Circle Properties

Enter any one property — radius, diameter, circumference or area — and get all the others. Add a central angle to also get the arc length, sector area, chord and segment.

Geometry2DCircles

Inputs

Input examples

Click Use on the size you know and, optionally, on one arc or sector value. All other fields are calculated. Each field has its own unit: click the unit to change it.

Circle size

Radius r

Diameter d

Circumference C

Area A

Arc & sector — optional, leave the used field empty to skip

Central angle θ

Arc length s

Sector area

Chord length c

Segment area

What is π?

For every circle, the circumference divided by the diameter is the same number: π ≈ 3.14159. That is why one measurement is enough to know everything about a circle.

Doubling the radius doubles the circumference but quadruples the area, because area grows with r². Angles in a circle are often measured in radians: a full turn is 2π rad, so the arc length is simply s = rθ.

d = 2rdiameter is twice the radius

C / d = πfor every circle

r × 2area × 4

360°= 2π radians

Live Diagram

r = 5 cm

radius

diameter

sector

arc

chord

Result

Enter a value above

Circle Formulas

θ in radians

Quantity	Formula

Worked Techniques

Radius from Area

Undo the square: divide the area by π, then take the square root. From the circumference it is simply r = C / 2π.

Example:

Degrees to Radians

Arc and sector formulas are simplest in radians. Convert first, then use s = rθ and A = ½r²θ.

Example:

Sector as a Fraction

A sector is a “slice of pizza”: the same fraction of the full area as its angle is of a full turn.

Example:

Sources & Verification

References

J. Stewart, L. Redlin & S. Watson, Precalculus: Mathematics for Calculus, 7th ed., Cengage, 2016 — Sec. 6.1 (Angle Measure).