Circle Calculator
A circle is fully determined by a single measurement. Enter whichever one you have — radius, diameter, circumference, or area — and get the other three, with the formula and substitution for each conversion.
Formulas & substitution
One number rules them all
Every property of a circle scales off the radius. Double it and the diameter and circumference double with it — but the area quadruples, because area grows with the square of the radius. That’s why a 16-inch pizza is not twice an 8-inch one, but four times the food. The constant tying it together is π ≈ 3.14159, the ratio of any circle’s circumference to its diameter. Going backward from area requires a square root: r = √(A/π).
How it’s calculated
d = 2r; C = 2πr = πd; A = πr². Inverses: r = d/2 = C/(2π) = √(A/π). All values use full double-precision π, displayed to 4 decimals. Units follow your input: a radius in cm returns circumference in cm and area in cm².
Results update as you type and are for education, not professional advice — double-check any number that matters.
Worked example
Radius r = 5: diameter = 10, circumference = 2π × 5 = 31.4159, area = π × 5² = 78.5398. Going backward from an area of 50: r = √(50/π) = 3.9894, so d = 7.9788 and C = 25.0663.
Common mistakes
- Squaring the diameter in the area formula — A = πr² uses the radius; with d it is πd²/4.
- Reporting area in plain units — area is always square units (cm², ft²).
- Rounding π to 3.14 early — on large circles the error compounds; round only the final answer.
Where it is used
- Sizing round tables, pools, pipes, and pizzas.
- Finding how much edging or fencing a circular bed needs (circumference).
- Converting a measured circumference (tape around a trunk or pipe) back to diameter.
Frequently asked questions
How do I find the radius from the circumference?
Divide by 2π: r = C ÷ 6.2832. A tree trunk taping 100 cm around has radius 15.92 cm and diameter 31.83 cm — this is exactly how foresters measure diameter with a tape.
Why does area grow faster than circumference?
Circumference is linear in r (2πr) while area is quadratic (πr²). Doubling r doubles the boundary but quadruples the enclosed surface — the reason bigger pizzas are usually better value per square inch.
What value of π does this use?
JavaScript’s full double-precision constant, 3.141592653589793. Displayed results are rounded to 4 decimals, but the chain of conversions is computed unrounded.
What units should I enter?
Any — the math is unit-agnostic. Enter the radius in meters and you get circumference in meters and area in square meters. Just do not mix units between reading the answer and using it.
Is there a formula straight from diameter to area?
Yes: A = πd²/4. For d = 10, A = π × 100 ÷ 4 = 78.54 — the same as using r = 5 in πr².