Mathematical formula circle

A circle’s area is A = πr², and its circumference is C = 2πr. The radius r runs from the center to the circle. The diameter is twice the radius, so circumference can also be written C = πd.

Meaning and context

Choose the formula for the quantity requested. Area measures the enclosed region and uses square units. Circumference measures the boundary length and uses ordinary length units. Confusing the two produces a different answer and a different unit.

Examples and usage

For a radius of 5 cm, the area is 25π cm², approximately 78.54 cm². The circumference is 10π cm, approximately 31.42 cm. If the given five centimeters were a diameter instead, both calculations would change.

What to check

Keep π in an exact answer when requested, and round only at the end for a decimal result. The formulas assume an ideal circle. An oval or irregular round outline is not generally described by one radius and these same formulas.

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