A circle calculator finds the diameter, circumference and area of a circle from its radius. Formula: Area = pi × r^2. Circumference = 2 × pi × r. Diameter = 2 × r. Headline is area to 4 decimal places. A circle with a radius of 5 has a diameter of 10, a circumference of about 31.42 and an area of about 78.54.
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How to use the circle calculator
- Enter the radius (half the diameter).
- Read the diameter, circumference and area.
Circle calculator formulas
- Diameter d = 2r
- Circumference C = 2πr = πd
- Area A = πr²
- From the circumference: r = C ÷ (2π); from the area: r = √(A ÷ π)
- π ≈ 3.14159265
The circle calculator takes the radius, the distance from the center to the edge, and returns the diameter, circumference and area.
Circle calculator worked example
| Radius | Diameter | Circumference | Area |
|---|---|---|---|
| 1 | 2 | 6.2832 | 3.1416 |
| 2 | 4 | 12.5664 | 12.5664 |
| 5 | 10 | 31.4159 | 78.5398 |
| 10 | 20 | 62.8319 | 314.1593 |
| 12.5 | 25 | 78.5398 | 490.8739 |
| 50 | 100 | 314.1593 | 7,853.9816 |
With a radius of 5, the diameter is 10, the circumference is 2 × π × 5 ≈ 31.4159 and the area is π × 25 ≈ 78.5398. The units follow your input: a radius in centimeters gives a circumference in centimeters and an area in square centimeters. Doubling the radius doubles the circumference but multiplies the area by four.
Working backward
Often you know the circumference or the area rather than the radius. A tree trunk with a 94 cm circumference has a radius of 94 ÷ 6.2832 ≈ 14.96 cm, so its diameter is about 29.9 cm. A circular garden bed of 20 m² has a radius of √(20 ÷ 3.1416) ≈ 2.52 m. Work out the radius first, then enter it in the circle calculator to get every other value.
Practical uses
- Pizza: a 16-inch pizza has about 201 square inches, while a 12-inch pizza has about 113, so one 16-inch pizza has nearly 80% more food.
- Edging and fencing: the circumference tells you how much edging a round bed needs.
- Paint and materials: the area tells you how much paint, seed or fabric to buy for a round surface.
- Wheels: one turn of a wheel moves it forward by its circumference.
Arcs, sectors and other parts
A slice of a circle is a sector. For a central angle θ in degrees, the arc length is C × θ ÷ 360 and the sector area is A × θ ÷ 360. A 90° quarter of the radius-5 circle has an arc of about 7.854 and an area of about 19.635. A chord is a straight line between two points on the circle; the diameter is the longest chord.
About π
π is the ratio of any circle’s circumference to its diameter, the same for every circle. It is irrational, so its decimals never end or repeat. For everyday measurements, 3.1416 is more than accurate enough; the circle calculator uses the full double-precision value and shows four decimal places.
Measuring real circles
Finding the center of a real object is hard, so it is usually easier to measure the diameter or the circumference and convert. To measure the diameter of a round table, run a tape across the widest point, passing through the middle; the largest reading you can find is the diameter. Halve it to get the radius for the circle calculator. For a pipe, a tree or a column, wrap a flexible tape around it to get the circumference, then divide by 2π.
Unit conversions for area are a common trap. A circle with a radius of 1 meter has an area of about 3.1416 square meters, which is 31,416 square centimeters, because one square meter contains 100 × 100 = 10,000 square centimeters. Convert the radius first, then calculate, rather than converting the area with a length factor.
Circles also turn up inside other shapes. The volume of a cylinder is the circle’s area times the height: a round pool 4 m across and 1.2 m deep holds about π × 2² × 1.2 ≈ 15.08 cubic meters of water, or roughly 15,080 liters. A volume calculator handles cylinders, cones and spheres directly, using the same circle calculator formulas underneath.
Related converters and calculators
Related calculators:
- Area calculator: area
- Triangle calculator: triangles
- Volume calculator: volume
- Square footage calculator: floor area
Sources
OpenStax Prealgebra 2e, 9.5: Circles and irregular figures.
Questions about this calculator
What is the area of a circle with radius 5?
About 78.54 square units.
How do I find the radius from the circumference?
Divide the circumference by 2π.
How do I find the radius from the area?
r = √(A ÷ π).
What is the circumference formula?
C = 2πr.
Is a 16-inch pizza bigger than two 12-inch pizzas?
No: 201 sq in versus 226 sq in.
Check the assumptions and units before relying on a result. Financial, tax and health estimates do not replace advice for your individual circumstances.
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