Ellipse Area Calculator
Ellipse area from the semi-major and semi-minor axes, plus Ramanujan's perimeter approximation.
In short
Ellipse area from the semi-major and semi-minor axes, plus Ramanujan's perimeter approximation.
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.
What this calculator does
Ellipse area from the semi-major and semi-minor axes, plus Ramanujan's perimeter approximation. Formula, worked example, sources, FAQs and limitations included.
You enter semi-major axis a, semi-minor axis b and unit (labels only — no conversion), and the ellipse area calculator shows the answer along with the working, so you can check it or try other numbers.
The page shows the formula, a numeric worked example, and the assumptions that affect this math calculation.
Inputs and what they mean
- Semi-major axis a
- — number value.
- Semi-minor axis b
- — number value.
- Unit (labels only — no conversion)
- — choice value.
How to use it
- Enter each value in the unit shown next to the box (use the unit converter first if your numbers are in other units).
- Check the breakdown to see every intermediate step.
- Read the limitations before relying on the result.
Formula
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).
Worked example
Ellipse with semi-axes 5 and 3
- Area = π × 5 × 3 = 15π.
- 15π ≈ 47.12389 cm².
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
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.
Reference: Wolfram MathWorld
Last reviewed:
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.
Sources
Method based on Wolfram MathWorld.
Cite this page
Free Calculator. (2026, November 3). Ellipse Area Calculator. https://freecalculator.tech/tools/ellipse-area-calculator
"Ellipse Area Calculator." Free Calculator, 3 Nov. 2026, https://freecalculator.tech/tools/ellipse-area-calculator.
Ellipse Area Calculator — Free Calculator, https://freecalculator.tech/tools/ellipse-area-calculator
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