How to Calculate Circumference in Feet

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The circumference of a circle is how far you'd walk if you started at one point on the circle and then walked all the way around the circle until you got back to the starting point. As you might imagine, there are lots of reasons you can't actually walk around most circles, measuring as you go. So instead, you'll almost always calculate a circle's circumference based off its radius or its diameter.

TL;DR (Too Long; Didn't Read)

To calculate circumference (C) from a circle's diameter, multiply the diameter by π, or C = π_d_. To calculate circumference from a circle's radius, multiply the radius by 2, and then multiply the result by π, or C = 2_r_π. If you need to convert into feet from another unit of measure, you can do it before or after performing this calculation; just make sure you always label your calculations with the units of measure used.

Calculating Circumference From Diameter

If you know the circle's diameter, multiply that number by π (pi) to get the circle's circumference. The value of π has been calculated to more than 22 trillion digits, but most teachers will let you abbreviate it to 3.14. Sometimes for construction or engineering work – or simply for the sake of the challenge – you may be asked to use 3.1416 or perhaps even more digits. So if the diameter of your circle is 10 feet, you'd calculate:

10 × 3.14 = 31.4 \text{ feet}

as the circumference, or

10 × 3.1416 = 31.416 \text{ feet}

if you're asked for a more exact answer.

Calculating Circumference From Radius

If you only know the radius of the circle, you're in luck: The radius is always half the diameter. So multiply that radius by 2, and then multiply the result by π to get the circle's circumference. If the radius of your circle is 3 feet, for example, its diameter is 3 × 2 = 6 feet; and the circumference is then:

6 × 3.14 = 18.84 \text{ feet}

Or

6 × 3.1416 = 18.8496 \text{ feet}

if you're asked for a more exact answer.

Warnings

  • Always check your units of measure. If the original measurements you worked from aren't in feet, either convert them to feet first or work out the circumference first (remembering to label that answer with whatever unit of measure you're using), and then convert the result to feet.

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