Starting from the radius
A circle with a radius of 5 has a diameter of 10, a circumference of about 31.42, and an area of about 78.54.
Circle calculator
Result
Fill in the fields to see your result.
How it works
The radius is the hub every other measurement is built from: diameter is just twice the radius, circumference scales with radius by 2π, and area scales with the square of the radius by π. Whichever value you start with, the calculator first works backward to the radius, then forward to the other three.
Because area involves the radius squared, doubling a circle's radius doesn't double its area — it quadruples it, which is why the radius-from-area step needs a square root to undo that squaring.
Formulas used
Circumference
C = 2πr
Area
A = πr²
Radius from area
r = √(A ÷ π)
Worked examples
Starting from the area
A circle with an area of 78.54 has a radius of exactly 5 — the same circle as above, reached in the opposite direction.
Assumptions and limits
- The shape is a perfect circle.
- π is used to a high but finite number of decimal digits, so results are precise to the digits shown, not infinitely exact.
Frequently asked questions
Why does area use π times radius squared, not diameter?
It works either way — A = π(d/2)² is exactly the same formula rewritten — but the radius form is more common because it is the more fundamental measurement most circle formulas are built from.
What is π, exactly?
The ratio between any circle's circumference and its diameter — approximately 3.14159, an irrational number with digits that never repeat, so calculators use a stored, highly precise approximation.
Why does doubling the radius quadruple the area?
Because area depends on r², not r — doubling r multiplies r² by 2² = 4. This is the same reason a pizza twice the diameter has roughly four times the amount of pizza, not twice.
Can I enter the diameter instead of the radius?
Yes — choose "Diameter" from the dropdown and enter that value directly; the calculator converts it to a radius first automatically.
Updated
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