Circle Calculator
A circle with a radius of 5 has an area of about 78.54 and a circumference of about 31.42. This circle calculator finds the area, circumference, and diameter from a radius or diameter. Enter one value and the calculator fills in the rest using the standard circle formulas.
Quick answer
Area is calculated as pi times the radius squared.
What this tells you
- •Area is calculated as pi times the radius squared.
- •Circumference is calculated as 2 times pi times the radius.
- •Diameter is twice the radius.
- •Results are rounded to 4 decimal places.
How to Use
- 1Choose whether you are entering the radius or the diameter.
- 2Enter the value.
- 3Click Calculate to get the area, circumference, and diameter.
How It Works
Formula
Area = pi x r squared. Circumference = 2 x pi x r. Diameter = 2 x r.The radius is the distance from the center to the edge. The diameter is twice the radius. Area uses pi times the radius squared, and circumference uses 2 times pi times the radius.
Calculation note: values are processed in the order shown above, using the current input units.
Worked Examples
Area of a circle with radius 5
Area = pi x 5 x 5 = 3.14159 x 25 = 78.54. Circumference = 2 x pi x 5 = 2 x 3.14159 x 5 = 31.42. Diameter = 2 x 5 = 10.
Circumference from diameter 10
A diameter of 10 means a radius of 5. The area and circumference are the same as the example above because the radius is the same.
Circle Area and Circumference by Radius
Common radius values and their corresponding area, circumference, and diameter.
| Radius | Diameter | Area | Circumference |
|---|---|---|---|
| 1 | 2 | 3.14 | 6.28 |
| 2 | 4 | 12.57 | 12.57 |
| 3 | 6 | 28.27 | 18.85 |
| 5 | 10 | 78.54 | 31.42 |
| 10 | 20 | 314.16 | 62.83 |
Common mistakes
- Using the diameter instead of the radius in the area formula. Area uses pi times radius squared, not diameter squared. If you have the diameter, divide it by 2 first.
- Forgetting to square the radius. The area formula is pi times r times r, not pi times r.
- Confusing circumference with area. Circumference is the distance around the circle (2 times pi times r), while area is the space inside it (pi times r squared).