Compute the radius, diameter, circumference, and area of a circle from any single known property. Pick which one you’re starting from, enter the value, and the tool fills in the other three using the standard identities — all in one step, with full π precision.
The four properties
A circle in the plane is fully described by any one of four numbers:
- Radius (r) — the distance from the centre to any point on the circle
- Diameter (d) — the straight-line distance across the circle through the centre; d = 2r
- Circumference (C) — the length of the boundary, the distance once around; C = 2πr
- Area (A) — the total surface enclosed; A = πr²
Given any one of them, the other three are fixed. The tool picks the right formula based on your input and works out the canonical radius first, then derives the rest from there.
Example: a circle of radius 5
Type 5, leave the input type on Radius. You get:
- radius = 5
- diameter = 10
- circumference = 10π ≈ 31.416
- area = 25π ≈ 78.540
These are the four numbers that describe the circle. Multiply any of them by 2 (except the area, which needs to multiply by 4) and you get the four numbers for a circle twice as big. This scaling comes up naturally in similarity problems in geometry.
Example: from circumference back to radius
You measured the outside of a cylindrical pipe at 40 cm and want to know its radius. Type 40, set input type to Circumference. You get radius = 40 / (2π) ≈ 6.366 cm, diameter ≈ 12.732 cm, area ≈ 127.324 cm². Useful for any “I can measure the outside but need the inside” problem.
Example: a pizza’s area
A 12-inch pizza has a 12-inch diameter, so radius = 6 inches. Set input type to Diameter, type 12. Area = π × 36 ≈ 113.1 square inches. A 14-inch pizza has area ≈ 153.9 — that’s 36% more pizza for a 17% bigger diameter, which is why large pizzas are almost always better value per square inch than small ones.
Full π precision
The tool uses JavaScript’s Math.PI constant — 3.141592653589793, the maximum precision a double-precision float can represent (about 15 decimal digits). That’s far more precision than any real-world input, so the limiting factor in your answer is always the precision of the number you typed in, never the precision of π.
For symbolic work where you want to preserve π as an exact symbol (say, “the area is exactly 25π” rather than “78.539816…”), this tool isn’t the right fit — it always emits a numeric answer. Use a computer algebra system for symbolic simplification.
Round-trip accuracy
Because all four properties route through a single canonical radius, the tool’s conversions round-trip cleanly. If you compute the area from a given radius, then feed that area back in as input, the recovered radius matches the original to floating-point precision. That’s a consequence of the single-π design — there’s no accumulated drift from chained multiplications and divisions.
The test suite verifies this explicitly: for every starting radius in a range of test cases, go forward to each derived property and then back to the radius. All cases match within about 10 decimal places, which is several orders of magnitude below any real-world measurement uncertainty.
What this tool does not do
It doesn’t visualise the circle. There’s no SVG drawn to scale, just the numeric values. For visual geometry, use a dedicated drawing tool.
It doesn’t handle arc length, sector area, or chord length. These are related to a circle but require additional inputs (angle, chord separation). This tool assumes a full circle every time. For partial circles, you’d need a dedicated sector/arc calculator.
It doesn’t handle ellipses. An ellipse has two different semi-axes and different formulas (A = πab for area, an approximation for perimeter). Use an ellipse-specific tool for those.
It doesn’t do spherical geometry. The formulas here are for circles in a flat Euclidean plane. Lines of latitude on the Earth, great circles on a sphere, and other curved-surface circles have different formulas.
It doesn’t compute circle intersections. “Where do these two circles meet?” is a different kind of problem — you need the two circles’ centres and radii, and the answer is a pair of intersection points. For the distance between two centres (useful when setting up an intersection problem by hand), the distance between two points calculator does that step.