Circle Sector Calculator
Sector area, arc length and chord from a radius and an angle.
Work out Circle Sector. Sector area, arc length and chord from a radius and an angle. Free, with no account and nothing to download.
Sector area (units²)
78.5398
Arc length 15.708 units · 25% of the circle
Arc length is rθ and area is r²θ⁄2, both with the angle in radians — 90° is 1.5708 radians. The chord is the straight line across the opening, which is shorter than the arc; here 14.1421 against 15.708.
How the Circle Sector Calculator works
A sector is the pizza slice: the region between two radii and the arc joining them. Its area is r²θ⁄2 and its arc is rθ, both with the angle in radians. The chord — the straight line across the opening — is always shorter than the arc, and this shows both.
Also known as: area of a sector · sector of a circle calculator · pie slice area calculator · sector area formula
Frequently asked questions
How do I find the area of a sector?
Take the fraction of the full circle the angle represents and apply it to the circle's area. A 90° sector is a quarter circle, so a radius of 10 gives a quarter of 100π, or 78.54 square units.
What is the arc length of a sector?
The radius times the angle in radians. A 90° angle is π⁄2 radians, so a radius of 10 gives an arc of 15.71 units.
What is the difference between an arc and a chord?
The arc is the curved edge; the chord is the straight line between its endpoints. The arc is always longer, and the gap widens as the angle grows.
How do I convert degrees to radians?
Multiply by π and divide by 180. A full circle is 2π radians, a half circle π, and a right angle π⁄2.
Put this calculator on your own site
Free to use, on any site, commercial or not. Paste this where you want it to appear. It is a plain iframe, so it works in WordPress, Squarespace, Wix, Webflow, Ghost and anything else that accepts HTML.
<iframe src="https://www.thecalclibrary.com/embed/circle-sector-calculator" width="100%" height="640" style="border:1px solid #e2e8f0;border-radius:12px" loading="lazy" title="Circle Sector Calculator"></iframe>The only condition is that the credit line stays visible. It sits inside the frame, so you do not have to do anything to keep it.
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