Circle Theorems Calculator
With our circle theorems calculator, you can understand all of the different circle theorems!
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 = 2rC = 2πr = πdA = 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.