What is the area of a sector?

The area of a sector of a circle is the fraction of the circle’s area corresponding to the central angle. The formula is A = (θ° / 360°) × πr² for degrees, or A = 0.5 × r² × θ for radians.

Can I calculate arc length, too?

Yes, arc length is L = (θ° / 360°) × 2πr for degrees, or L = r × θ for radians. This calculator shows both area and arc length.

What if I only know the arc length and the radius?

If arc length L and radius r are known, the angle is θ = L / r (in radians) and the area is A = 0.5 × r × L.

Sector Area Calculator

Calculate the area of a circle sector in multiple ways: from radius and angle (deg or rad), from diameter, or from arc length. You also get arc length, sector perimeter, central angle in both degrees and radians, and the sector’s percentage of the full circle.

Radius (r)

same unit for all

Angle (°)

central angle

Prism height (opt.)

Sector formulas used

Area from degrees: \( A = \frac{\theta}{360^\circ} \cdot \pi r^2 \)

Area from radians: \( A = \frac{1}{2} r^2 \theta \)

Arc length (deg): \( L = \frac{\theta}{360^\circ} \cdot 2 \pi r \)

Arc length (rad): \( L = r \theta \)

From arc length and radius: \( \theta = \frac{L}{r} \) (rad), then \( A = \frac{1}{2} r L \)

Sector perimeter: \( P = 2r + L \)

FAQs

What units does this calculator support?

Any length unit: cm, m, in, ft — just be consistent. Area will be in the squared version of that unit.

What’s the fastest way if I only know the arc length?

Use the “Arc length + Radius” tab; it computes the angle automatically and then the area.

What if I want semicircle or quarter circle?

Use the % tab: 50% → semicircle, 25% → quarter circle, 12.5% → 45° sector.

Sector Area Calculator

Results

Sector formulas used

FAQs