Basics

Sector area formula: A = ½r²θ

A=12r2θA = \tfrac{1}{2} r^{2} \theta

A sector with central angle θ on a circle of radius r has area ½r²θ, with θ in radians. It is the whole circle's πr² scaled by the fraction θ/2π that the sector occupies. Pair it with the arc-length formula for any "slice of a circle" question.

circlesector

Related Basics identities

Common questions

What is the Sector area identity?

A sector with central angle θ on a circle of radius r has area ½r²θ, with θ in radians. It is the whole circle's πr² scaled by the fraction θ/2π that the sector occupies.

When do you use the Sector area identity?

Pair it with the arc-length formula for any "slice of a circle" question.

Which identities are related to Sector area?

Sector area belongs to the Basics group. The identities used alongside it most often are SOHCAHTOA, Degrees ↔ radians and Arc length.

Practise it

Reading a formula is not the same as recalling it under time pressure. The workspace drills Basics questions in the quiz, and the triangle solver shows a worked solution for any triangle you type in.

Or browse all 45 identities in the full reference, or read the trigonometry guides for the method behind them.