Circle Area Calculator
Calculate the area of a circle from its radius or diameter. Free circle area calculator that also returns the circumference and diameter with the formula shown.
Updated 2026-06-14 · Free · No sign-up · Runs privately in your browser
Show the formula & steps
How the Circle Area Calculator Works
Enter the radius or diameter of a circle and this calculator returns its area, circumference and diameter instantly. Switch the input type with the dropdown, and the calculator handles the conversion for you.
The Formulas
Area = π × r² Circumference = 2 × π × r
If you start from the diameter, halve it first to get the radius (r = d ÷ 2), then apply the formulas.
Worked Example
For a circle with a radius of 5:
- Area = π × 5² = π × 25 ≈ 78.54 square units
- Circumference = 2 × π × 5 ≈ 31.42 units
- Diameter = 2 × 5 = 10 units
Radius, Area and Circumference
| Radius | Area (πr²) | Circumference (2πr) |
|---|---|---|
| 1 | 3.14 | 6.28 |
| 5 | 78.54 | 31.42 |
| 10 | 314.16 | 62.83 |
| 12 | 452.39 | 75.40 |
Where Circle Area Is Used
Circle area calculations come up everywhere: sizing pizzas and round tables, estimating paint or turf for circular surfaces, calculating the cross-section of pipes and cables, and engineering anything round. Because area grows with the square of the radius, doubling the radius quadruples the area — a useful rule of thumb when scaling circular objects.
Frequently asked questions
What is the formula for the area of a circle?+
The area of a circle is A = π × r², where r is the radius and π is approximately 3.14159. You square the radius and multiply by pi. For a circle with radius 5, the area is π × 25 ≈ 78.54 square units.
How do I find the area of a circle from the diameter?+
Divide the diameter by 2 to get the radius, then use A = π × r². Alternatively, use A = π × d² ÷ 4 directly. For a diameter of 10, the radius is 5 and the area is π × 25 ≈ 78.54. This calculator accepts either the radius or the diameter.
What is the difference between area and circumference?+
Area measures the surface enclosed by the circle, in square units, using A = πr². Circumference measures the distance around the circle, in linear units, using C = 2πr. They answer different questions: how much space inside versus how far around.
What value of pi does the calculator use?+
It uses the full-precision value of π built into the browser (about 3.141592653589793), so results are accurate to many decimal places. For hand calculations, 3.14 or 3.14159 is usually close enough for everyday work.
How do I find the radius if I know the area?+
Rearrange the area formula: r = √(A ÷ π). Divide the area by pi, then take the square root. For an area of 78.54, r = √(78.54 ÷ 3.14159) = √25 = 5 units.