Last updated: July 31, 2026
Ellipse Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
area = πab; perimeter ≈ π[3(a+b)-√((3a+b)(a+3b))]; focalDistance = √(a²-b²); eccentricity = focalDistance/a
Where:
- a=a
- b=b
Worked Examples
Ellipse with a=8, b=5
Typical horizontal ellipse.
- 1area = πab
- 2perimeter via Ramanujan approximation
- 3c = √(a²-b²), e = c/a
Near-circle case
a and b close to each other.
- 1Compute using same formulas
- 2Observe low eccentricity
Circle boundary
a=b behaves like a circle.
- 1area = π·16
- 2perimeter approximation equals circumference
Introduction
Compute key geometric properties of an ellipse from semi-major axis a and semi-minor axis b in one step.
Formula and Method
Ellipse Calculator uses: area = πab; perimeter ≈ π[3(a+b)-√((3a+b)(a+3b))]; focalDistance = √(a²-b²); eccentricity = focalDistance/a
Enter all required inputs
Apply the underlying math formula(s)
Compute supporting terms where needed
Round numeric outputs for stable display
Input Fields
Provide values for: a, b.
- 1
a: a
- 2
b: b
Output Fields
The calculator returns: area, perimeter, eccentricity, focalDistance.
- 1
area: Area of the ellipse
- 2
perimeter: Approximate perimeter (Ramanujan I)
- 3
eccentricity: Eccentricity of the ellipse
- 4
focalDistance: Distance from center to each focus
Validation Rules
Input validation is applied before calculation to prevent invalid math states.
a and b must be finite and positive.
For this calculator, a must be greater than or equal to b.
Perimeter is an approximation, not an exact elementary expression.
Outputs are rounded to 6 decimals.
How to Use This Calculator
Fill in the inputs, run the calculator, and review primary output first.
Enter the required values
Click calculate
Check the primary output
Use example scenarios for verification
Practical Uses
This calculator supports learning, quick checks, and day-to-day technical problem solving.
Homework and exam preparation
Engineering and science sanity checks
Classroom demonstrations
Fast recalculation with different inputs
FAQs
What does the Ellipse Calculator compute?
Compute key geometric properties of an ellipse from semi-major axis a and semi-minor axis b in one step.
Which inputs are required?
Required inputs: a, b.
How should I format numbers?
Use finite numeric values; decimals and negative numbers are allowed unless restricted by validation rules.
How are results rounded?
Numeric outputs are rounded to about 6 decimal places for readability.
Why might I see an error?
a and b must be finite and positive.
Can I use this for learning and verification?
Yes. Use the examples and formula section to verify manual calculations quickly.