Ellipse Area Calculator
Calculate the area of an ellipse
By Drew Budwin · Last updated July 2026 · Methodology
Recent Calculations (0)
Results
Area
Embed this calculator
Add it to your website or blog
Ellipse Area Calculator Formula
Area of an ellipse:
A = π × a × b
How to Use This Calculator
- Enter the semi-major axis (a), the longer half-axis from the center to the edge.
- Enter the semi-minor axis (b), the shorter half-axis from the center to the edge.
- Click Calculate Area to see the result.
Frequently Asked Questions
What are the semi-major and semi-minor axes?
An ellipse has two axes of symmetry. The semi-major axis (a) is the longer distance from the center to the edge, and the semi-minor axis (b) is the shorter distance. Together they define the shape: a circle occurs when a = b.
What if a = b?
When both axes are equal, the ellipse is a circle. The formula A = π × a × b becomes A = π × r², which is the standard circle area formula. You can also use the dedicated circle calculator for that case.
Does it matter which axis is a and which is b?
No. The formula π × a × b is symmetric, so the result is the same regardless of which axis you label a or b.
What units are used?
This calculator is unit-agnostic. The result is in the square of whatever unit you use for the axes.
What is the circumference of an ellipse?
Unlike a circle, the circumference of an ellipse has no simple closed-form formula. A common approximation is C ≈ π(3(a+b) - sqrt((3a+b)(a+3b))), known as Ramanujan's approximation. This calculator computes area only.
Where are ellipses used in real-world calculations?
Ellipses appear in planetary orbits, oval stadium designs, elliptical pool tables, and cross-sections of oblique cylinders. Engineers model bone cross-sections as ellipses to estimate structural strength from scan measurements.
How do I find the area of a semiellipse?
Divide the full ellipse area by two: A_semi = (π × a × b) / 2. Semiellipses show up in arch bridge design and architectural doorways. Enter the two semi-axes here and divide the result by two.
How does an ellipse's area compare to its bounding rectangle?
The bounding rectangle has dimensions 2a × 2b (area = 4ab). The inscribed ellipse has area πab, which is π/4 ≈ 78.5% of the rectangle. The same ratio holds between a circle and its circumscribed square.