Area of Circle Formula

Formula

Summary

This formula calculates the area of a circle in terms of the geometric constant (pi). This is the traditional form of the area of a circle formula, see the alternative formula in terms of the circle constant (tau).

Expression	Description
	The area of the circle.
	The geometric constant (pi), where
	The radius of the circle.

Note: This website uses the constant (tau) instead of (pi) as the default circle constant. The substitution can be used to translate between the two constants. See this page for the area of the circle in terms of (tau).

How to use

The area of a circle is given by the constant (pi) multiplied by the radius of the circle squared. For example, to find the area of a circle with a radius of length 5 the formula is:

Substituting the value of into the formula, approximately , and evaluating the multiplication gives the area of the circle

The area of a circle with radius length is approximately units squared.

Explanation

The area of the circle formula can be derived using calculus^[1] or using a visual proof^[2].

References

Derive Area of Circle Formula Example

https://wumbo.net/examples/derive-area-of-circle-formula/
Area of Circle Visual Proof Example

https://wumbo.net/examples/derive-area-of-circle-visual-proof/