Last updated: July 31, 2026
Foci of an Ellipse Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
c = √(a² - b²), e = c/a, foci at (±c, 0)
Where:
- semiMajorAxis=Semi-major Axis
- semiMinorAxis=Semi-minor Axis
Worked Examples
Standard ellipse
Use a=10 and b=6.
- 1Compute c = √(100-36) = 8
- 2Compute eccentricity e = 8/10 = 0.8
- 3Foci are at x=8 and x=-8
Near circle
Use a=5 and b=4.9.
- 1Compute c = √(25-24.01)
- 2c ≈ 0.994987
- 3Eccentricity ≈ 0.198997
Highly stretched ellipse
Use a=13 and b=5.
- 1Compute c = √(169-25)=12
- 2Compute e = 12/13
- 3Set focus coordinates ±12
Introduction
Ellipse foci determine how stretched an ellipse is and are essential in geometry, optics, and orbital models.
Formula and Method
Foci of an Ellipse Calculator applies c = √(a² - b²), e = c/a, foci at (±c, 0) and returns deterministic outputs from validated inputs.
Validate each required input
Apply the stated formula
Round numeric outputs where needed
Return safe defaults when validation fails
Input Fields
Use these keys exactly as defined in calculation.ts.
- 1
semiMajorAxis: Semi-major Axis
- 2
semiMinorAxis: Semi-minor Axis
Output Fields
These values map directly to calculation.ts return keys.
- 1
focalDistance: Distance from center to each focus
- 2
eccentricity: Shape stretch ratio c/a
- 3
focus1X: Positive x-coordinate of first focus
- 4
focus2X: Negative x-coordinate of second focus
Validation Rules
Both axes must be positive finite values and semi-major axis must satisfy a ≥ b.
Finite numeric values are required
Domain restrictions are enforced before solving
Invalid input returns default-safe outputs
Check examples to confirm expected behavior
How to Use This Calculator
Enter inputs, run the calculation, and read the primary output first.
Enter all required values
Click calculate
Review primary output first
Use supporting outputs for interpretation
Practical Uses
This calculator is useful for study, verification, and fast applied math checks.
Conic section homework
Orbital approximation models
Reflective property demonstrations
Coordinate-geometry verification
FAQs
What does the Foci of an Ellipse Calculator compute?
It computes Focal Distance (c) and supporting outputs from your inputs.
Which inputs are required?
Required inputs are: Semi-major Axis, Semi-minor Axis.
How are invalid inputs handled?
When validation fails, the calculator returns safe default values and does not attempt invalid math.
Are results rounded?
Yes. Numeric outputs are rounded inside calculation.ts (typically to 6 decimal places).
Can I use negative or decimal values?
Positive values only; semi-major axis must be at least as large as semi-minor axis.
How should I verify my answer?
Use the worked examples and compare each output key with your manual steps.