Area of an Ellipse Calculator
The area of an ellipse is π × a × b, using the two semi-axes: a = 6 cm and b = 4 cm give 75.3982 cm².
Half of the longest diameter.
Half of the shortest diameter.
75.398223686155 cm²
Full answer, then cut to fewer decimals (not rounded):
- 75.398223686155 cm²
- 75.39822368615 cm²
- 75.3982236861 cm²
- 75.398223686 cm²
- 75.39822368 cm²
- 75.3982236 cm²
- 75.398223 cm²
- 75.39822 cm²
- 75.3982 cm²
- 75.398 cm²
- 75.39 cm²
- 75.3 cm²
- Area
- 75.3982 cm²
- Perimeter (Ramanujan)
- 31.7309 cm
In other units: 0.00753982 m² · 7539.82 mm² · 7.53982 × 10⁻⁹ km² · 7.53982 × 10⁻⁷ ha · 0.081158 ft² · 11.6867 in² · 0.00901755 yd² · 0.00000186313 ac · 2.91114 × 10⁻⁹ mi²
Step-by-step solution
- A = π × a × b
- A = π × 6 × 4 = 75.3982 cm²
Area of an Ellipse Formula
A = π a b
a semi-major axis, b semi-minor axis
Worked Example
An ellipse with semi-axes 6 cm and 4 cm:
- A = π × a × b
- A = π × 6 × 4 = 75.3982 cm²
Perimeter (Ramanujan): 31.7309 cm
Same area in other units: 0.00753982 m² · 7539.82 mm² · 7.53982 × 10⁻⁹ km² · 7.53982 × 10⁻⁷ ha · 0.081158 ft²
Frequently asked questions
What is the difference between the axes and semi-axes?
The semi-axes a and b are half the longest and shortest diameters. An oval 12 cm long and 8 cm wide has a = 6 and b = 4.
Is there an exact formula for the perimeter of an ellipse?
No simple one: it needs an elliptic integral. Ramanujan's approximation P ≈ π(a + b)[1 + 3h/(10 + √(4 − 3h))], with h = (a − b)²/(a + b)², is accurate to better than 0.04 %.
How is the ellipse area formula derived?
An ellipse is a circle of radius a stretched by b/a in one direction, so its area is πa² × b/a = πab. Integration gives the same result.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
- Guide for the Use of the International System of Units (SI), NIST Special Publication 811, 2008 Edition, National Institute of Standards and Technology .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Area of an Ellipse Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/area-of-an-ellipse/
IEEE
Scientific Converters, "Area of an Ellipse Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/area-of-an-ellipse/