Circle Calculator
Area, circumference and diameter of a circle from its radius.
- Diameter10.0000
- Circumference31.4159
- Area78.5398
Inputs used
- Radius5
About this calculator
Everything about a circle follows from its radius: the diameter is twice the radius, the circumference is 2πr, and the area is πr². A circle with radius 5 has a diameter of 10, a circumference of about 31.42 and an area of about 78.54.
If you know the diameter instead, halve it for the radius. If you know the circumference, divide by 2π; if you know the area, the radius is √(area ÷ π).
A useful intuition: doubling the radius doubles the circumference but quadruples the area — which is why a 12-inch pizza is more than twice the pizza of an 8-inch one.
Quick reference
Area by radius
Area A = πr² for each radius.
| Radius | Area |
|---|---|
| 1 | 3.1416 |
| 2 | 12.5664 |
| 3 | 28.2743 |
| 4 | 50.2655 |
| 5 | 78.5398 |
| 6 | 113.0973 |
| 7 | 153.9380 |
| 8 | 201.0619 |
| 9 | 254.4690 |
| 10 | 314.1593 |
| 12 | 452.3893 |
| 15 | 706.8583 |
Circumference by radius
Circumference C = 2πr for each radius.
| Radius | Circumference |
|---|---|
| 1 | 6.2832 |
| 2 | 12.5664 |
| 3 | 18.8496 |
| 4 | 25.1327 |
| 5 | 31.4159 |
| 6 | 37.6991 |
| 7 | 43.9823 |
| 8 | 50.2655 |
| 9 | 56.5487 |
| 10 | 62.8319 |
| 12 | 75.3982 |
| 15 | 94.2478 |
Frequently asked questions
What is the formula for the area of a circle?
Area equals π times the radius squared: A = πr². A circle with radius 5 has an area of π × 25 ≈ 78.54 square units.
How do you find the circumference from the radius?
Multiply the radius by 2π: C = 2πr. For a radius of 5 that is 2 × π × 5 ≈ 31.42, and the diameter is simply twice the radius, or 10.
Why does the area quadruple when the radius doubles?
Because area depends on the radius squared. Doubling r multiplies r² by four, so a circle of radius 10 has four times the area of one with radius 5, even though its circumference only doubles.
How do I find the radius if I know the area?
Reverse the area formula: r = √(A ÷ π). An area of 78.54, for instance, gives √(78.54 ÷ π) ≈ 5.
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Results are informational only — not financial, medical or legal advice.