This circle calculator works from any single property — radius, diameter, circumference or area — and instantly returns the other three. It is handy for geometry homework, engineering, crafts and construction, where you often know one measurement and need the rest. It is unit-agnostic: enter a value in any unit and lengths come back in that unit, with area in that unit squared.
How it works
The calculator first derives the radius from whatever you supply, then computes everything else from it:
| Known value | Radius from it |
|---|---|
| radius (r) | r |
| diameter (d) | d ÷ 2 |
| circumference (C) | C ÷ (2π) |
| area (A) | √(A ÷ π) |
Once it has the radius, it returns diameter = 2r, circumference = 2πr and area = πr². It uses JavaScript’s full-precision Math.PI (3.141592653589793) before rounding for display.
Worked examples
Starting from a radius of 5:
diameter = 2 × 5 = 10 circumference = 2π × 5 ≈ 31.416 area = π × 5² ≈ 78.540
Starting from a circumference of 100 (useful when you have measured around a circular object):
radius = 100 ÷ (2π) ≈ 15.915 diameter ≈ 31.831 area ≈ 795.775
Starting from an area of 200 (useful in garden design or flooring calculations):
radius = √(200 ÷ π) ≈ 7.979 diameter ≈ 15.958 circumference ≈ 50.133
Practical situations where this comes up
Home and DIY. You are laying a circular patio and know its diameter — you need the area to order the right amount of paving. Or you are buying a round rug and want to know if it will fit; knowing the circumference from a tape measure lets you recover the diameter.
Engineering and fabrication. A pipe’s nominal diameter is known; you need the cross-sectional area for flow calculations. Or you have measured the circumference of a shaft with a string and need the diameter.
Screen and lens sizes. Display panels and camera lenses are often described by diagonal or radius. Finding the area tells you how much glass or screen material is involved.
Geometry coursework. Circle problems almost always give you one of the four values and ask for the others. The derivation chain is the same every time: get radius first, then apply the two formulas.
A note on units
The calculator is unit-agnostic, so the result carries whatever units you used for the input. Enter centimetres and you get centimetres for lengths and cm² for area; enter inches and you get in and in². Never mix units in the same calculation — convert first if your measurements come from different systems.