Circle & Ellipse Calculator

First find the radius from the area using r = sqrt(A / pi), then calculate circumference with C = 2 * pi * r. For example, a circle with area 100 square centimeters has radius sqrt(100 / 3.14159) = 5.642 cm, giving circumference 2 * 3.14159 * 5.642 = 35.449 cm. This calculator handles these inverse calculations automatically: just enter the area and all other values appear instantly.

The Ramanujan approximation estimates an ellipse perimeter as P approximately equals pi times (3(a + b) minus the square root of (3a + b)(a + 3b)), where a and b are the semi-major and semi-minor axes. Unlike circles, there is no exact closed-form formula for an ellipse perimeter. Ramanujan published this approximation in 1914, and it is accurate to within 0.01% for most ellipses. For highly eccentric ellipses (very elongated), more complex series expansions provide better accuracy.

Eccentricity measures how much an ellipse deviates from being a perfect circle. It is calculated as e = sqrt(1 - b squared / a squared), where a is the semi-major axis and b is the semi-minor axis. A circle has eccentricity 0 (a = b), while values approaching 1 indicate increasingly elongated ellipses. Earth's orbit around the Sun has an eccentricity of about 0.017, making it nearly circular. Pluto's orbit has eccentricity 0.25, noticeably more elliptical.

A sector is the pie-slice-shaped region bounded by two radii and an arc. Think of a slice of pizza. Its area equals (angle / 360) times pi times r squared. A segment is the region between a chord and the arc it cuts off. Think of cutting a circle with a straight line. A segment area equals the sector area minus the triangle formed by the two radii and the chord. This calculator computes sector area and arc length for any angle you enter.