Area of Circle π (pi) Formula

This figure illustrates the area of circle formula using the constant π (pi).

Formula

Summary

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

Usage

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.

Area of Circle Radius 1

Circle of Radius 1

To calculate the area of a circle given a radius of one, set up the equation for the area of the circle and substitute the value of the radius into the equation.

  1. Set up the formula and subsitute the radius in for the variable .

  2. Evaluate the exponent expression.

  3. Evaluate the multiplication expression.

  4. The area of the circle is equal to units squared or approximately units squared.

Area of Circle Radius 2

Circle of Radius 2

To calculate the area of a circle given a radius of one, set up the equation for the area of the circle and substitute the value of the radius into the equation.

  1. Set up the formula and subsitute the radius in for the variable .

  2. Evaluate the exponent expression.

  3. Evaluate the multiplication expression.

  4. The area of the circle is equal to units squared or approximately units squared.