This circle calculator finds everything about a circle from any single measurement: enter the radius, diameter, circumference or area, and get the other three with the formulas shown.
The Four Circle Formulas
- Diameter: d = 2r
- Circumference: C = 2πr = πd
- Area: A = πr²
- Radius from area: r = √(A ÷ π) — a square root doing geometry’s work (see the Square Root Calculator)
This calculator is part of our Math Calculators collection.
Worked Example (Verified)
A circle with radius 7:
- Diameter = 2 × 7 = 14
- Circumference = 2π × 7 = 43.98
- Area = π × 7² = 153.94 square units
- Reverse check: √(153.94 ÷ π) = √49 = 7 ✔ — enter 153.94 as the area above and you recover r = 7.
What Is π (Pi)?
π is the ratio of any circle’s circumference to its diameter — the same 3.14159… for every circle in the universe. It is irrational (its decimals never end or repeat) and transcendental, which is why circle answers are usually left “in terms of π” in exact work (49π) and approximated in applied work (153.94). A pizza with double the radius has four times the area — πr² is why the 14-inch pizza is a much better deal than two 7-inch ones (153.9 vs 77.0 total square inches).
Common Circle Tasks
- Fencing a round garden / running a track: circumference.
- Paint, fabric, pizza value: area.
- Fitting a round table through spacing: diameter is the number that matters — and its midpoint is the center, a job for the Pythagorean Theorem Calculator when coordinates are involved.
Related Tools
- Square Root Calculator — radius from area by hand
- Pythagorean Theorem Calculator
- Math Calculators — the full collection
Frequently Asked Questions
How do I find the area of a circle?
A = πr². Square the radius, multiply by π (3.14159). A radius-7 circle: π × 49 ≈ 153.94.
How do I find circumference from diameter?
Multiply the diameter by π: C = πd.
What is the radius if I know the area?
r = √(A/π). For an area of 153.94, r = √(49) = 7.
Is the diameter always twice the radius?
Yes — by definition the diameter passes through the center, so it is two radii end to end.
Why do area answers have “square units”?
Because area measures covering, not length: cm², m², in². Circumference stays in plain units.
Is this circle calculator free?
Yes — free, instant, no sign-up.