How do I calculate the area of a sector?

Enter the radius and the central angle in degrees. The calculator uses the formula (angle/360) * π * r² to compute the sector area. For example, with radius 5 and angle 60°, the area is (60/360) * π * 25 ≈ 13.09 square units.

What is arc length and how is it calculated?

Arc length is the distance along the curved edge of the sector. It is calculated using (angle/360) * 2πr. For radius 5 and angle 60°, the arc length is (60/360) * 2π * 5 ≈ 5.24 units.

Can I use this calculator for angles in radians?

No, this calculator specifically requires the central angle in degrees. If you have radians, convert to degrees first (multiply by 180/π) before entering.

Math

Instant, private, and free

Sector Area Calculator.

Calculate circular-sector area and arc length.

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Set your values

Results update as you type.

02 / ANSWER

Radius

Central angle (degrees)

Area

19.634954

Arc length

7.853982

Results update automatically as you type.

Use Cases

Geometry homework and exams

Quickly verify sector area and arc length calculations for math assignments, quizzes, or test preparation.

Example: Check the area of a sector with radius 10 and angle 45°.

Design and engineering projects

Compute material or space requirements for circular segments in designs, such as fan blades, gears, or architectural elements.

Example: Find the area of a 90° sector with radius 8 for a circular garden layout.

Frequently Asked Questions

How do I calculate the area of a sector?: Enter the radius and the central angle in degrees. The calculator uses the formula (angle/360) * π * r² to compute the sector area. For example, with radius 5 and angle 60°, the area is (60/360) * π * 25 ≈ 13.09 square units.
What is arc length and how is it calculated?: Arc length is the distance along the curved edge of the sector. It is calculated using (angle/360) * 2πr. For radius 5 and angle 60°, the arc length is (60/360) * 2π * 5 ≈ 5.24 units.
Can I use this calculator for angles in radians?: No, this calculator specifically requires the central angle in degrees. If you have radians, convert to degrees first (multiply by 180/π) before entering.

Tips & Common Mistakes

Tips

Ensure the central angle is in degrees, not radians, for accurate results.
Double-check your radius value; a small error can significantly affect the area and arc length.
Use the arc length result when you need the length of the curved boundary, such as for fencing or trim.
For a full circle, use 360° as the angle to verify the formulas: area = πr² and arc length = 2πr.

Common Mistakes to Avoid

Entering the angle in radians instead of degrees, leading to incorrect results.
Confusing the sector area with the arc length; they are different measurements.
Using the diameter instead of the radius; always use the radius value.

Last updated: August 13, 2026