A focused calculator that solves for radius specifically, whichever of the three common starting measurements you happen to have.
How it works
From diameter: divide by 2. From circumference: divide by 2π. From area: divide by π and take the square root.
What this does not include
This does not include solving for diameter, circumference, or area as the primary output — for those, use this site’s circumference-to-diameter or circle-diameter calculators instead. This one is built specifically around radius.
How to use this calculator
- Select which measurement you know, then enter its value.
A worked example
From a diameter of 10: radius = 5.
From a circumference of 31.4159: radius = circumference ÷ (2π) = 5.
From an area of 78.5398: radius = √(area/π) = 5 — all three starting points agree on the same circle.
What the variables mean
| Variable | Meaning |
|---|---|
| Diameter, circumference, or area | Any one known circle measurement |
Edge cases worth knowing
Any single circle measurement is enough to find the radius — diameter, circumference, and area each fully determine the same circle, which is why this calculator accepts any one of the three as a starting point.
A diameter of zero collapses the circle to a point, so the calculator declines to show a result for that input.
Frequently asked questions
Why does area require a square root to find the radius?
Because area scales with the radius squared (area = πr²), so reversing the formula to solve for radius requires undoing that square with a square root.
Is the radius always half the diameter?
Yes, by definition — the diameter is the full distance across a circle through its center, and the radius is exactly half of that.
What’s a practical use for solving from circumference?
Measuring around a round object with a tape measure is often easier than measuring straight across it, making circumference the practical starting point for many real-world objects.
