How to Find a Circumference

Determining the circumference of a circle can be compared to determining the perimeter of any polygon. The circumference is simply the distance around the outside of the circle. Instead of having sides to add together like on a polygon, however, how to find a circumference of a circle includes using a formula based on the length of the diameter or the radius of the circle.

What is the Diameter of a Circle?

Imagine a pie of any flavor. One slice cuts the pie directly in half, giving two people very large pieces. The line that cuts the pie directly in half is the diameter of the circle. It goes all the way across the circle in a straight line, effectively cutting the circle into two equal halves.

What is the Radius of a Circle?

Imagine the same pie is cut again, this time into quarters or more. All of the pieces end in a point, with the point shared between all of them in the exact center of the pie. The length of the pieces from the outside of the pie to the center point is the radius. It goes halfway across the pie, meaning it’s half the length of the diameter.

Finding the Diameter or the Radius

If the diameter is known, simply divide this in half to find the radius of the circle. If the radius is known, it’s possible to simply multiply it by two to determine the diameter. The radius will always be half of the diameter of the circle.

Determining the Circumference Based on the Diameter

If the diameter of the circle is known, it’s possible to find the circumference of the circle using pi (π). Pi is the ratio between the circumference of the circle and the diameter. Pi is infinite, but can be rounded to the first two decimal points, 3.14, to make it easier to solve for the circumference. To determine the circumference when the diameter is known, multiply 3.14 times the diameter. Written out, the formula is C=πd.

If a circle has a diameter of 7, use C=π(7) to find the circumference. In this case, the circumference of the circle would be 21.99.

Determining the Circumference Based on the Radius

If the diameter is not known, but the radius is known, it’s possible to solve using the same formula. In this case, the student should find the diameter first. Then, they can use C=πd to solve for the circumference. If the radius is 3, for example, the diameter would be 6. This means the circumference would be 18.85.

Alternatively, the circumference can be found by using the formula C=2πr. In this case, the above calculations are done in one step instead of two different ones. If the circle has a radius of 9, the formula would be done as C=2π(9). Solved, this equals 56.55.

When either the radius or the diameter is known, it is possible for a student to find the circumference of a circle. This can tell them how big around the circle is and can be necessary for more advanced calculations of the circle.