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Geometry · Circles

Circle, Arc, Sector & Chord Calculator

Connect radius, circumference, area, central angle, arc length, sector area, chord length, and sagitta in one explained circle model.

Formula shown Runs locally Reviewed Aug 11, 2026
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Equation guide

A circle of positive radius and a central angle from 0° through 360°

Whole circle

C=2πrK=πr²

Arc and sector

s=rθKsector=θr²/2θ in radians

Chord geometry

chord=2r sin(θ/2)sagitta=r[1−cos(θ/2)]
Geometry · Circles

Connect a circle, arc, sector, and chord

Inputs and displayed decimal results use at most three decimal places. Exact internal values are retained during calculation.

s = rθ ; Ksector = θr²/2

Enter a radius and a central angle measured in degrees.

θr

Using the model

Symbols, assumptions and limitations

Interpretation notes

The central angle is entered in degrees and converted internally to radians for arc formulas. Radius must be positive and the central angle must lie in (0°, 360°]. Chord and sagitta refer to the minor-or-major oriented central angle shown by the sector.

Worked examples

See the method in practice

01

Quarter circle

For r = 2 and θ = 90°, the arc length and sector area are both π, while the chord is 2√2.

02

Semicircle

At 180°, the arc length is πr, the sector is half the circle, and the chord equals the diameter.

Questions

Frequently asked

Why does s = rθ require radians?

A radian measures arc length divided by radius, making arc length directly equal to rθ.

What is the sagitta?

It is the perpendicular height from the midpoint of a chord to the corresponding arc.

Are units required?

No unit is imposed. Length results use the radius unit, while areas use its square.

Sources & review

Equations and examples are checked against the references below. Results are educational and should be independently verified for safety-critical work.

OpenStax Precalculus — Circles

Written by the STEM Hub editorial team · Reviewed August 11, 2026 · Review methodology