Arc Length Calculator

The formulas

arc = rθ, sector area = ½r²θ (θ in radians)

Radians make these formulas simple

arc = rθ only works with θ in radians. In degrees you need the fraction of the circle instead: arc = 2πr × θ/360. That is the same equation once you notice 2π/360 is the degree-to-radian factor — which is exactly why radians exist.

Everything follows from the radius

A circle has one degree of freedom, so any single measurement fixes all the others:

• d = 2r
• C = 2πr = πd
• A = πr² = πd²/4 = C²/4π

Going backwards, r = C/2π and r = √(A/π). The calculator above accepts whichever you happen to have.

Area grows with the square

Double the radius and the circumference doubles, but the area quadruples. That is why a 16-inch pizza is more than twice the food of a an 11-inch one, and why pipe capacity rises so sharply with bore.