Math calculator

Free circle calculator

Calculate circle area, circumference, and diameter — enter a radius and see all measurements instantly, updated live, as you type.

InputsLive
Known measurement
Radius
Result
Area
78.5398
Circumference: 31.4159
Radius5
Diameter10
Circumference31.4159
Area78.5398

C = 2πr, A = πr². Source: Euclidean geometry.

Results are estimates. Consult a professional.

How it's calculated

How the circle calculator works

A circle is defined by a single measurement — its radius. Every other property (diameter, circumference, area) follows directly. Enter any one value and the calculator derives the rest.

Diameter = 2r
Circumference = 2πr = πd
Area = πr²
π ≈ 3.14159265358979…

π (pi) is an irrational constant approximately equal to 3.14159. The calculator uses the full IEEE 754 double-precision value so results are accurate to at least 15 significant figures before rounding.

Weisstein, Eric W. — Circle. MathWorld, Wolfram Research.
Example

Worked example: circle with radius 7 cm

Example: r = 7 cm

A circle has a radius of 7 cm. Find its diameter, circumference, and area.

Diameter = 2 × 7 = 14 cm
Circumference = 2 × π × 7 = 43.982 cm
Area = π ×= π × 49 = 153.938 cm²
Area 153.94 cm² · Circumference 43.98 cm
A circle of radius 7 cm has roughly the area of a side-plate and a perimeter just under half a metre.
Quick reference

Circle measurements for radii 1–10

Use the table below as a quick lookup for common radii. All values use π ≈ 3.14159 and are rounded to two decimal places.

RadiusDiameterCircumferenceArea
126.283.14
2412.5712.57
3618.8528.27
4825.1350.27
51031.4278.54
61237.70113.10
71443.98153.94
81650.27201.06
91856.55254.47
102062.83314.16

All measurements in the same unit as the radius. Circumference = 2πr; Area = πr².

Practical tips

Tips for circle calculations

Circles appear in construction, engineering, cooking, and design. These tips help you apply the formulas correctly in real-world situations.

  • Measure diameter, not radius, in practice — it is easier to measure across a circle than from centre to edge; enter the diameter and let the calculator halve it.
  • Area scales with the square of the radius — doubling the radius quadruples the area, so small radius errors grow quickly; measure carefully.
  • Circumference for fencing or edging — to border a circular garden bed or pool, use the circumference formula; add 5–10% for overlap and joins.
  • Area for coverage problems — paint, turf, or flooring quantities depend on area; divide the area by the product coverage rate to get the amount needed.
  • Semi-circles and sectors — halve the area for a semicircle (πr²/2); for a sector, multiply area by (angle/360°) to get the slice area.
Accuracy & limits

Accuracy and limitations

All calculations use JavaScript's built-in Math.PI (accurate to 15+ significant figures). Results are displayed rounded to a configurable number of decimal places. The formulas apply to perfect mathematical circles; real-world objects have manufacturing tolerances and irregular edges that the calculator cannot account for. For engineering or structural work, add an appropriate safety margin beyond the calculated value.

Glossary

Key terms

The distance from the centre of a circle to any point on its edge.
The longest chord through the centre; equal to twice the radius.
The perimeter (total boundary length) of a circle; C = 2πr.
The total surface enclosed by the circle; A = πr².
The mathematical constant equal to the ratio of a circle's circumference to its diameter; ≈ 3.14159265…
A "pie slice" portion of a circle bounded by two radii and an arc; its area is (θ/360°) × πr².
About

About this calculator

Part of our math calculators suite — explore all calculators.

Questions

Frequently asked questions about the free circle calculator

A circle calculator is a free online tool that helps you derive all four circle properties — radius, diameter, circumference, area — from any one. A circle is fully determined by its radius. Diameter, circumference, and area all derive from r through simple formulas involving π. It runs entirely in your browser with instant results and no sign-up.
Because area scales with two dimensions, not one. Doubling r doubles the diameter and circumference (one-dimensional) but quadruples the area. This is why a 12-inch pizza has 4× the area of a 6-inch one — not 2×.
The ratio of any circle's circumference to its diameter, approximately 3.14159265358979. It's irrational and transcendental — no finite decimal or fraction equals it exactly. The SI defines it implicitly through the constants k and c.
Not with these formulas — they're specific to circles. Ellipses have two radii (semi-major and semi-minor) and their area is π × a × b, but the circumference doesn't have a closed-form expression (it requires an elliptic integral).

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