Geometry desk
Circle Circumference Calculator
Find the circumference of a circle from its radius.
Circle Circumference Calculator: Find the length of one complete trip around a circular edge. Supply the radius to calculate circumference in the same length unit, for example when estimating a band around a round container or the ideal distance travelled in one wheel revolution. Runs 100% locally in your browser with zero server file uploads.
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- Calculators
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Circumference
31.416 cm
Circumference = 2 × π × radius- Dimensions are measured in the same unit.
- Values must be finite and greater than zero.
Formula and worked example
Circumference = 2 × π × radius
A worked example with sample values:
| Inputs | |
|---|---|
| Radius | 5 cm |
| Results | |
|---|---|
| Circumference | 31.416 cm |
The constant ratio around every circle
Write C for circumference, r for radius and d for diameter. π is the ratio C ÷ d for a circle, so multiplying by d gives C = πd. Substituting d = 2r gives C = 2 × π × r. Similar circles have the same ratio: enlarging the radius stretches the entire boundary by that scale factor.
With radius 5 cm, first double it to get diameter 10 cm. Then C = π × 10 = 31.415926… cm. The result sheet shows Circumference = 31.416 cm. Keep π until the final step; using 3.14 earlier would instead give 31.4 cm.
OpenStax's circle lesson (https://openstax.org/books/prealgebra-2e/pages/9-5-solve-geometry-applications-circles-and-irregular-figures) sets out this radius-and-diameter relationship. A wheel model assumes a perfect circle without slipping or deformation.
From a full boundary to a shorter arc
An arc covering one quarter of a circle has length C ÷ 4, so the example's quarter arc is about 7.854 cm. For an angle θ in degrees, arc length is C × θ ÷ 360. This arc calculation must be done separately; the widget always reports the complete circumference. Convert a final length using ordinary length factors: 31.416 cm is 0.31416 m. Changing the menu to m leaves the radius number untouched, so enter the converted radius yourself.
How to use it
- Enter positive dimensions in the same unit.
- Choose the unit used for every dimension.
- Calculate, then review the result and formula.
Privacy & limitations
Every value and calculation stays in your browser. No dimensions are uploaded or sent to an external service.
Related tools
Frequently asked questions
Can I use a diameter to calculate circumference?
Yes, by converting it to radius before entering it. Diameter d is twice radius r, so C = πd and C = 2πr describe the same boundary. A diameter of 10 cm needs a radius entry of 5 cm.
What radius matches a measured circular perimeter?
Divide the circumference by 2π: r = C ÷ (2π). For a perimeter of 10π cm, the radius is 5 cm. Dividing by π alone gives the diameter, which is twice the radius.
Why is circumference in cm rather than cm²?
It measures a line around the edge, not the enclosed region. A tape laid along that edge measures length. Square units belong to circle area, so a value in cm² cannot be used directly as a circumference.
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