# Ellipse Area Calculator

> Ellipse area from the semi-major and semi-minor axes, plus Ramanujan's perimeter approximation.

Page: https://freecalculator.tech/tools/ellipse-area-calculator
Last reviewed: 2026-11-03

## Formula

A = π × a × b, where a and b are the semi-axes (half of each full axis). Perimeter ≈ π(a+b)(1 + 3h ÷ (10 + √(4 − 3h))), h = ((a−b)/(a+b))².

- Source: Wolfram MathWorld, Ellipse.
- Enter half-axes. If you measured the full width and height, divide each by 2 first.
- A = π × a × b, where a and b are the semi-axes (half of each full axis). Perimeter ≈ π(a+b)(1 + 3h ÷ (10 + √(4 − 3h))), h = ((a−b)/(a+b))².
- Inputs used: Semi-major axis a, Semi-minor axis b, Unit (labels only — no conversion).

## Inputs

- Semi-major axis a
- Semi-minor axis b
- Unit (labels only — no conversion)

## Worked example: Ellipse with semi-axes 5 and 3

π × 5 × 3 ≈ 47.12389 cm².
1. Area = π × 5 × 3 = 15π.
2. 15π ≈ 47.12389 cm².

## Common questions

### What are semi-axes?

Half of the longest and shortest diameters of the ellipse.

### Is the perimeter exact?

No. It uses Ramanujan's approximation, which is extremely close for most ellipses but not an exact closed form.

### Is a circle an ellipse?

Yes. When a = b = r the area becomes πr².

### How do I use the Ellipse Area Calculator?

Enter the required values for Semi-major axis a, Semi-minor axis b, Unit (labels only — no conversion). The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.

### What formula does the Ellipse Area Calculator use?

A = π × a × b, where a and b are the semi-axes (half of each full axis). Perimeter ≈ π(a+b)(1 + 3h ÷ (10 + √(4 − 3h))), h = ((a−b)/(a+b))². The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone.

### Can the Ellipse Area Calculator be used for exact decisions?

Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.

## Limitations and assumptions

- Perimeter is an approximation.
- Plane ellipses only; not ellipsoids.
- Exact mathematical relationships, rounded for display. Check units and rounding before using a result in graded, engineering or financial work.
- The result depends on the values you enter for this ellipse area calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.

## Sources

- Wolfram MathWorld — https://mathworld.wolfram.com/Ellipse.html

## Cite this page

- APA: Free Calculator. (2026, November 3). Ellipse Area Calculator. https://freecalculator.tech/tools/ellipse-area-calculator
- MLA: "Ellipse Area Calculator." Free Calculator, 3 Nov. 2026, https://freecalculator.tech/tools/ellipse-area-calculator.
- Link: Ellipse Area Calculator — Free Calculator, https://freecalculator.tech/tools/ellipse-area-calculator