Circumference-to-Radius Calculator
Convert from circumference to radius and vice versa with this circumference-to-radius calculator. It can also show the diameter and area when needed.
Radius0.795775from circumference 5
Radius0.795775
Diameter1.591549
Circumference5
Area1.989437
Area of the enclosing square2.53303the circle fills 78.54% of it
Working
| Radius | 0.79577472 |
| C = 2πr | 2 × π × 0.795775 = 5 |
| A = πr² | π × 0.795775² = 1.989437 |
The formulas
C = 2πr, A = πr², d = 2r
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.