What units are used for ellipse area?

Ellipse area is expressed in square units. For example, measurements in meters produce an area in square meters.

How is ellipse perimeter calculated?

Ellipse perimeter generally requires an approximation. This calculator uses Ramanujan's second approximation.

Geometry and measurement

Ellipse Area Calculator

Q: What is the formula for the area of an ellipse?

The area of an ellipse is A = pi times a times b, where a is the semi-major axis and b is the semi-minor axis.

Q: What is the difference between an axis and a semi-axis?

A full axis runs across the ellipse through its center. A semi-axis is half of that length and runs from the center to the edge.

Calculate the area enclosed by an ellipse using its major and minor axes. Choose semi-axis measurements or full axis lengths, view the calculation steps, and explore related measurements including eccentricity, focal distance, and an approximate perimeter.

Calculate ellipse area

Enter both measurements in the same unit. The major axis must be at least as long as the minor axis.

Measurement type Semi-axes are half the full axis lengths.

Measurement unit Both axes use this unit.

Semi-major axis (a) The longer measurement of the ellipse.

Semi-minor axis (b) The shorter measurement of the ellipse.

Decimal places

Reset calculator

Ellipse area formula

Area of an ellipse A = πab where a is the semi-major axis, b is the semi-minor axis, and π is approximately 3.141592653589793.

Semi-major axis (a): Half the longest diameter, measured from the center to the edge.
Semi-minor axis (b): Half the shortest diameter, measured from the center to the edge.
Area (A): The two-dimensional space enclosed by the ellipse, expressed in square units.
Full axis lengths: The complete distances across the ellipse. Divide each full axis by 2 before applying the formula.

Worked example

Suppose an ellipse has a semi-major axis of 5 meters and a semi-minor axis of 3 meters.

Start with A = πab.
Substitute the values: A = π × 5 × 3.
Multiply: A = 15π.
The area is approximately 47.1239 square meters.

What if you know the full axes?

If the full major axis is 10 meters and the full minor axis is 6 meters, their semi-axis lengths are 5 meters and 3 meters. The resulting area is the same: approximately 47.1239 m².

Explore more calculators for area, circles, and geometric measurements.

Frequently asked questions

What is the formula for the area of an ellipse?

The formula is A = πab, where a is the semi-major axis and b is the semi-minor axis. Multiply the two semi-axis lengths and then multiply by π.

What is the difference between an axis and a semi-axis?

A full axis runs all the way across the ellipse through its center. A semi-axis is half that length, from the center to the edge. Use the correct input mode in this calculator.

Can the ellipse be a circle?

Yes. When the two semi-axes are equal, the ellipse is a circle. Its area formula reduces to A = πr².

Why must the major axis be at least as long as the minor axis?

By convention, the major axis is the longer axis and the minor axis is the shorter one. Enter the longer measurement first to keep the labels and derived measurements consistent.

Is the ellipse perimeter exact?

No. Unlike the area, the perimeter of a general ellipse does not have a simple elementary formula. This calculator provides a useful approximation using Ramanujan's formula.