How to Find the Radius of an Ellipse

By Chance E. Gartneer; Updated April 24, 2017

Finding the radius of an ellipse is more than just a single simple operation; it's two simple operations. The radius is the line from the center of an object to its perimeter. An ellipse, which is like a circle that has been elongated in one direction, has two radii: a longer one, the semimajor axis, and a shorter one, the semiminor axis. These two radii are calculated using the focal points, which are two points that are equidistant of the ellipse's center, and a point on the ellipseā€™s perimeter.

Measure the distance in between the two focal points and then square it. For this example, the distance between the focal points, or foci, is 6. The square of 6 is 36.

Measure the distance of the point on the perimeter from each of the foci. For this example, the point is 4 from one focal point and 6 from the other.

Add the two distances calculated in Step 2 together and then square that sum. For this example, 4 added to 6 equals 10, and the square of 10 is 100.

Subtract the square of the foci length from the square calculated in Step 3 and then calculate the square root of that sum. For this example, 36 subtracted from 100 equals 64, and the square root of 64 is 8.

Halve the amount calculated in Step 4 to find the semiminor axis. For this example, half of 8 is 4. The semiminor axis is 4.

Add the distances from a point on the perimeter to each of the foci together and halve that sum to find the semimajor axis. These are the same distances calculated in Step 2. For this example, 6 added to 4 results in 10. Half of 10 is 5; the semi-major axis is 5.

About the Author

Chance E. Gartneer began writing professionally in 2008 working in conjunction with FEMA. He has the unofficial record for the most undergraduate hours at the University of Texas at Austin. When not working on his children's book masterpiece, he writes educational pieces focusing on early mathematics and ESL topics.