Calculate the circumference of circles

Circumference is the distance around a circle, determined by the constant ratio of circumference to diameter, $\pi$ , so it can be calculated as $C=\pi d$ or $C=2\pi r$ . The calculation requires distinguishing radius from diameter, interpreting $\pi$ as either an exact constant or a suitable decimal approximation, and reporting a result in linear units; this understanding supports proportional reasoning and later work with circle area, but does not include arc length or sector measures.

Detailed Explanation: Calculate the circumference of circles

The circumference of a circle is the distance around it.

Use one of these formulas:

If you know the diameter $d$ :

C=\pi d

If you know the radius $r$ :

C=2\pi r

Remember that the diameter is twice the radius: $(d=2r)$ . The answer must be in linear units, such as centimetres or metres.

Example

A circle has a radius of $(6\text{ cm})$ . Find its circumference.

Step 1: Choose the formula.

The radius is given, so use

C=2\pi r

Step 2: Substitute the radius.

C=2\pi(6)

Step 3: Simplify.

C=12\pi\text{ cm}

This is the exact circumference. Using $\pi\approx3.14$ ,

C\approx12(3.14)=37.68\text{ cm}

So the circumference is

\boxed{12\pi\text{ cm}\approx37.7\text{ cm}}

Use $\pi$ when an exact answer is requested, and use a decimal approximation when a rounded answer is requested.

Learn by doing: Calculate the circumference of circles

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Circumference from Diameter - to Pi Value

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