Circle Calculator
Calculate the area and circumference of a circle from its radius.
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How to use this tool
- Enter radius in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your area and the full breakdown beneath it.
Calculate the area (πr²) and circumference (2πr) of a circle from its radius.
Formula
Area: A = π × r²
Circumference: C = 2 × π × r
Where r is the radius and π ≈ 3.14159265…
How it works
The calculator uses the exact value of π from JavaScript's Math.PI constant to compute both the area enclosed by the circle and its circumference (perimeter) from the radius alone. Results are in square units and linear units respectively, matching the unit of the input radius.
Worked example
Worked example: circle with radius 5
- Input: r = 5.
- Area: π × 5² = π × 25 ≈ 78.5398.
- Circumference: 2 × π × 5 = 10π ≈ 31.4159.
Area ≈ 78.5398; Circumference ≈ 31.4159
Common mistakes to avoid
- Entering diameter instead of radius; using diameter makes area 4× too large because r is squared.
- Using pi = 3.14 and getting a slightly off answer when high precision is needed; use at least 3.14159.
- Confusing circumference (perimeter of the circle) with area in word problems asking for fencing vs grass coverage.
Key terms
- Radius (r)
- The distance from the centre of a circle to any point on its boundary.
- Diameter
- Twice the radius; the longest chord of a circle, passing through the centre.
- Circumference
- The perimeter (total boundary length) of a circle, equal to 2πr.
- Area
- The amount of two-dimensional space enclosed inside the circle, equal to πr².
- Pi (π)
- The mathematical constant ≈ 3.14159 defined as the ratio of a circle's circumference to its diameter.
Frequently asked questions
- How do you calculate circle area and circumference?
- Area = π × r², Circumference = 2 × π × r, where r is the radius and π ≈ 3.14159.