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Ellipse Standard Form Calculator.

Generate an ellipse standard-form equation from its center and semi-axes.

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01

Set your values

Results update as you type.

area: 125.66370614

area

0.00000000
equation: (x − 0)²/64 + (y − 0)²/25 = 1

equation

(x − 0)²/64 + (y − 0)²/25 = 1

Results update automatically as you type.

Generate an ellipse standard-form equation from its center and semi-axes.

Use Cases

Graphing an ellipse from its equation

Quickly convert your ellipse's dimensions and center into the standard form, which is the format needed for graphing or further analysis.

Example: Enter center (2, -3), semi-major 5, semi-minor 3 to get ((x-2)^2)/25 + ((y+3)^2)/9 = 1.

Checking your algebra homework

Verify that you've correctly written the standard-form equation for a given ellipse, ensuring your center and axis lengths are accurate.

Example: Compare your manual result with the calculator's output for center (0,0), semi-major 4, semi-minor 2.

Frequently Asked Questions

What does the Ellipse Standard Form Calculator do?
It takes the center coordinates (Center x, Center y), the semi-major axis, and the semi-minor axis, and outputs the standard-form equation of the ellipse: ((x-h)^2)/a^2 + ((y-k)^2)/b^2 = 1, where (h,k) is the center and a,b are the semi-axes.
How do I enter the semi-major and semi-minor axes?
Enter the lengths of the semi-major axis (the longer radius) and the semi-minor axis (the shorter radius) in the corresponding fields. The calculator uses these values directly to form the equation.
Can I use this calculator for ellipses not centered at the origin?
Yes. You can specify the center coordinates (Center x and Center y) to generate the standard-form equation for an ellipse centered at any point (h,k).

Tips & Common Mistakes

Tips

  • Ensure the semi-major axis is the longer of the two radii; if you swap them, the equation will represent a different ellipse.
  • Double-check the signs of the center coordinates: a positive center x means the ellipse is shifted right, and a negative center y means it's shifted down.
  • The calculator outputs the equation in the form ((x-h)^2)/a^2 + ((y-k)^2)/b^2 = 1, where a is the semi-major axis and b is the semi-minor axis.
  • Use the generated equation to plot the ellipse by hand or with graphing software; the center and axes are directly visible.

Common Mistakes to Avoid

  • Entering the full diameter instead of the semi-axis length. The semi-major and semi-minor axes are half the major and minor diameters.
  • Forgetting to include the center coordinates when the ellipse is not centered at the origin, leading to an incorrect equation.
  • Confusing the semi-major and semi-minor axes, which changes the orientation of the ellipse in the equation.

Last updated: August 13, 2026