Ellipse Area Perimeter and Foci Calculator
Calculate ellipse area, numerical perimeter, eccentricity and focus positions from two semi-axis lengths.
YOUR CALCULATION
Result
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Calculation steps
Work through one step at a time or reveal the complete calculation. The steps use your current inputs.
How to calculate
Order the semi-axes and integrate the parametric arc-speed over one quadrant. Compute area and focal distance separately; plot the boundary in output coordinates.
Area=πab; perimeter=4∫₀^(π/2)√(a²sin²t+b²cos²t)dt; c=√(a²−b²)
Worked example
Semi-axes 3 m and 2 m give area 6π m², perimeter approximately 15.8654396 m and center-to-focus distance √5 m.
Assumptions and input details
Inputs are semi-axes, not full diameters. Positive lengths up to 1e9 m; minor/major ratio at least 1e−6. Adaptive numerical quadrature supplies perimeter, not an elementary exact expression. Axis lengths and focus distances share the selected output unit; area uses its square. The equal-scale outline is sampled at 120 intervals; perimeter is independently calculated by quadrature.
References: Wolfram Research: ellipse geometry
Unit definitions
Unit selection is independent of language. Each selector contains only units for its physical quantity. Calculations use defined base units internally.
Choose from 23 length definitions, including explicitly labelled regional measures. Area conversions square the length factor; geometric volumes cube it.
Regional measures are not interchangeable merely because their names look similar. This is a documented selection, not a claim to include every historical unit.
NIST measurement tables · Japanese traditional units · Mainland China and Hong Kong unit distinctions
Using this calculator
Can I enter my own problem?
Yes. Replace the example values with your own inputs. The result, calculation steps, tables and applicable diagrams update from those inputs. Blank or invalid values clear the result; example values are never silently substituted for missing inputs.
Are the results exact?
Results use floating-point arithmetic and displayed rounding. Read the formula, assumptions and any stated data precision before interpreting the result.
Is my input uploaded?
The calculation runs in your browser. No account, file upload or external AI service is required. Inputs are not saved between page reloads.
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