Math

Ellipse Calculator

Enter the semi-major and semi-minor axes of an ellipse.

By TheCalcTools Updated Formula checked and tested

Your numbers

Your results

Area
Area
—
Perimeter (Ramanujan approx.)
—
Eccentricity
—

Ellipse Calculator by TheCalcTools

How the Ellipse Calculator works

Enter half of the longest diameter and half of the shortest diameter.

The area is exact: π × a × b.

No simple exact formula exists for the perimeter, so Ramanujan’s accurate approximation is used.

The formula

A = πabh = ((a − b) ÷ (a + b))²

Worked example

Using the default values shown in the calculator:

Semi-axis a5
Semi-axis b3
  1. Area = π × 5 × 3 = 47.1239.
  2. Eccentricity = √(1 − 9 ÷ 25) = 0.8000.
  3. Perimeter ≈ 25.5270.

Result:

Area47.1239
Perimeter (Ramanujan approx.)25.5270
Eccentricity0.8000

Frequently asked questions

What is eccentricity?

A measure of how stretched the ellipse is. 0 is a circle; values close to 1 are very elongated.

Is the perimeter approximation accurate?

Ramanujan’s second formula is very accurate, with errors far below 0.01% for ordinary shapes.

Sources and further reading

Circle CalculatorEnter the radius to get the diameter, circumference and area of a circle Arc Length and Sector Area CalculatorEnter the radius and central angle in degrees to find arc length, sector area and chord… Triangle Calculator (Solve Any Triangle: SSS, SAS, ASA)Choose what you know and enter the values Triangle Area Calculator (Heron's Formula)Enter three side lengths to find the triangle's area, perimeter and angles Pythagorean Theorem CalculatorSolve for any side of a right triangle using a² + b² = c² Rectangle CalculatorEnter the length and width to find the area, perimeter and diagonal

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This calculator gives estimates for information only. Check important results independently before you rely on them. See our disclaimer.