Free Circle Calculator
Enter any one circle measurement — radius, diameter, circumference, or area — and this calculator instantly solves for the other three using exact geometry formulas.
Choose one known value, enter it, and get the radius, diameter, circumference, and area.
Quick answer
A circle is fully defined by a single measurement, so from one value you can derive the rest. The core formulas are d = 2r, C = 2πr, and A = πr². For example, a radius of 5 gives a diameter of 10, a circumference of about 31.4159, and an area of about 78.5398.
Formula & method
d = 2r
- d — diameter
- r — radius
Diameter is twice the radius (the radius is the distance from the center to the edge).
C = 2πr = πd
- C — circumference
- π — the constant pi ≈ 3.14159
Circumference is the distance around the circle; it scales linearly with the radius.
A = πr²
- A — area
- r — radius
Area grows with the square of the radius, so doubling r quadruples the area.
r = C / (2π) = √(A / π)
Inverse forms used when you start from circumference or area instead of radius.
Examples
- Input
- r = 5
- Result
- d = 10, C ≈ 31.4159, A ≈ 78.5398
- Why
- d = 2 × 5 = 10. C = 2 × π × 5 = 10π ≈ 31.41593. A = π × 5² = 25π ≈ 78.53982.
- Input
- d = 14
- Result
- r = 7, C ≈ 43.9823, A ≈ 153.938
- Why
- r = 14 ÷ 2 = 7. C = π × 14 = 14π ≈ 43.98230. A = π × 7² = 49π ≈ 153.93804.
- Input
- C = 31.4159
- Result
- r ≈ 5.0000, d ≈ 10.0000, A ≈ 78.5396
- Why
- r = C ÷ (2π) = 31.4159 ÷ 6.28319 ≈ 4.99999. d = 2r ≈ 10.0000. A = πr² ≈ 78.53965 (rounding of C feeds tiny rounding into A).
- Input
- A = 100
- Result
- r ≈ 5.6419, d ≈ 11.2838, C ≈ 35.4491
- Why
- r = √(A ÷ π) = √(100 ÷ 3.14159) = √31.83099 ≈ 5.64190. d = 2r ≈ 11.28379. C = 2πr ≈ 35.44908.
When to use this tool
- Quickly converting between a circle's radius, diameter, circumference, and area for geometry homework or design work.
- Sizing round objects — pipes, tanks, wheels, plates, or garden beds — when you know only one dimension.
- Checking a measured circumference against an expected diameter (e.g., wrapping a tape around a tree or pipe).
- Estimating material needed for circular areas like flooring, pizza, or a circular pool cover.
Common mistakes
- Confusing radius and diameter: the diameter is twice the radius, so plugging a diameter into a radius formula (or vice versa) doubles or halves your answer.
- Forgetting that area scales with r², not r — doubling the radius multiplies the area by four, not two.
- Using 3.14 instead of a fuller value of π for precise work; the small truncation compounds in area calculations.
- Mixing units: if the radius is in centimeters, circumference is in centimeters and area is in square centimeters — keep units consistent before comparing.
Frequently asked questions
What is the formula for the area of a circle?
The area is A = πr², where r is the radius. If you only have the diameter d, first find the radius with r = d/2, then square it and multiply by π. For example, a radius of 5 gives A = π × 25 ≈ 78.54 square units.
How do I find the radius from the circumference?
Rearrange C = 2πr to get r = C / (2π). Divide the circumference by 2π (about 6.28319). A circumference of 31.4159 gives a radius of about 5.
What is the difference between radius and diameter?
The radius is the distance from the center of the circle to its edge, while the diameter is the full distance across the circle through the center. The diameter is always exactly twice the radius: d = 2r.
How do I calculate the radius from the area?
Use r = √(A / π). Divide the area by π, then take the square root. For an area of 100, r = √(100 / π) = √31.831 ≈ 5.642.
Why does the calculator reject zero or negative values?
A circle must have a positive size. A radius, diameter, circumference, or area of zero or less has no real geometric meaning, so the calculator requires a value greater than zero.
What value of π does this calculator use?
It uses JavaScript's built-in Math.PI, which is accurate to roughly 15–16 significant digits (3.141592653589793). Results are then displayed to six significant figures for readability.
Sources & references
External references open in a new tab. We are independent and not affiliated with these organizations.
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- ✓ Formula and method shown above
Provided “as is” for general information only — results may be inaccurate, so verify before you rely on them. No warranty; use at your own risk.
Built and reviewed by HIFreeTools against the formula shown above and any authoritative references cited on this page. See our methodology and editorial standards.
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