How to Calculate the Area of a Circle With the Diameter

By Jessica Smith
The area formula can be used on circles of any size.

Finding the area of a circle requires a short formula. But not every problem or assignment will give you all the pieces you'll need to use the formula. You can take the information that you have, including the diameter, and figure out what you'll need to solve for area. Once you understand these steps, you can find the area of any circle, regardless of its size.

The Area formula

The area of a circle can be found using the formula: A = pi(r^2), where the "^" symbol indicates that the No. 2 is an exponent. You can read this as: Area equals pi times the radius squared. The value of pi is often approximated as 3.14. In the area formula, the radius is a segment inside a circle that goes from the center to one edge. Before you can use the area formula, check whether you have the diameter or the radius of your circle. The radius only goes halfway across the circle, but the diameter goes all the way across from one side to the other, passing through the center.

Converting Diameter to Radius

If you only have the diameter of a circle, convert it to the radius. Do not try to find area until you convert the diameter to the radius. A radius is half the length of the diameter. Divide the diameter by 2 to get the radius, for example: A circle with a diameter of 10 would have a radius of 5. A circle with a diameter of 1,050 would have a radius of 525.

Substitute the Values

Once you have found the radius, go back to the area formula. For example, suppose you want to find the area of a circle with a diameter of 18 centimeters. You have the radius of 9, so substitute it into the formula, as follows: A = pi(r^2), so A = (3.14)(9^2). Remember that squaring a number means multiplying it times itself, so 9 squared is 9 times 9.

Simplify to Solve

Once you have substituted the values into the formula, simplify to find the solution, as follows:

  • A = pi(r^2)
  • A = (3.14) (9^2)
  • A = (3.14) (9 * 9)
  • A = (3.14) (81)
  • A = 254.41 centimeters^2

As long as you begin by carefully identifying whether you have diameter or a radius, you can apply the area formula to any circle using these steps.

About the Author

With hands-on experience in the traditional classroom, the online setting, and the world of curriculum development, Jessica Smith is a veteran educator who is passionate about learning. Smith earned a M.Ed. in curriculum and instruction from Concordia University and is certified in mathematics and exceptional student education.