Interactive — Areas Related to Circles

Radius r: 80

Change the radius and watch how the circumference (2πr) and area (πr²) grow. Area grows with the square of r — double r and area quadruples.

Angle θ: 90°

An arc is a fraction of the circumference: ℓ = (θ/360)·2πr. The highlighted arc grows as you increase the angle.

Angle θ: 90°

A sector is a "pizza slice" bounded by two radii and an arc. Area = (θ/360)·πr². Its perimeter = arc + 2r.

Angle θ: 120°

A segment is the region between a chord and its arc. Minor segment = sector − triangle = (θ/360)πr² − ½r²sinθ.

Outer R: 130 Inner r: 80

A ring (annulus) is the region between two concentric circles. Area = π(R² − r²) = π(R+r)(R−r).

The minute hand sweeps a sector each minute — 360° per hour, 6° per minute.

An animal tied to a post grazes a circular sector; the rope length is the radius.

Distance travelled = number of turns × circumference (2πr).

Semicircular windows combine a rectangle with a half-circle area.

Circular and sector-shaped beds in gardens use these area formulas for turf and fencing.

A pizza slice is literally a sector; its crust length is the arc.

From clocks to gardens, circular areas describe the round parts of the world around us.