Ellipse Calculator

Calculate ellipse area, circumference approximation, axis lengths and eccentricity from the semi-major and semi-minor axes

Your result will appear here.

About the Ellipse Calculator

Ellipse Calculator works with the geometry of an oval defined by two semi-axes. It can calculate area and approximate circumference from the major and minor dimensions used in design, geometry and layout work.

Unlike a circle, an ellipse has different radii along its major and minor axes. Circumference does not have a simple elementary formula, so practical calculators use accurate approximations.

How to Use the Ellipse Calculator

  1. Enter the major and minor axis lengths or their semi-axis values as requested.
  2. Confirm whether the fields expect full axes or half-axes.
  3. Calculate area and circumference.
  4. Keep the two axes assigned correctly when the ellipse is not circular.

How the Calculation Works

For semi-major axis a and semi-minor axis b, area A=πab.

Ellipse circumference has no simple elementary closed form. A common high-quality approximation is Ramanujan’s formula, such as C≈π[3(a+b)−√((3a+b)(a+3b))], which is very accurate for many practical ellipses.

Worked example

Ellipse Calculator Worked Example

Ellipse with semi-axes 6 cm and 4 cm

Area = π×6×4 = 24π ≈ 75.40 cm².

Result guide

Understanding Your Ellipse Calculator Result

If a=b, the ellipse becomes a circle and the formulas reduce to the circular case. As the axes become more unequal, the ellipse becomes more elongated.

Before you rely on the answer

Assumptions and Limitations

  • Axis inputs are interpreted consistently as full or semi-axis lengths.
  • The shape is an ideal ellipse.
  • Circumference is understood as an approximation when using an approximate formula.

Practical tip

Using This Result in Practice

Check whether a drawing labels 12×8 as full width and height or as radii. Confusing full axes with semi-axes can make the area four times too large.

Related calculations

Useful Calculations to Continue With

If both semi-axes are equal, use the Circle Calculator for the simpler circular geometry.

If the ellipse is only one section of a composite shape, use the Area Calculator for the combined layout.

Common questions

Ellipse Calculator FAQ

What is the area formula for an ellipse?

A=πab, where a and b are the semi-axis lengths.

Why is ellipse circumference approximate?

There is no simple elementary formula analogous to 2πr for a circle.

When does an ellipse become a circle?

When the two semi-axes are equal.