How do you calculate ellipse area?

Multiply pi by the semi-major axis and the semi-minor axis:.

Do I enter full axes or semi-axes?

Enter semi-axes. If the full major axis is 10 and the full minor axis is 6, enter 5 and 3.

Why is ellipse perimeter approximate?

The exact perimeter is not an elementary formula. This calculator uses Ramanujan's accurate approximation.

What is eccentricity?

Eccentricity measures how stretched an ellipse is. A circle has eccentricity 0; values closer to 1 are more elongated.

Ellipse Area Calculator

Calculate ellipse area from semi-major and semi-minor axes, with Ramanujan perimeter estimate, eccentricity, focal distance, and a visual sketch.

Semi-major axis (m)

Semi-minor axis (m)

Unit

Enter semi-axes, not full diameters. If you know the full axes, divide each value by two first.

Area uses the two semi-axes; perimeter is shown with the Ramanujan II approximation.

Ellipse area from semi-axes

English SERPs for ellipse area calculator usually expect the simple semi-major and semi-minor axis formula, with perimeter and eccentricity as helpful checks rather than the primary task.

A = π ab

A is ellipse area; a is semi-major axis; b is semi-minor axis.

Enter the semi-axes, not the full width and height. If you know full axes, divide each by two first.

Additional ellipse values

c = a^{2} - b^{2}

c is the distance from the center to each focus.

e = \frac{c}{a}

e is eccentricity, a unitless measure of how stretched the ellipse is.

P \approx π (a + b) (1 + \frac{3 h}{10 + 4 - 3 h})

P is Ramanujan's perimeter approximation; exact ellipse perimeter uses an elliptic integral.

Example

Semi-major axis	Semi-minor axis	Area
5	3	47.1239 square units
10	4	125.6637 square units
2	2	12.5664 square units

If both semi-axes are equal, the ellipse is a circle and the formula becomes the standard circle area formula.

Frequently Asked Questions

Sources and References

Calculations are based on the listed reference sources. Links open in a new tab.

Updated: June 2, 2026

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