Calculators
Ellipse Calculator
Calculate ellipse area, approximate circumference, and shape from the two semi-axes locally in your browser.
Enter the semi-major axis and the semi-minor axis from 0 (exclusive) to 1000000000 to see the area (pi x a x b), the approximate circumference (Ramanujan second approximation), and shape. The calculation runs locally in your browser; your values are not uploaded or stored.
Find ellipse measurements without uploading anything.
Enter a semi-major axis and a semi-minor axis from 0 (exclusive) to 1000000000 to see the area, the approximate circumference, and the shape. Everything runs locally in your browser, so your values are not uploaded or stored.
Frequently Asked Questions
Everything you need to know about this tool, how it works, and privacy.
What does the ellipse calculator show?
Enter a semi-major axis and a semi-minor axis from 0 (exclusive) to 1000000000. The calculator returns the area (pi times a times b), the approximate circumference with the Ramanujan second approximation, and the shape (circle when both axes are equal, otherwise ellipse). For example, axes 5 and 3 give area about 47.1238898038, circumference about 25.5269988628, and ellipse shape.
Which formulas does the ellipse calculator use?
It uses area = pi x a x b, where a and b are the semi-major and semi-minor axes. The circumference uses the Ramanujan second approximation: with h = ((a - b) / (a + b)) squared, circumference is about pi x (a + b) x (1 + 3h / (10 + square root of (4 - 3h))). When both axes are equal, the shape is a circle and the circumference equals 2 x pi x a.
Which inputs are accepted?
Enter a semi-major axis and a semi-minor axis greater than zero through 1000000000. Decimal values are accepted. Zero, negative numbers, non-numeric text, and values above the limit show a clear error instead of a result.
Do my numbers stay private?
Yes. The calculation and copy action run locally in your browser. CodeASystem does not upload or store the values you enter.