Radius of a Circle Calculator
The radius runs from a circle’s center to its edge. Enter whichever measurement you have — circumference, diameter, or area — and get the radius with the math written out.
Example: with I know the Circumference (C) · Value 31.42 → Radius (r): 5.00.
Computed by the calculator below using its default values. Change any input to see your own numbers.
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Check it outHow to find the radius of a circle
The radius is the distance from a circle’s center to its edge, and every other circle measurement encodes it. The three radius formulas: r = d ÷ 2 from the diameter, r = C ÷ (2π) from the circumference, and r = √(A ÷ π) from the area.
Worked through: how to find the radius with circumference — a circle measuring 31.42 around has r = 31.42 ÷ 6.2832 ≈ 5. From an area of 100, r = √(100 ÷ π) = √31.83 ≈ 5.64. And a 9 in diameter pie tin has a 4.5 in radius. The calculator returns the matching diameter and area alongside, so you can confirm all three numbers describe the same circle.
How it’s calculated
r = C ÷ (2π) from a circumference; r = d ÷ 2 from a diameter; r = √(A ÷ π) from an area (A = πr² solved for r). π ≈ 3.14159 via JavaScript’s full-precision Math.PI; results round only at display (2 decimals).
Results update as you type and are estimates, not professional advice — verify important decisions with a qualified professional.
Common mistakes
- Dividing the circumference by π only — that gives the diameter; divide by 2π for the radius.
- Forgetting the square root when starting from area — A ÷ π is r², not r.
- Measuring center-to-edge on something slightly oval — average two perpendicular measurements instead.
Frequently asked questions
How do you find the radius of a circle?
Use whichever measurement you have: r = d ÷ 2, r = C ÷ (2π), or r = √(A ÷ π). All three recover the same radius.
How do I find the radius from the circumference?
Divide by 2π ≈ 6.2832. A circumference of 31.42 gives r ≈ 5.
What is the radius if the area is 100?
r = √(100 ÷ π) ≈ 5.64, because the area is πr² and you undo the square with a square root.
What is the radius of a circle, exactly?
The distance from the center to any point on the circle — half the diameter, and the r in πr² and 2πr.