
- Use C = 2πr, or equivalently C = πd. A circle with radius 5 has a circumference of 2 × π × 5 ≈ 31.42 units.
- What is the difference between radius and diameter?
- The radius is the distance from the centre to the edge; the diameter is the distance straight across through the centre. The diameter is twice the radius: d = 2r and r = d / 2.
- What is pi (π)?
- Pi is the ratio of a circle's circumference to its diameter — the same for every circle, about 3.14159. It is irrational, so its decimals never end or repeat.
- How do I find the radius from the area?
- Rearrange A = πr² to r = √(A / π): divide the area by pi, then take the square root. An area of 78.54 gives r ≈ 5.
- How do I find the diameter from the circumference?
- Since C = πd, rearrange to d = C / π: divide the circumference by pi. A circumference of 31.42 gives d ≈ 10.