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Circumference Formula

The circumference is the perimeter of a circle—the total distance around its outer boundary. Finding the circumference is a classic geometry problem used in construction, design, and manufacturing. For a fast calculation, use the circumference calculator to compute the distance using either the radius or diameter.

6 min read

Blake Boege
Blake BoegeFounder, Calculator AnswersPublished May 29, 2026

What is the circumference formula?

The circumference formula calculates the boundary length of a circle. Because a circle's perimeter is always proportional to its width, the formula relies on the constant value Pi (π).

You can calculate circumference using one of two standard formulas, depending on whether you know the circle's radius or its diameter.

The circumference formulas

The two equivalent formulas for finding the circumference are:

Formula 1: Using Radius

C = 2πr

Formula 2: Using Diameter

C = πd

The variables

  • C = circumference
  • r = radius (distance from center to edge)
  • d = diameter (distance all the way across)
  • π = Pi (constant value ≈ 3.14159)

Because the diameter of a circle is exactly double the radius (d = 2r), both equations represent the exact same geometric relationship.

Worked example: Calculating circumference

Let's find the circumference of a circular pool that has a radius of 7 feet. We will use the radius formula (C = 2πr) and approximate Pi as 3.14159.

  1. Identify the radius: r = 7 ft.
  2. Set up the equation: C = 2 × π × 7.
  3. Multiply the numbers: C = 14 × π.
  4. Multiply by Pi: C ≈ 14 × 3.14159 = 43.98 ft.

The pool's circumference is approximately 43.98 feet.

Common circumference mistakes

  • Confusing radius and diameter. If you are given a diameter of 10 inches and plug it into 2πr as the radius, you will double the correct answer. Double check which measurement you have before selecting a formula.
  • Confusing circumference and area. The formula for area is A = πr², which calculates the flat space inside. The circumference is C = 2πr, which measures the boundary length.
  • Rounding Pi too early. Using just "3" or "3.1" for Pi causes rounding errors on larger circles. Use 3.14159 or the π key on your calculator.

Working it out by hand, from a radius

A circle of radius 5 cm, worked through with every value shown.

  1. Write the formula. C = 2 × π × r.
  2. Double the radius. 2 × 5 = 10.
  3. Multiply by π. 10 × 3.14159 = 31.4159 cm.
  4. Round for the job. 31.4 cm is enough for most work, and 31.42 cm for anything that has to fit.

Working it out by hand, backwards from a tape measure

This is the harder direction and the one that comes up in practice. You can put a tape around a tree or a pipe; you usually cannot measure straight through the middle of it. Say the tape reads 47.1 cm.

  1. Start from C = π × d and rearrange to d = C ÷ π.
  2. Divide. 47.1 ÷ 3.14159 = 14.9924 cm.
  3. So the diameter is about 15 cm, and the radius is half of that: 7.4962 cm.
  4. Check by going forwards. 2 × 3.14159 × 7.4962 = 47.0999, which is the tape reading back again.

That last step is worth the habit. Running the calculation in reverse catches a misplaced decimal point immediately, and costs one multiplication.

How much precision in Pi you actually need

Each row is the circumference of a 10 metre diameter circle computed with a different value of π, against the error that introduces.

Value usedC for d = 10 mOff by
330.0000 m1.42 m
22/731.4286 m13 mm
3.1431.4000 m16 mm
3.141631.4160 m0.07 mm
3.1415926531.4159265 munder a micron

Note that 22/7 and 3.14 are wrong by similar amounts in opposite directions: 22/7 is high and 3.14 is low. Neither is better than the other, and both are fine for anything measured with a tape.

Where the arithmetic usually goes wrong

  • Using the diameter in C = 2πr. The most common error by a distance, and it doubles the answer. If you have a diameter, the formula is C = πd with no 2 in it.
  • Squaring the radius. That is the area formula. Circumference has one factor of r, not two.
  • Mixing units mid-calculation. A radius in centimetres and an answer wanted in metres needs the conversion done once, at the end, not halfway through.
  • Rounding π before multiplying. Rounding at the end costs nothing; rounding at the start propagates.

