Sector Area Calculator
Calculate the area of a circular sector — a pie-shaped slice defined by a radius and a central angle. Enter your radius and angle in degrees or radians, and this calculator computes the sector area, arc length, and perimeter instantly.
1. Enter Measurements
Results
Sector Area Calculator
A sector is the region between two radii of a circle and their intercepted arc. It looks like a pizza slice. The area depends on 2 things: how big the circle is (radius) and how wide the slice is (central angle).
What makes sectors useful
Sectors model partial circular areas. A radar sweep covers a sector. A windshield wiper cleans a sector. An irrigation pivot waters a sector. Knowing the sector area tells you the coverage, material needed, or capacity of these partial-circle regions.
Degrees vs. radians
Both measure the same angle differently. Degrees split a full rotation into 360 parts. Radians use the ratio of arc length to radius — one full rotation = 2π ≈ 6.283 radians. This calculator accepts both. Common Core Math standards introduce degrees first; calculus courses use radians.
Sector Area Formula
The sector area formula takes the full circle area and scales it by the angle fraction. Click each part below.
Click each part to explore
How to Calculate Sector Area
Four steps from measurements to sector area. Enter a radius to follow along.
Measure the Radius
rFind the radius of the circle — the distance from the center to the edge.
Measure the Central Angle
θFind the central angle (θ) in degrees between the two radii forming the sector.
Compute the Fraction
θ / 360Divide the angle by 360° to get the fraction of the full circle.
Multiply by πr²
A = (θ/360)πr²Multiply the fraction by the full circle area (πr²) to get the sector area.
Formula Variations
Three ways to calculate sector area depending on your angle unit or whether you know the arc length.
The standard sector area formula using degrees. The ratio θ/360 tells you what fraction of the full circle the sector occupies. Multiply that fraction by the total area πr².
Example
Work through a sector area problem with a 45° angle. Change the radius to try different sizes.
A circle with radius 8 cm and a central angle of 45 degrees.
Frequently Asked Questions
Common questions about sectors, angles, and this calculator.