Sector Area Calculator
Find the area and arc length of a circular sector.
Results update as you type.
How it works
A circular sector is a pie-slice-shaped region of a circle bounded by two radii and the arc between them, and this calculator finds its area and arc length from the radius and the central angle. You enter the radius and the angle in degrees, and it returns the sector's area and the length of its curved edge. The idea is simple proportion: a sector covers a fraction of the full circle equal to its central angle divided by 360 degrees, so its area is that fraction of the whole circle's area, and its arc length is the same fraction of the circle's circumference. A 90-degree sector, for instance, is exactly a quarter of the circle. Sectors appear everywhere: slices of pie and pizza, pie-chart segments, fan and gear shapes, irrigation coverage, and windshield-wiper sweeps. Engineers, designers, and students use these calculations to find areas of curved regions and lengths of arcs. Make sure the angle is between zero and 360 degrees, since a full circle is 360 degrees and a sector cannot exceed the whole circle. Enter the radius and central angle to compute the sector's area and arc length.
Area = (θ/360)·π·r²
A sector is a pie-slice piece of a circle. Its area is the fraction of the full circle it covers, the central angle divided by 360 degrees, times the whole circle's area, pi times the radius squared. The arc length, the curved edge of the slice, is the same fraction of the circle's full circumference, two pi times the radius.
Source:Euclidean geometry
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter radius and central angle.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Sector area updates instantly as you type — no button to press.
Frequently asked questions
What is a sector of a circle?
A sector is a region of a circle shaped like a pie slice, bounded by two radii and the arc between their endpoints. Its size is set by the central angle at the circle's centre. A sector with a 360-degree angle is the whole circle, and a 180-degree sector is a semicircle.
How do you find the area of a sector?
Take the central angle divided by 360, then multiply by the area of the full circle, which is pi times the radius squared. This works because the sector covers that fraction of the circle. For a radius of two and a 90-degree angle, the sector area is pi, about 3.14 square units.
What is the arc length of a sector?
The arc length is the length of the curved outer edge of the sector. It equals the central angle divided by 360, times the full circumference, which is two pi times the radius. It is the same fraction of the circle's perimeter that the sector's area is of the circle's area.
How is a sector different from a segment?
A sector is bounded by two radii and an arc, like a pie slice reaching the centre. A segment is bounded by a chord and an arc, the region cut off by a straight line across the circle. A sector includes the centre point, while a segment does not, so their areas are calculated differently.
Can the angle be more than 360 degrees?
No. A full circle is 360 degrees, so a sector's central angle must be between zero and 360. An angle of 360 degrees gives the whole circle, and anything larger would wrap around more than once, which is not a valid sector. This calculator requires the angle to fall within that range.