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Circle & Ellipse Calculator

DeveloperMath

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INPUT

Auto Process

Shape

Unit

Decimal Places

Circle Inputs

Solve From

Radius

Diameter

Circumference

Area

Sector & Segment

Angle (°)

Ellipse Inputs

Semi-Major Axis (a)

Semi-Minor Axis (b)

OUTPUT

Client Side

Circle Results

Property	Value
Radius	-
Diameter	-
Circumference	-
Area	-

Sector & Segment Results

Property	Value
Arc Length	-
Sector Area	-

Ellipse Results

Property	Value
Area	-
Perimeter (Ramanujan)	-
Eccentricity	-
Foci Distance (c)	-
Semi-Latus Rectum	-

Diagram

Formulas

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Guide

Circle & Ellipse Calculator

Calculate all properties of circles and ellipses instantly. Enter any single known measurement — radius, diameter, circumference, or area — and get every other circle property derived automatically. For ellipses, enter the semi-major and semi-minor axes to get area, perimeter (Ramanujan approximation), eccentricity, and foci distance. Includes a visual canvas diagram with labeled measurements and sector/segment calculations for circles.

How to Use

Select either Circle or Ellipse mode. Choose your preferred unit of measurement and decimal precision. For circles, pick which value you know (radius, diameter, circumference, or area), enter it, and all other properties calculate instantly. Optionally enter a sector angle to compute arc length and sector area. For ellipses, enter the semi-major and semi-minor axis lengths to see area, perimeter, eccentricity, foci distance, and a labeled diagram.

Features

Circle Solver – Solve from any input: radius, diameter, circumference, or area
Ellipse Calculator – Area, perimeter (Ramanujan approximation), eccentricity, foci distance, and semi-latus rectum
Sector & Segment – Arc length and sector area for any angle (0-360°)
Unit Selector – Supports mm, cm, m, inches, feet, and yards
Visual Diagram – Canvas-based diagram with labeled measurements, foci points, and sector highlighting
Adjustable Precision – Choose 0 to 10 decimal places
Copy Results – One-click copy of all calculated values

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 FAQ

What is the Ramanujan approximation for ellipse perimeter?

The Ramanujan approximation estimates the perimeter of an ellipse using the formula: P ≈ π[3(a+b) - √((3a+b)(a+3b))], where a and b are the semi-major and semi-minor axes. It is one of the most accurate simple approximations available, with error less than 0.04% for most ellipses.
How is eccentricity of an ellipse calculated and what does it mean?

Eccentricity (e) is calculated as e = √(1 - b²/a²), where a is the semi-major axis and b is the semi-minor axis. It measures how much the ellipse deviates from a perfect circle. A value of 0 means a perfect circle, while values approaching 1 indicate a very elongated ellipse.
What is the relationship between a circle and an ellipse?

A circle is a special case of an ellipse where both semi-axes are equal (a = b = radius). All formulas for ellipses reduce to the standard circle formulas when a equals b. For example, the ellipse area formula πab becomes πr² when a = b = r.
What are the foci of an ellipse and why are they important?

The foci (plural of focus) are two special points inside an ellipse. The sum of distances from any point on the ellipse to both foci is constant and equals the length of the major axis (2a). The distance from the center to each focus is c = √(a² - b²). Foci are fundamental in optics, astronomy (planetary orbits are ellipses with the sun at one focus), and engineering.