Radius of a Circle Calculator

Frequently Asked Questions

How to Find the Radius of a Circle

The radius is the distance from the center of a circle to any point on its edge — half the diameter. Depending on what measurement you already have, you can find the radius three different ways: from the diameter (r = d/2), from the circumference (r = C/(2π)), or from the area (r = √(A/π)). This calculator takes whichever quantity you know, computes the radius, and then derives the other three quantities (radius, diameter, circumference, and area) from it.

Choosing the right formula for your known quantity

If you measured straight across the widest point of the circle, that is the diameter, so divide by 2. If you measured (or were given) the distance around the outside of the circle, that is the circumference, so divide by 2π ≈ 6.2832. If you know the area the circle covers, divide the area by π and take the square root — this comes from solving A = πr² for r. Once the radius is known, the other three values follow directly: diameter is 2r, circumference is 2πr, and area is πr².

Common mistakes when finding a radius

The most common error is confusing radius and diameter — the diameter is always twice the radius, not the same value. A second common error is applying the diameter formula (divide by 2) to a circumference value, or vice versa; check which quantity you actually measured before dividing. Finally, remember that area is in square units (ft², m², etc.) while radius, diameter, and circumference are in linear units — do not mix them when entering a known area.