What this guide does not cover

It covers circles, and only the distance around them.

  • Ellipses and ovals. There is no exact elementary formula for the perimeter of an ellipse, only approximations, and nothing here applies to one.
  • Area. A different formula with a different shape, covered by the area calculator.
  • Arc length and sectors. Part of a circumference rather than all of it, and the arc length guide is the page for that.
  • Solving from an area. The circumference calculator takes a radius or a diameter. Going from an area is the circle calculator's job.

Run the numbers

Explore circle and geometry calculators to verify your answers:

Circumference Calculator

Find a circle's circumference from its radius or diameter, with the pi step shown in the working.

Open

Circle Calculator

Solve for area, radius, diameter, or circumference in one step.

Open

Area Calculator

Calculate flat surfaces for circles, rectangles, triangles, and other shapes.

Open

Frequently asked questions

The distance around the outside edge of a circle. It is the circle's version of a polygon's perimeter, and it is a length rather than an area: it is measured in centimetres or inches, not in square ones.

C = 2πr from the radius, or C = πd from the diameter. They are the same formula, because the diameter is twice the radius. Use whichever measurement you actually have rather than converting first.

The ratio of a circle's circumference to its diameter, the same for every circle. It is irrational, so it has no exact decimal, and 3.14159265 is the value used throughout this guide.

The radius runs from the centre to the edge; the diameter runs all the way across through the centre. The diameter is exactly twice the radius, so d = 2r and r = d / 2. Measuring a diameter is usually easier in practice because you do not have to find the centre.

Yes, for rough work. 22/7 is 3.142857..., which rounds to 3.1429 rather than the 3.1428 this page used to print. It is high by about 0.04%, so on a circle of circumference 100 it puts you out by four centimetres. Fine for a school exercise, not for anything that has to fit.

Multiply by π. A 10 cm diameter gives 10 × 3.14159 = 31.4159 cm. This is the shortest version of the calculation and the one to use when you can measure straight across.

Divide by π. A tape reading 47.1 cm around gives 47.1 ÷ 3.14159 = 14.99 cm across, so a 15 cm diameter. This is how you size a pipe or a tree you cannot cut in half.

Divide by 2π, which is 6.28319. A circumference of 31.4159 cm gives 31.4159 ÷ 6.28319 = 5 cm. Or divide by π first and halve the result, which is the same arithmetic in two steps.

2 × 3.14159 × 5 = 31.4159 units. Doubling the radius to 10 doubles the circumference to 62.8319: circumference grows in direct proportion to radius, which is not true of area.

Because circumference has one factor of r and area has two. C = 2πr is linear in r, so twice the radius is twice the distance around. A = πr² is quadratic, so twice the radius is four times the space inside. It is the single most useful thing to know about the two formulas.

Fewer than you think. At 3.14 you are within 0.05% of the true value, which on a 10 metre circle is 5 millimetres. At 3.14159 you are within 0.0000085%. NASA uses about fifteen digits for interplanetary navigation; a workshop needs three or four.

About 40,075 km around the equator. Working backwards, that gives a radius of 40,075 ÷ 6.28319 = 6,378 km, which is the equatorial radius. The same two-step arithmetic as a tree trunk, at a different scale.

No. An ellipse has no exact elementary formula for its perimeter, only approximations, and applying C = 2πr to one will be wrong by an amount that grows with how elongated it is. The formulas here are for circles only.

Whatever units you put in. Pi is a pure ratio with no units of its own, so a radius in inches gives a circumference in inches and a radius in metres gives metres. Mixing units in one calculation is the most common way to get a plausible wrong answer.

For a circle, yes, and circumference is simply the word used for it. Perimeter is the general term for the distance around any closed shape; circumference is reserved for circles and for a few other curved figures.

The circumference calculator takes a radius or a diameter and shows each step, so you can compare its intermediate values against yours rather than only the final figure. It is linked at the end of this guide.
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