Free · Geometry and function relationships

Ellipse Center from Paired Points

The center is the midpoint of opposite vertices, opposite co-vertices or the two foci. For the standard ellipse equation, it is the pair of horizontal and vertical offsets.

Formula & worked example
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How to use this calculator

Enter the known values in the units shown. Results update as you type.
Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
Use the worked example to check the method. Reset restores the starting fields.

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Formula and method

For ellipse_info = 2, vertex1x = -3, vertex1y = 2, vertex2x = 7, vertex2y = 6, center12 = 2, center22 = 4.

center=((x₁+x₂)/2,(y₁+y₂)/2)

Worked example

Enter these known values and leave the other values blank.

I know...: 2
x-coordinate: -3
y-coordinate: 2
x-coordinate: 7
y-coordinate: 6

x-coordinate: 2
y-coordinate: 4

Assumptions and limitations

The center is the midpoint of opposite vertices, opposite co-vertices or the two foci. For the standard ellipse equation, it is the pair of horizontal and vertical offsets.
Clear the unknown field before solving. Locks preserve known quantities; an inverse may have multiple solutions and this model selects its principal branch.
Numerical rounding does not describe measurement uncertainty. Extremely large arguments or near-singular inverses can exceed the available precision; use moderate values for interpretable finite results.

Common questions

How do I enter a consistent set of values?

The center is the midpoint of opposite vertices, opposite co-vertices or the two foci. For the standard ellipse equation, it is the pair of horizontal and vertical offsets.

Can I calculate a missing input?

Clear that field and provide enough independent known quantities. Output-only fields and nonunique inverse branches may need a different mode.

References

Calculation definition and unit reference

The calculation equations, inverse formulas, units, and input rules were imported from this source. Bookify provides the interface and equation solver.

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