Ellipse Foci Calculator

How to Use This Calculator

1. Enter the length of the semi-major axis (a) of your ellipse. This is the longest radius from the center to the ellipse edge.
2. Enter the length of the semi-minor axis (b) of your ellipse. This is the shortest radius from the center to the ellipse edge.
3. Click the "Calculate" button to compute the distance from the center to each focus (c).
4. The calculator will display the foci distance (c) based on the formula c² = a² - b².

Understanding the Formula

The foci of an ellipse are two fixed points inside the ellipse such that the sum of the distances from any point on the ellipse to the two foci is constant. The distance from the center of the ellipse to each focus is calculated using the formula:

c² = a² - b²

Where:

• c = distance from center to each focus
• a = semi-major axis (the longer radius)
• b = semi-minor axis (the shorter radius)

Example

If you have an ellipse with a semi-major axis of 5 units and a semi-minor axis of 3 units:

1. a = 5
2. b = 3
3. c² = 5² - 3² = 25 - 9 = 16
4. c = √16 = 4

This means the distance from the center of the ellipse to each focus is 4 units.