Ellipse Area Calculator

Calculate area and circumference of an ellipse

Semi-major axis (a)

Semi-minor axis (b)

How the Ellipse Area Calculator Works

Enter Semi-Major Axis

Input the longer radius (a) - half the length of the ellipse's longest diameter.

Enter Semi-Minor Axis

Input the shorter radius (b) - half the length of the ellipse's shortest diameter.

Get Area and Circumference

Receive instant calculations for both the area and approximate circumference of the ellipse.

Features of This Ellipse Calculator

Area and Circumference

Calculate both the area (using πab) and circumference using Ramanujan's approximation formula.

High Precision Results

Get results accurate to 4 decimal places for precise mathematical and engineering calculations.

Ramanujan's Formula

Uses the renowned mathematician's highly accurate approximation for ellipse circumference.

Formula Display

Shows the mathematical formulas used so you can understand and verify the calculations.

Free Math Tool

Completely free ellipse calculator for students, teachers, engineers, and designers.

Mobile-Friendly Design

Calculate ellipse measurements on any device - perfect for homework and field work.

Ellipse Formulas Reference

Measurement	Formula	Variables
Area	A = πab	a = semi-major, b = semi-minor
Circumference	C ≈ π(a+b)(1 + 3h/(10+√(4-3h)))	h = (a-b)²/(a+b)²
Eccentricity	e = √(1 - b²/a²)	0 < e < 1 for ellipses

Frequently Asked Questions

How do you calculate the area of an ellipse?

The area of an ellipse is calculated using the formula A = πab, where 'a' is the semi-major axis (longer radius) and 'b' is the semi-minor axis (shorter radius). For example, an ellipse with a=5 and b=3 has an area of π × 5 × 3 = 47.12 square units.

What is the difference between major and semi-major axis?

The major axis is the full length of the ellipse's longest diameter. The semi-major axis is half of this length - essentially the "radius" along the longest direction. The calculator uses semi-major axis (a) in its formulas.

Why is ellipse circumference approximate?

Unlike area, there is no simple exact formula for ellipse circumference. The calculation requires an elliptic integral. Ramanujan's approximation used here is accurate to within 0.01% for most ellipses, making it practical for real-world use.

What is eccentricity in an ellipse?

Eccentricity (e) measures how stretched an ellipse is. A circle has e=0. As e approaches 1, the ellipse becomes more elongated. Earth's orbit has e≈0.0167 (nearly circular), while Halley's Comet has e≈0.967 (highly elliptical).

Where are ellipses used in real life?

Ellipses appear in planetary orbits, whispering galleries, elliptical exercise machines, architectural arches, optics (lens shapes), and engineering designs. Kepler's First Law states that planets orbit the sun in elliptical paths.

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