Ellipse Area Calculator
Calculate the area of an ellipse from its semi-major axis (a) and semi-minor axis (b). Formula: Area = pi x a x b. Instant and accurate.
How to use this tool
- Enter semi-major axis (a) and semi-minor axis (b) in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your area and the full breakdown beneath it.
Formula
Area = pi x a x b
How it works
An ellipse has two axes: the semi-major axis (a, the longer half) and the semi-minor axis (b, the shorter half). Multiply pi by both to get the area. When a = b the ellipse becomes a circle.
Worked example
Ellipse with a = 6 m and b = 4 m
- Area = pi x 6 x 4
- Area = 24 x pi
- Area = 75.3982 m^2
75.3982 m^2
Common mistakes to avoid
- Entering the full major and minor axis lengths instead of the semi-axes; a and b must be half the full axis lengths.
- Using the circle area formula (pi x r^2) when the two axes are unequal, which gives the wrong area.
- Confusing which axis is the semi-major (longer) vs semi-minor (shorter); the formula is symmetric so the area result is the same, but labeling matters for other ellipse properties.
Key terms
- What is the semi-major axis?
- The longest radius of the ellipse, measured from the center to the farthest edge.
- What is the semi-minor axis?
- The shortest radius of the ellipse, measured from the center at a right angle to the semi-major axis.
Frequently asked questions
- What is the semi-major axis vs the major axis?
- The major axis is the full length of the longest diameter. The semi-major axis a is half that length, measured from the center to one end.
- When does this formula reduce to the circle area formula?
- When a = b = r (both semi-axes are equal), the ellipse is a circle and Area = pi x r^2.
- Can I use this to estimate the area of an oval room or stadium?
- Yes, if the shape is a true ellipse. Measure the longest and widest perpendicular diameters, halve each to get a and b, then compute the area.