Sector Area Calculator

Sector Area
Arc Length
Fraction of Circle

How It Works

This sector area calculator uses established formulas to provide accurate results.

The basic rule:

  • A(sector) = ½r²θ (radians)
  • A(sector) = πr²(θ/360) (degrees)
  • Arc length = rθ (radians)
  • Fraction = θ/360 (degrees)

Results are estimates. Consult a professional for critical decisions.

Want to Actually Learn Algebra?

Calculators give you answers — but if you want to understand the math, Allday Everyday Math teaches Algebra 1 fast with structured lessons, worked examples, and practice quizzes that build real confidence.

Explore Allday Everyday Math →

Frequently Asked Questions

What is a sector of a circle?

A sector is a pie-shaped region bounded by two radii and the arc between them. Think of it as a slice of pizza. The central angle determines how large the sector is.

How do you calculate sector area?

In radians: A = ½r²θ. In degrees: A = πr²(θ/360). Both formulas give the same result; they just use different angle units.

What is the difference between a sector and a segment?

A sector is bounded by two radii and an arc (pie slice shape). A segment is bounded by a chord and an arc. Segment area = sector area - triangle area formed by the chord and radii.

How do I find the angle if I know the sector area?

Rearrange the formula: θ = 2A/r² (radians) or θ = 360A/(πr²) (degrees). Divide the sector area by the total circle area and multiply by 360° (or 2π).