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All calculatorsMethodology

Circle Calculator

Enter a circle’s radius, diameter, circumference or area to get all four measures with the working, plus arc length and sector area for any angle.

Interactive calculator · Method CIRCLE-MEASURES-1.0 · Last reviewed: 2026-11-04

Calculate your scenario

From radius r: diameter d = 2r, circumference C = 2πr, area A = πr².

Your inputs

Try an example

Default worked example. Edit the inputs to calculate your scenario.

Default worked example

Radius 5 cm
Diameter 10 cm
Circumference 31.4159 cm
Area 78.5398 cm²
Arc length 7.854 cm
Sector area 19.635 cm²

r = 5 cm; d = 2r = 10 cm; C = 2πr = 31.4159 cm; A = πr² = 78.5398 cm²; a 90° sector has arc 2πr × 90/360 = 7.854 cm and area πr² × 90/360 = 19.635 cm².

How to use the calculator

Choose which measure you know, enter it with a unit label, and set a sector angle if you need an arc length or sector area (360° gives the whole circle).

What the result means

A circle of radius 5 cm has a 10 cm diameter, a circumference of about 31.4159 cm and an area of about 78.5398 cm²; a 90° quarter sector has a 7.854 cm arc.

Formula and units

From radius r: diameter d = 2r, circumference C = 2πr, area A = πr². From a diameter r = d ÷ 2; from a circumference r = C ÷ 2π; from an area r = √(A ÷ π). For a sector of θ degrees, arc length = C × θ ÷ 360 and sector area = A × θ ÷ 360.

Worked examples

Radius 5 cm, quarter sector: Known value (area in square units): 5 units; Length unit label: cm e.g. cm, in, ft; Sector angle: 90 degrees; Known measure: radius.
Example result: Radius: 5 cm; Diameter: 10 cm; Circumference: 31.4159 cm; Area: 78.5398 cm²; Arc length: 7.854 cm; Sector area: 19.635 cm².

Circumference 100 in, 45° sector: Known value (area in square units): 100 units; Length unit label: in e.g. cm, in, ft; Sector angle: 45 degrees; Known measure: circumference.
Example result: Radius: 15.9155 in; Diameter: 31.831 in; Circumference: 100 in; Area: 795.7747 in²; Arc length: 12.5 in; Sector area: 99.4718 in².

Limitations and common mistakes

Uses π to full double precision and displays 4 decimal places. Enter an area in square units of the same length unit; the unit label is a name only and does not convert anything. A circumference is the perimeter of a full circle; a sector’s full perimeter would add two radii to the arc length.

Using the diameter in A = πr², which gives four times the true area.

Sources and assumptions

Method CIRCLE-MEASURES-1.0; last formula review 2026-11-04. Sources and their supported claims. Calculation methodology.