Circumference and area of a circle calculator

What is the circumference and area of a circle calculator?

A circle is described completely by a single number. Once you know its radius, every other property of the circle follows from it. This calculator captures that idea: type in any one of the four quantities — radius, diameter, circumference, or area — and the other three are filled in instantly.

The tool is useful whenever you measure one feature of a round object and need the rest. You might tape-measure the distance around a pipe (its circumference) and want its diameter, or know the area a circular flower bed should cover and need to know how wide to dig it.

Radius

The radius $(r)$ is the distance from the center of the circle to any point on its edge. It is the building block for every other formula on this page.

Diameter

The diameter $(d)$ runs straight across the circle through its center, so it is exactly twice the radius: $d = 2r$.

Circumference

The circumference $(C)$ is the length of the circle’s outer boundary — the distance you would walk all the way around it. It is given by $C = 2\pi r$.

Area

The area $(A)$ is the amount of flat space enclosed by the circle, found with $A = \pi r^2$.

How does the calculator work?

The calculator keeps the four fields synchronized. Whichever field you edit last is treated as the known value, and the constant $\pi \approx 3.14159$ links them together. Internally every value is first reduced to the radius, and then the remaining quantities are produced from it.

Formulas

Starting from the radius, the relationships are:

1. Diameter from radius:

   $$d = 2r$$

2. Circumference from radius:

   $$C = 2\pi r$$

3. Area from radius:

   $$A = \pi r^2$$

When you supply a different quantity, the formulas are rearranged to solve for the radius first:

1. Radius from diameter:

   $$r = \frac{d}{2}$$

2. Radius from circumference:

   $$r = \frac{C}{2\pi}$$

3. Radius from area:

   $$r = \sqrt{\frac{A}{\pi}}$$

Examples

Example 1: From the radius

Suppose a circle has a radius of 10 cm. Then:

$$d = 2 \times 10 = 20 \text{ cm}$$ $$C = 2\pi \times 10 \approx 62.83 \text{ cm}$$ $$A = \pi \times 10^2 \approx 314.16 \text{ cm}^2$$

Example 2: From the diameter

A circle is measured across the middle as 20 cm. Halving gives the radius, and the rest follow:

$$r = \frac{20}{2} = 10 \text{ cm}$$ $$C = 2\pi \times 10 \approx 62.83 \text{ cm}$$ $$A = \pi \times 10^2 \approx 314.16 \text{ cm}^2$$

Example 3: From the circumference

A circular track measures about 62.83 m around. Solve for the radius first:

$$r = \frac{62.83}{2\pi} \approx 10 \text{ m}$$ $$d = 2 \times 10 = 20 \text{ m}$$ $$A = \pi \times 10^2 \approx 314.16 \text{ m}^2$$

Example 4: From the area

A round plot covers about 314.16 m². Work back to the radius:

$$r = \sqrt{\frac{314.16}{\pi}} \approx 10 \text{ m}$$ $$d = 2 \times 10 = 20 \text{ m}$$ $$C = 2\pi \times 10 \approx 62.83 \text{ m}$$

Practical notes

• Units: Lengths (radius, diameter, circumference) share length units, while the area uses squared units. Pick units that match your measurement; the calculator converts between them automatically.
• Precision: Results use $\pi \approx 3.14159$. For most everyday tasks two or three decimal places are more than enough.
• Scaling: Because area depends on the radius squared, doubling the radius does not double the area — it multiplies it by four.

Frequently asked questions

What is the area of a circle with a 7 cm radius?

Use $A = \pi r^2$:

$$A = \pi \times 7^2 \approx 153.94 \text{ cm}^2$$

How do I get the diameter from the circumference?

Divide the circumference by $\pi$, since $C = \pi d$:

$$d = \frac{C}{\pi}$$

Why does the area use the radius squared?

The area grows with the square of the radius because it measures a two-dimensional region. Each unit added to the radius adds proportionally more enclosed space, so area increases faster than the radius itself.

Can I start from the area to find the circumference?

Yes. The calculator first recovers the radius with $r = \sqrt{A / \pi}$ and then computes $C = 2\pi r$. For a related single-purpose tool, see the circle area calculator and the circumference calculator.