Ellipse Axis Calculator
Choose one input method. The calculator will derive the major axis, minor axis, area, eccentricity, focal distance, and related values.
Example Data Table
| Input Type | Given Values | Major Axis | Minor Axis | Eccentricity | Area |
|---|---|---|---|---|---|
| Axes | Major = 20 cm, Minor = 12 cm | 20 cm | 12 cm | 0.800 | 188.496 cm² |
| Semi-axes | a = 8 m, b = 5 m | 16 m | 10 m | 0.781 | 125.664 m² |
| Equation | x²/144 + y²/64 = 1 | 24 units | 16 units | 0.745 | 301.593 units² |
Formula Used
An ellipse has a semi-major axis a and a semi-minor axis b. The full major axis equals 2a. The full minor axis equals 2b.
Major axis = 2a
Minor axis = 2b
Area = πab
c² = a² - b²
e = c / a = √(1 - b²/a²)
For the standard equation x²/A + y²/B = 1, the larger denominator is a². The smaller denominator is b².
How to Use This Calculator
Select the method that matches your known values. Enter only the fields required for that method. Use positive values. Keep eccentricity from zero to less than one.
Press the calculate button. The result will appear above the form. Review the major axis, minor axis, semi-axes, area, focal distance, eccentricity, ratio, and flattening.
Use the CSV button for spreadsheet work. Use the PDF button for printable notes, assignments, or project records.
Understanding Ellipse Axes
What the Axes Mean
An ellipse is a stretched circle. It has two central widths. The longest width is the major axis. The shortest central width is the minor axis. These axes always cross at the center. They are perpendicular in a standard ellipse. Their half lengths are called semi-axes. The semi-major axis is written as a. The semi-minor axis is written as b.
Why Axis Length Matters
Axis length controls the shape of the ellipse. A large difference between a and b creates a narrow oval. A small difference creates a rounder oval. Designers use this idea in geometry, drawing, optics, mechanics, astronomy, and layout planning. Engineers may also use the values when checking clearances, rotation paths, or projected areas.
Using Different Inputs
This calculator supports several routes. You can enter full axes directly. You can enter semi-axes. You can also use area with eccentricity. Another option uses the focal distance. The equation mode helps when you already have a standard ellipse equation. This flexibility makes the tool useful for school problems and practical work.
Reading the Results
The major axis equals twice the semi-major axis. The minor axis equals twice the semi-minor axis. Area shows the surface enclosed by the ellipse. Eccentricity describes how stretched the ellipse is. A value near zero means the shape is close to a circle. A value near one means it is very elongated.
Accuracy Notes
Use matching units for every length input. Do not mix centimeters with inches in the same calculation. For equation mode, enter only positive denominators. For focal distance mode, c must be smaller than a. If c equals or exceeds a, the shape is not a valid ellipse. Rounding may slightly change final decimals.
FAQs
1. What is the major axis of an ellipse?
The major axis is the longest line through the center of an ellipse. It passes from one end of the ellipse to the opposite end.
2. What is the minor axis of an ellipse?
The minor axis is the shortest central line across the ellipse. It is perpendicular to the major axis in a standard ellipse.
3. How do I calculate the major axis?
Find the semi-major axis a first. Then multiply it by two. The formula is major axis = 2a.
4. How do I calculate the minor axis?
Find the semi-minor axis b first. Then multiply it by two. The formula is minor axis = 2b.
5. Can eccentricity be equal to one?
No. An ellipse has eccentricity from zero to less than one. A value of one represents a parabola limit, not a valid ellipse.
6. What does c mean in an ellipse?
The value c is the distance from the center to each focus. It is found with c² = a² - b².
7. Which denominator is a squared in the equation?
In standard equation form, the larger denominator is a². The smaller denominator is b².
8. Can I export the result?
Yes. Use the CSV button for spreadsheet data. Use the PDF button for a simple printable calculation report.