Circle perimeter calculator

What is the circle perimeter calculator?

The perimeter of a circle is the length of its boundary — the distance you would travel going once all the way around it. For a circle this perimeter has a special name, the circumference, but it means exactly the same thing as the perimeter of any other shape. This calculator turns any single circle measurement into the perimeter, and fills in the rest of the circle’s properties at the same time.

Enter any one of the four quantities — radius, diameter, perimeter, or area — and the calculator instantly derives the other three. That makes it handy whether you measured the distance across a round table and want the distance around its edge, or you know the area of a circular lawn and need to know how much edging to buy.

Radius

The radius $(r)$ is the distance from the center of the circle to any point on its edge. Every other property of the circle can be built from it.

Diameter

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

Perimeter

The perimeter $(P)$, also called the circumference, is the total length of the circle’s boundary. It is given by $P = 2\pi r$.

Area

The area $(A)$ is the flat space enclosed inside 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 $\pi \approx 3.14159$ ties them together. Behind the scenes 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. Perimeter from radius:

   $$P = 2\pi r$$

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 perimeter:

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

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:

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

Example 2: From the diameter

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

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

Example 3: From the perimeter

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:

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

Practical notes

• Units: The radius, diameter, and perimeter 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.
• Naming: “Perimeter” and “circumference” describe the same length for a circle. The word circumference is reserved for circles, while perimeter applies to any closed shape.

Frequently asked questions

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

Use $P = 2\pi r$:

$$P = 2\pi \times 7 \approx 43.98 \text{ cm}$$

How do I find the perimeter from the diameter?

Multiply the diameter by $\pi$, since $P = \pi d$:

$$P = \pi d$$

Is the perimeter of a circle the same as its circumference?

Yes. For a circle the two terms are interchangeable: both name the length of the outer boundary. Circumference is simply the traditional word used for the perimeter of a round shape.

Can I find the perimeter starting from the area?

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