About this calculator
The Ellipse Calculator finds area and approximate perimeter from the semi-major and semi-minor axes. It is useful for oval shapes, design sketches, geometry revision, and comparing an ellipse with a circle.
ellipse calculator method
Ellipse area is exact using pi times the two semi-axes. Ellipse perimeter has no simple elementary exact formula, so the calculator uses Ramanujan approximation.
- Area = pi x a x b
- Perimeter approx. = pi(3(a+b) - sqrt((3a+b)(a+3b)))
How to use the ellipse calculator
- Enter the semi-major axis a.
- Enter the semi-minor axis b.
- Multiply pi, a, and b for area.
- Use Ramanujan approximation for perimeter.
- Check that a and b are semi-axis lengths, not full width and height.
- Round the approximate perimeter sensibly.
Worked examples
Ellipse axes
Input: a = 8, b = 4
Calculation: Area = pi x 8 x 4
Result: Area about 100.53
Circle-like ellipse
Input: a = 5, b = 5
Calculation: Area = pi x 5 x 5
Result: Same as circle area with radius 5
Semi-axis warning
The semi-major and semi-minor axes are half the full width and height. If you have full axis lengths, divide each by 2 before using the calculator.
Practical geometry checks
- Use one unit system
- Keep all lengths in the same unit before calculating. Mixing centimetres, metres, inches, or feet in the same formula will produce misleading results.
- Perimeter vs area
- Perimeter is a distance around the outside. Area is the amount of flat space inside a shape. Surface area is the total outside covering of a 3D shape.
- Rounded answers
- Pi, square roots, and trigonometric values are often irrational, so decimal answers are approximations. Keep extra decimal places until the final result.
Edge cases
- Zero or negative dimensions do not describe a real physical shape.
- Regular polygon formulas assume all sides and angles are equal.
- Circle and ellipse formulas use pi, so most decimal answers are rounded.
- A trapezoid/trapezium perimeter needs all four side lengths, not just the parallel sides and height.
Limitations
This calculator is for educational and planning use. For construction, manufacturing, surveying, engineering, or safety-critical work, confirm dimensions, tolerances, and rounding rules with the appropriate professional method or specification.
Frequently asked questions
What units should I enter?
Use any length unit you like, but keep every length in the same unit. If you enter metres, area is in square metres and surface area is also in square metres.
Why are some answers approximate?
Calculations involving pi, square roots, or curved shapes often produce irrational numbers. The calculator rounds the displayed decimal result.
What is the difference between area and surface area?
Area measures a flat 2D region. Surface area measures the total outside area of a 3D object.
Can I use these calculators for homework?
Yes. They are useful for checking answers and understanding formulas, but you should still show the working required by your class or exam.
Do regular polygon formulas work for irregular polygons?
No. Regular polygon formulas assume equal sides and equal angles. Irregular polygons usually need to be split into simpler shapes.
Related calculators
- Area Calculator
- Circumference Calculator
- Circle Calculator