Circle Calculator
A circle is completely described by any one of its measurements, because the radius, diameter, circumference and area are all linked by π. Enter whichever one you know and this calculator returns the other three, giving both a decimal value and the exact answer in terms of π.
How to use the circle calculator
- Choose which measurement you know.
- Enter its value.
- Read the radius, diameter, circumference and area, plus the exact forms with π.
Formula
- Diameter d = 2r
- Circumference C = 2πr = πd
- Area A = πr²
- From circumference: r = C ÷ 2π. From area: r = √(A ÷ π).
Worked examples
From the radius
A circle with radius 5 has diameter 10, circumference 10π ≈ 31.416 and area 25π ≈ 78.540.
From the area
An area of 9π gives a radius of 3, a diameter of 6 and a circumference of 6π.
Circles and π
Where the formulas come from
Circumference is the distance around, and it is always π times the diameter, whatever the size. Area comes from cutting the circle into thin wedges and rearranging them into an almost-rectangle of width πr and height r.
Relationships worth knowing
| If you double the radius… | the circumference | the area |
|---|---|---|
| ×2 | doubles | quadruples |
| ×3 | triples | ×9 |
That is why a 16-inch pizza has far more than 1.33 times the area of a 12-inch one: its area is (16/12)² ≈ 1.78 times bigger.
Using π
π is irrational, so its decimal digits never end or repeat. For everyday use, 3.14 or 22/7 is fine. Engineers use more digits. Keeping answers in terms of π, such as 25π, keeps them exact.
Related shapes
A semicircle has half the area, ½πr², and a sector with angle θ has area (θ/360) × πr². For solids, see the geometry calculator.
Practice problems
Try these yourself first, then check your answer. The answers come from the calculator above.
- A circle has diameter 14. Find its area and circumference.
Show answer
Radius: 7 · Diameter: 14 · Circumference: 43.98229715
- A circle has circumference 31.4. Find its radius.
Show answer
Radius: 4.997465213 · Diameter: 9.994930426 · Circumference: 31.4
Common mistakes to avoid
- Using the diameter in the area formula without halving it.
- Rounding π too early to 3.14 when accuracy matters.
- Mixing linear units (cm) with area units (cm²).
Frequently asked questions
What is π?
The ratio of any circle’s circumference to its diameter, about 3.14159.
How do I find the area of a circle from its diameter?
Halve it to get the radius, then use A = πr².
Why does the answer include π?
Leaving π in the answer keeps it exact. Use the decimal only when you need a measurement.
What about other shapes?
Try the geometry calculator.
Reviewed September 26, 2026 by the SolveCalcPro editorial team. Found a mistake? Tell us; see our editorial policy.