Radius of a Circle Calculator
Calculate the radius of a circle from its diameter, circumference, or area — with reverse calculations too.
Frequently Asked Questions
How do you find the radius from the diameter?
Radius is exactly half the diameter: r = d / 2. Example: a circle with a 10 cm diameter has a radius of 5 cm. This is the simplest of the three relationships, since diameter and radius are directly proportional with no other variables involved.
How do you find the radius from the circumference?
Since circumference C = 2πr, solving for r gives r = C / (2π). Example: a circle with a circumference of 31.4159 has a radius of 31.4159 / (2 × 3.14159) = 31.4159 / 6.28318 = 5. This relationship comes directly from the definition of π as the ratio of circumference to diameter (π = C/d, and d = 2r).
How do you find the radius from the area?
Since area A = πr², solving for r gives r = √(A / π). Example: a circle with an area of 78.54 has a radius of √(78.54 / 3.14159) = √25 = 5. Note that area grows with the square of the radius — doubling the radius quadruples the area, which is why even modest increases in radius significantly increase a circle's area.
What is the relationship between radius, diameter, circumference, and area?
All four measurements of a circle are derived from the radius (r): Diameter d = 2r. Circumference C = 2πr = πd. Area A = πr². Knowing any single one of these four values lets you calculate all the others, since they are all directly related through r and the constant π ≈ 3.14159.