Area of Circle Formula

This figure illustrates the area of circle formula.

formula

summary

The area of a circle is given by mutiplied by the circle constant (tau) multiplied by the radius of the circle squared.

Expression Description
The area of the circle.
The circle constant (tau), 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 traditional circle area formula.

usage

The area of a circle is given by mutiplied by the circle constant (tau) 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:

Examples

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.

Steps
  1. Substitute the length of the radius into the formula.

  2. Evaluate the exponent expression and simplify.

  3. Substitute the value of into the expression.

  4. Evaluate the multiplication.

  5. The area of a circle of radius is approximately units squared.

Circle of Radius 2

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

Steps
  1. Substitute the length of the radius into the formula.

  2. Evaluate the exponent expression and simplify.

  3. Simplify the fraction.

  4. Substitute the value of into the expression.

  5. Evaluate the multiplication.

  6. The area of a circle of radius is approximately units squared.

Circle of Radius 3

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

Steps
  1. Substitute the length of the radius into the formula.

  2. Evaluate the exponent expression and simplify.

  3. Substitute the value of into the expression.

  4. Multiply the fraction by the value of .

  5. The area of a circle of radius is approximately units squared.