Formulas & tables/Mathematics/Plane geometry/Circumference of a circle

Circumference of a circle

L=2πrL=2\pi r

Result unit: length units

What it describes

The length of a circle of radius rr.

Symbols

LL
circumference (length of the circle)
rr
radius

Where it comes from

The circumference is directly proportional to the radius. The constant π\pi is the ratio of the circumference to the diameter.

When to use it

Circumferences of circles, arc lengths, circular motion.

Example

The radius is r=5r=5. Find the circumference of the circle.
Substitutionr=5r=5.
ResultL=2π⋅5=10π≈31.4L=2\pi\cdot5=10\pi\approx31.4.

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