Ellipse Calculator
Calculate ellipse area, circumference approximation, eccentricity, and foci
About this calculator
The Ellipse Calculator computes an ellipse's area πab, its circumference via Ramanujan's second approximation, its eccentricity, and the focal distance from the two semi-axes. It also reports the full major and minor axis lengths, and automatically treats the larger input as the semi-major axis. Both semi-axes must be positive; equal axes give a circle with zero eccentricity. Useful for geometry homework, orbital shapes, and engineering layouts.
How to use the Ellipse Calculator calculator
- Enter the measurements you know into the input fields.
- Read the computed properties — they update instantly as you type.
- Compare the diagram with your figure to confirm the setup is right.
- Copy the page URL to share the exact calculation.
Common examples
- Semi-axes a = 6, b = 4 → area 75.398224, circumference ≈ 31.730879, eccentricity 0.745356
- a = b = 5 (a circle) → area 78.539816, circumference 31.415927, eccentricity 0
- a = 10, b = 3 → eccentricity 0.953939, foci ≈ ±9.539392 from the center
- a = 6, b = 4 → major axis 12, minor axis 8, focal distance 4.472136
Frequently asked questions
How does the Ellipse Calculator calculator work?
Enter the known measurements of your figure and the calculator applies the standard geometric formulas to find the remaining properties, alongside a diagram that reflects your numbers. All values are computed with high-precision arithmetic.
When would I use the Ellipse Calculator calculator?
It helps with geometry homework, technical drawing, construction and DIY layout, and any situation where you know some measurements of a shape and need the rest.
How accurate are the results?
Formulas are evaluated at 30 significant digits of precision internally, including roots and trigonometric functions. Displayed values are rounded for readability, but the underlying computation does not accumulate floating-point drift.
Can I share a specific calculation with someone else?
Yes. Every value you enter updates the URL, so copying the address bar and sharing the link reopens the exact same figure and results for whoever clicks it.