Ellipse Calculator

Half the length of the longest diameter (a ≥ b).
Half the length of the shortest diameter (b ≤ a).
Math Updated 16 Jun 2026

Ellipse Calculator is a mathematics calculator that helps you calculate ellipse values from your input data. The formula used is: Area = π×a×b; Perimeter ≈ π(a+b)[1 + 3h/(10+√(4−3h))] where h=(a−b)²/(a+b)²; e = √(1−(b/a)²); c = √(a²−b²). Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.

Formula

Area = π×a×b; Perimeter ≈ π(a+b)[1 + 3h/(10+√(4−3h))] where h=(a−b)²/(a+b)²; e = √(1−(b/a)²); c = √(a²−b²)
  • Ellipse Calculator gives you a fast estimate using your inputs and updates instantly when you change any value.
  • Formula: Area = π×a×b; Perimeter ≈ π(a+b)[1 + 3h/(10+√(4−3h))] where h=(a−b)²/(a+b)²; e = √(1−(b/a)²); c = √(a²−b²)
  • Input definitions: • Semi-Major Axis a: the numeric semi-major axis a used in the calculation • Semi-Minor Axis b: the numeric semi-minor axis b used in the calculation
  • Manual method: write down each input, apply the formula step by step, then compare your manual result with the calculator output.
  • Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.
  • Results are mathematically exact given the formula and your inputs. Rounding to decimal places may introduce small display differences.
  • Check that all inputs are in the valid range for the formula. Some operations (e.g. square root, division) require non-negative or non-zero values.
  • Practical tip: test a low, medium, and high scenario to understand sensitivity before making decisions.

Example Calculation

Inputs
  • Semi-Major Axis a: 8
  • Semi-Minor Axis b: 5

Suppose you enter: Semi-Major Axis a = 8, Semi-Minor Axis b = 5. The calculator applies the formula (Area = π×a×b; Perimeter ≈ π(a+b)[1 + 3h/(10+√(4−3h))] where h=(a−b)²/(a+b)²; e = √(1−(b/a)²); c = √(a²−b²)) and shows all output values below. Change any input field to immediately see how the result changes.

Frequently asked questions

What is the Ellipse?
The Ellipse Calculator is a mathematics calculator that helps you calculate ellipse values from your input data. Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.
When should I use this calculator?
Use this calculator whenever you need a quick, accurate result for ellipse values from your input data without working through the arithmetic manually.
What units should I enter?
Ensure all inputs share the same unit system (e.g. all metres or all feet) unless the formula converts between units.
How accurate are the results?
Results are mathematically exact given the formula and your inputs. Rounding to decimal places may introduce small display differences.
How do I interpret the result?
Check that all inputs are in the valid range for the formula. Some operations (e.g. square root, division) require non-negative or non-zero values.
How can I verify the calculation manually?
Use the displayed formula and work through the numbers step by step. If your manual result differs slightly, check rounding and unit conversions first.
Can I use this for planning and budgeting?
Yes. Run best-case, expected, and worst-case inputs to compare outcomes and make safer planning decisions.

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