Sector area formula: A = ½r²θ
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.
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.