Circle Calculator

A Circle Is Built From One Number

Every circle is built from a single measurement - the radius, the distance from the center to the edge. Everything else follows from it:

• The diameter is the distance all the way across through the center - exactly two radii ($d = 2r$).
• The circumference is the distance around the outside (the circle’s perimeter).
• The area is the amount of space inside.

The picture by the calculator shows the radius (the solid line from the center) and the diameter (the dashed line all the way across). Enter any one measurement and the tool finds the other three.

Where π comes in

Walk all the way around any circle and you will have travelled about 3.14 times its diameter. That number is π (pi), and it is the same for every circle, big or small - which is why it shows up in both the circumference and the area. Use the π value switch above the figure to pick 22/7, 3.14, or full π so your answer matches your class.

Circle Formulas

$$d = 2r \qquad C = 2\pi r = \pi d \qquad A = \pi r^2$$

Working backward for the radius:

$$r = \sqrt{\frac{A}{\pi}} \qquad r = \frac{C}{2\pi}$$

How to Use It

1. Choose what you know (radius, diameter, circumference, or area).
2. Enter its value.
3. Read the radius, diameter, circumference, and area.

Worked Examples

Known	Value	Radius	Diameter	Circumference	Area
Radius	5	5	10	31.42	78.54
Diameter	10	5	10	31.42	78.54
Radius	7	7	14	43.98	153.94

FAQ

How do you find the area of a circle?

Use $\text{area} = \pi \times r^2$. For a radius of 5: $\pi \times 25 \approx 78.54$.

How do you find the circumference?

Use $\text{circumference} = 2 \times \pi \times r$ (or $\pi \times \text{diameter}$). For a radius of 5: $\approx 31.42$.

Can I start from the area or circumference?

Yes. Pick what you know and the tool works backward — for example, the radius from an area is $\sqrt{\text{area} / \pi}$.