What is the formula for circumference?

Circumference is the distance around a circle, and it equals C = 2πr, where r is the radius. Since the diameter d equals 2r, you can also write it as C = πd — both give the same result. For example, a circle with a radius of 5 has a circumference of 2 × π × 5 ≈ 31.42.

How do I find circumference from the diameter?

Use C = πd: multiply the diameter by π (about 3.14159). A wheel 20 inches across has a circumference of π × 20 ≈ 62.83 inches. In this tool, switch the toggle to Diameter and type the value — it converts to radius internally (r = d/2) and shows the result.

What value of π does this calculator use?

It uses your device's built-in full-precision value of π (about 3.14159265358979), not a rounded 3.14 or 22/7. That keeps results accurate to many decimal places, which matters most on large circles where rounding π early would introduce a visible error.

What is the difference between circumference and area?

Circumference is the perimeter — the one-dimensional distance around the edge (C = 2πr) — while area is the two-dimensional space inside the circle (A = πr²). They answer different questions: circumference tells you how much edging to buy, area tells you how much surface to cover. This calculator shows both.

What units does the circumference come out in?

The circumference comes out in the same unit you entered. If you type a radius in centimetres, the circumference is in centimetres, and the area is in square centimetres. The tool doesn't assume any unit, so just keep your input consistent.

Circumference Calculator | Free Online Tool

How to use

1.Pick Radius or Diameter, then type the measurement of your circle into the input.
2.Read the circumference instantly below — it updates as you type, with no button to press.
3.Check the extras: area (πr²) plus the matching radius and diameter, all in your unit.

About Circumference Calculator

The circumference of a circle is the distance around its edge, and it equals C = 2πr, where r is the radius. Because the diameter d is twice the radius (d = 2r), the same value can be written as C = πd. Enter either measurement above and this calculator returns the circumference the moment you type, along with the area and the matching radius and diameter.

Why does the formula work? π (pi) is defined as the ratio of any circle's circumference to its diameter: π = C ÷ d ≈ 3.14159. Rearranging that definition gives C = πd directly, and substituting d = 2r turns it into C = 2πr. The two forms are identical — pick whichever matches the number you have. If you know the radius (the distance from the centre to the edge), use 2πr; if you know the diameter (the full width through the centre), use πd.

π is an irrational number, so its decimal expansion never ends or repeats. For quick mental math people often use 3.14 or the fraction 22/7, but this tool uses the full-precision value built into your device, so results are accurate to many decimal places. That precision matters when a small radius error is multiplied across a large circle.

The radius and diameter are tightly linked: r = d ÷ 2 and d = 2r. Switch the input toggle to enter whichever you have — the calculator converts internally (r = d/2) and reports both. It also shows the area, A = πr², so you can compare the two most common circle measurements side by side without a second tool.

Circumference comes up constantly in real work. You need it to cut the right length of edging, trim, or weatherstrip for a round table or window; to size a belt, pulley, or O-ring; to work out how far a wheel travels in one rotation (one turn covers exactly one circumference); to lay out a circular garden bed or running track; and in geometry homework where the perimeter of a circle is asked for. Engineers, machinists, seamstresses, and students all reach for the same 2πr.

A few edge cases: a radius of 0 describes a single point, so its circumference is 0. Negative lengths are rejected because a radius or diameter is a physical distance. Every unit stays the length unit you entered — feed centimetres and the circumference is in centimetres, while the area comes back in square centimetres. Everything runs locally in your browser, so nothing you type is uploaded.

Frequently asked questions

What is the formula for circumference?: Circumference is the distance around a circle, and it equals C = 2πr, where r is the radius. Since the diameter d equals 2r, you can also write it as C = πd — both give the same result. For example, a circle with a radius of 5 has a circumference of 2 × π × 5 ≈ 31.42.
How do I find circumference from the diameter?: Use C = πd: multiply the diameter by π (about 3.14159). A wheel 20 inches across has a circumference of π × 20 ≈ 62.83 inches. In this tool, switch the toggle to Diameter and type the value — it converts to radius internally (r = d/2) and shows the result.
What value of π does this calculator use?: It uses your device's built-in full-precision value of π (about 3.14159265358979), not a rounded 3.14 or 22/7. That keeps results accurate to many decimal places, which matters most on large circles where rounding π early would introduce a visible error.
What is the difference between circumference and area?: Circumference is the perimeter — the one-dimensional distance around the edge (C = 2πr) — while area is the two-dimensional space inside the circle (A = πr²). They answer different questions: circumference tells you how much edging to buy, area tells you how much surface to cover. This calculator shows both.
What units does the circumference come out in?: The circumference comes out in the same unit you entered. If you type a radius in centimetres, the circumference is in centimetres, and the area is in square centimetres. The tool doesn't assume any unit, so just keep your input consistent.

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