mathematics calculator
Ellipse Area Calculator
Calculate ellipse area from two semi-axis or full-axis lengths with normalized major and minor measurements.
Ellipse Area Calculator
Ellipse area
Choose semi-axis or full-axis input and enter two positive lengths.
This tool models an ideal planar ellipse.
Formula version 1.0.0
How to use this calculator
- Choose semi-axes or full axes as the input type.
- Enter both positive axis measurements in one unit.
- Select Calculate.
- Read area and normalized major, minor, semi-major, and semi-minor axes.
Symbols and units
| Symbol | Meaning | Unit or domain |
|---|---|---|
a | Semi-major axis | length |
b | Semi-minor axis | length |
A | Ellipse area | square length |
Checked examples
Semi-axes known
Inputs: Semi-axes 3 and 2
Calculation: A=π×3×2
Result: 6π square units; full axes 6 and 4
The larger input is normalized as semi-major axis.
Check: ellipse-area-core.test.ts
Full axes known
Inputs: Full axes 4 and 6
Calculation: Semi-axes 2 and 3; A=π×2×3
Result: 6π square units
Input order does not change normalized geometry.
Check: ellipse-area-core.test.ts
Assumptions, rounding, and limits
- The shape is an ideal planar ellipse.
- Both axes are positive and use one unit.
- Full-axis mode halves each input before calculation.
- Perimeter and three-dimensional ellipsoid properties are excluded.
Frequently asked questions
What is a semi-axis?
It is half of the corresponding full axis through the ellipse.
Does input order matter?
No. The calculator normalizes the larger value as the major axis.
Does the formula work for a circle?
Yes. Equal semi-axes reduce A=πab to A=πr².
Sources and review
- OpenStax: The Ellipse — Major and minor semi-axes
- OpenStax: Circles — Circle area as the equal-axis case
- Formula version
- ellipse.area@1.0.0
- Formula review
- Equatara formula review
- Editorial review
- Equatara editorial review
- Last verified
- 2026-10-25
- Applicability
- Ideal planar ellipse from positive compatible axes.
- Next review
- On material formula/source change, or by 2028-10-25.
Related calculators
Found a problem?
Report a formula, result, example, source, or accessibility issue through the calculator correction process. Do not include sensitive input values.