Circle calculator
Area, circumference, diameter and radius from any one of them.
Fill in the fields and the result will appear here automatically.
Solves a circle from whatever you happen to know: radius, diameter, circumference or area. That matters more than it sounds — a pipe or barrel is usually specified by diameter, a flower bed by the length of its edging, and a blank by its area, and each case runs a different way by hand. Math.PI ≈ 3.141592653589793 is used: a machine approximation of π, rather than the exact infinite number or 3.14. At r = 3 m, using 3.14 would reduce circumference by about 9.56 mm; final results are rounded.
How it works
Formula and logic
S = πr², C = 2πr and d = 2r; the radius comes from the circumference as r = C ÷ 2π and from the area as r = √(S ÷ π).
Example
A circle of radius 3 m has an area of 28.274 m² and a circumference of 18.85 m.
Fields and units
- Length unit — list option
- What is known — list option
- Radius — cm
- Diameter — cm
- Circumference — cm
- Area — cm²
How to use
- — Choose one length unit.
- — In area mode enter its square: cm² for centimetres.
- — Choose the known quantity and fill only the visible field.
- — Radius, diameter and circumference must be positive; changing the unit does not convert the entered number.
Method and limitations
- Calculation method
- Formula and logic
- Data or methodology source
- OpenStax: radius, diameter, circumference and area
- Limitation
- Planar circle with positive area. π and results are numerical approximations; a pipe’s outside diameter does not give its internal cross-sectional area. An error appears if all required results cannot be represented numerically.
FAQ
Which value of π is used?
Math.PI ≈ 3.141592653589793 is used: a machine approximation of π, rather than the exact infinite number or 3.14. At r = 3 m, using 3.14 would reduce circumference by about 9.56 mm; final results are rounded.
How do radius and diameter differ on input?
The diameter is twice the radius, so swapping them changes the area fourfold. That is exactly why the input mode is chosen explicitly.
Can I get the radius from the area?
Yes — choose the area mode; the radius is the square root of the area divided by π.
What does circumference mean here?
The length of the closed line around the edge of the circle — what you would measure with a tape around a pipe or a barrel.
How do I convert a circle’s area between cm² and m²?
1 m = 100 cm, so 1 m² = 10,000 cm². For example, 100 cm² = 0.01 m². Selecting metres changes the interpretation of the number; it does not convert it.