Ellipse Formulas
2D Shapes
Ellipse
- Area
- A = πab
- Perimeter (approx.)
- P ≈ π[3(a + b) − √((3a + b)(a + 3b))]
- a semi-major axis
- b semi-minor axis
Ellipse formulas explained
An ellipse is a stretched circle with a semi-major axis a and a semi-minor axis b. The perimeter has no simple exact formula, so Ramanujan’s approximation is used. Below are all the ellipse formulas with what each letter means, a worked example and a free calculator.
- Area:
A = πab - Perimeter (approx.):
P ≈ π[3(a + b) − √((3a + b)(a + 3b))]
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Ellipse calculator
Worked example: area of a ellipse
Given Semi-major a = 8 cm, Semi-minor b = 5 cm, substitute the values into each ellipse formula:
- A = π × 8 × 5 = 125.66 cm²
- P = π[3(a + b) − √((3a + b)(a + 3b))] = 41.39 cm
Ellipse Formula SheetFormulas, variables, a worked example and practice questions with answers.Download PDFOpen
Ellipse formulas FAQ
What is the formula for the area of a ellipse?
The area of a ellipse is A = πab, where a is the semi-major axis, b is the semi-minor axis.
What is the formula for the perimeter (approx.) of a ellipse?
The perimeter (approx.) of a ellipse is P ≈ π[3(a + b) − √((3a + b)(a + 3b))], where a is the semi-major axis, b is the semi-minor axis.
Can I download the ellipse formulas as a PDF?
Yes. Use the Download PDF button on this page for a free printable ellipse formula sheet with a worked example and practice questions.
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