Circle Sector Calculator
Enter a circle's radius and the sector's angle to calculate its arc length and area.
Last updated: September 5, 2026
Frequently asked questions
What is the arc length of a 90° sector with radius 10?
About 15.71 - convert 90° to radians (π/2 ≈ 1.5708), then arc length = 10 × 1.5708 ≈ 15.71.
What is the area of a 90° sector with radius 10?
About 78.54 - area = 0.5 × 10² × 1.5708 (90° in radians) ≈ 78.54, which is exactly 1/4 of the full circle's area (π × 10² ≈ 314.16), matching the 90°/360° = 25% fraction.
Why does the formula need the angle in radians, not degrees?
Radians directly relate arc length to radius (an angle of 1 radian subtends an arc equal to the radius), which is what makes the simple formulas arc length = r×θ and area = 0.5×r²×θ work - degrees don't have that direct relationship, so this calculator converts for you automatically.
How is a sector different from a segment?
A sector is the full "pie slice" bounded by two radii and the arc between them. A segment is just the region between a chord (straight line connecting the two arc endpoints) and the arc itself - a segment is always smaller than its corresponding sector.
What's the difference between a sector's arc length and its chord length?
Arc length follows the curved edge of the sector (r×θ in radians), while the chord is the straight line directly connecting the two endpoints of that arc - the chord is always shorter than the arc except in the limiting case of a very small angle.
How do I find the sector area if I only know the arc length, not the angle?
First find the angle in radians by dividing arc length by radius (θ = s/r), then plug that into the area formula: area = 0.5 × r² × θ. This calculator does it directly from the angle, so convert first if arc length is all you have.
What's the area of a full 360° sector?
It equals the full circle's area, πr² - a 360° sector is just the entire circle, since the two bounding radii coincide and the 'arc' wraps all the way around.