What is the formula for the area of an ellipse?

The area of an ellipse is A = π × a × b, where a is the semi-major axis (half the longest diameter) and b is the semi-minor axis (half the shortest diameter). If a = b, the ellipse becomes a circle and the formula reduces to A = π × r².

What is the semi-major axis?

The semi-major axis (a) is half the length of the longest diameter of the ellipse. It extends from the center to the far edge along the longest direction.

What is the semi-minor axis?

The semi-minor axis (b) is half the length of the shortest diameter. It extends from the center to the edge along the shortest direction, perpendicular to the semi-major axis.

Yes. When a = b, the ellipse is a perfect circle, and the formula A = π × a × b becomes A = π × r², the standard circle area formula.

Must a be greater than b?

By convention, a ≥ b, but the formula is symmetric — swapping a and b gives the same result. This calculator accepts any positive values for both fields.

What units does this calculator support?

You can enter measurements in centimeters, meters, millimeters, inches, or feet. Both inputs must use the same unit. The result is given in the corresponding square unit (e.g., cm²).

Area of an Ellipse Calculator

Name: Area of an Ellipse Calculator
Availability: InStock
Author: Nham Vu

Enter the semi-major and semi-minor axes of an ellipse to instantly calculate its area using A = π × a × b.

Calculator Inputs

Semi-major axis (a)

Semi-minor axis (b)

Unit

Area

—

Enter values and click Calculate

Ellipse diagram

a = semi-major axis | b = semi-minor axis

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Summary

Enter the semi-major and semi-minor axes of an ellipse to instantly calculate its area using A = π × a × b.

How it works

Enter the semi-major axis (a) — the longest radius of the ellipse.
Enter the semi-minor axis (b) — the shortest radius of the ellipse.
Choose your preferred unit (cm, m, mm, in, or ft).
Click "Calculate Area" to apply the formula A = π × a × b.
The result and step-by-step working appear instantly below.

Use cases

Geometry homework and exam problems involving ellipses.
Engineering calculations for elliptical cross-sections or openings.
Architecture and design work with oval shapes.
Calculating the surface area of oval pools, gardens, or track fields.
Astronomy — estimating the cross-sectional area of planetary orbits.
Fabric or material estimation for oval-shaped cuts.
Verifying manual ellipse area calculations quickly.

Frequently Asked Questions

Last updated: 2026-06-13 · Reviewed by Nham Vu