Ellipse Axis Length Calculator

Enter ellipse information

Calculation method

Measurement unit

Decimal precision

Axis orientation

Equation and coordinate modes infer orientation automatically.

Semi-major axis, a

Semi-minor axis, b

Major axis length

Minor axis length

Ellipse area

Eccentricity, e

Centre-to-focus distance, c

Distance between both foci

Denominator under (x − h)²

Denominator under (y − k)²

Centre x-coordinate, h

Centre y-coordinate, k

Major-axis vertices

Vertex 1, x

Vertex 1, y

Vertex 2, x

Vertex 2, y

Minor-axis co-vertices

Co-vertex 1, x

Co-vertex 1, y

Co-vertex 2, x

Co-vertex 2, y

Major endpoint, x

Major endpoint, y

Minor endpoint, x

Minor endpoint, y

Formula used

Major axis = 2a Minor axis = 2b Area: A = πab Focal distance: c = √(a² − b²) Eccentricity: e = c/a Ramanujan perimeter: P ≈ π[3(a + b) − √((3a + b)(a + 3b))]

The semi-major axis is the longer radius. The semi-minor axis is the shorter radius. Full axes are twice their corresponding semi-axes.

How to use this calculator

Select the calculation method matching your known values.
Choose a unit and decimal precision.
Enter every visible field with valid numbers.
Select Calculate to view axes and ellipse properties.
Copy, download, or print the completed results.

Use consistent units for every length. Enter area in squared selected units. Coordinate values must share the same scale.

Example data

Example	Semi-major axis	Semi-minor axis	Major axis	Minor axis
Horizontal ellipse	8	5	16	10
Vertical ellipse	10	6	20	12
Nearly circular	7	6.5	14	13
Circle case	5	5	10	10

Frequently asked questions

What is an ellipse axis?

An ellipse has two perpendicular axes. The major axis is longer. The minor axis crosses its centre.

What is a semi-major axis?

It is half the major axis. It runs from centre to vertex. Its symbol is usually a.

What is a semi-minor axis?

It is half the minor axis. It reaches a co-vertex. Its symbol is usually b.

How do I find full axis lengths?

Multiply each semi-axis by two. The longer result is major. The shorter result is minor.

How does the equation reveal orientation?

The larger denominator identifies the major direction. Under x means horizontal. Under y means vertical.

Can an ellipse have equal axes?

Yes, but it becomes a circle. Its eccentricity equals zero. Both focal points meet centrally.

What eccentricity values are valid?

An ellipse uses values from zero through below one. Zero describes a circle. One is not included.

Is ellipse perimeter exact here?

The calculator uses Ramanujan’s approximation. It is highly accurate. General ellipse perimeter lacks an elementary formula.

Why must coordinates share units?

Distances compare coordinate differences directly. Mixed units distort axis lengths. Convert them before entering values.