Convertools

Ellipse Eccentricity from Semi-Axes

Calculate ellipse eccentricity using e = sqrt(1 - b²/a²).

Author

Prof. Ingrid Johansson

Math editorial contributor

Norwegian political scientist at the University of Oslo, studying democratic resilience in Nordic welfare states

Reviewed by

Dr. Emeka Nwosu

Math content reviewer

Nigerian legal scholar with an SJD from Yale, focused on international trade law and African continental free trade agreements

Last updatedFebruary 22, 2026

PublishedFebruary 22, 2026

Table of Contents

  1. Reference values
  2. Calculator
  3. Reference table
  4. FAQs
  5. Methodology and review
  6. Related conversions

20 units Semi-major Axis; 8 units Semi-minor Axis =

0.916515 Eccentricity

Representative value from the Ellipse Eccentricity from Semi-Axes reference table.

Reference Values

Browse 111 reference values with individual detail pages for quick lookup.

Browse all reference values

Ellipse Eccentricity from Semi-Axes

Calculate ellipse eccentricity using e = sqrt(1 - b²/a²).

Calculated Result

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Reference Table

Use this complete table for quick lookup and internal linking to specific value pages.

Ellipse Eccentricity from Semi-Axes Reference
ScenarioEccentricity
1 units Semi-major Axis; 0.5 units Semi-minor Axis0.866025 Eccentricity
1 units Semi-major Axis; 1 units Semi-minor Axis0 Eccentricity
2 units Semi-major Axis; 0.5 units Semi-minor Axis0.968246 Eccentricity
2 units Semi-major Axis; 1 units Semi-minor Axis0.866025 Eccentricity
2 units Semi-major Axis; 2 units Semi-minor Axis0 Eccentricity
3 units Semi-major Axis; 0.5 units Semi-minor Axis0.986013 Eccentricity
3 units Semi-major Axis; 1 units Semi-minor Axis0.942809 Eccentricity
3 units Semi-major Axis; 2 units Semi-minor Axis0.745356 Eccentricity
3 units Semi-major Axis; 3 units Semi-minor Axis0 Eccentricity
5 units Semi-major Axis; 0.5 units Semi-minor Axis0.994987 Eccentricity
5 units Semi-major Axis; 1 units Semi-minor Axis0.979796 Eccentricity
5 units Semi-major Axis; 2 units Semi-minor Axis0.916515 Eccentricity
5 units Semi-major Axis; 3 units Semi-minor Axis0.8 Eccentricity
5 units Semi-major Axis; 4 units Semi-minor Axis0.6 Eccentricity
5 units Semi-major Axis; 5 units Semi-minor Axis0 Eccentricity
8 units Semi-major Axis; 0.5 units Semi-minor Axis0.998045 Eccentricity
8 units Semi-major Axis; 1 units Semi-minor Axis0.992157 Eccentricity
8 units Semi-major Axis; 2 units Semi-minor Axis0.968246 Eccentricity
8 units Semi-major Axis; 3 units Semi-minor Axis0.927025 Eccentricity
8 units Semi-major Axis; 4 units Semi-minor Axis0.866025 Eccentricity
8 units Semi-major Axis; 5 units Semi-minor Axis0.780625 Eccentricity
8 units Semi-major Axis; 8 units Semi-minor Axis0 Eccentricity
10 units Semi-major Axis; 0.5 units Semi-minor Axis0.998749 Eccentricity
10 units Semi-major Axis; 1 units Semi-minor Axis0.994987 Eccentricity
10 units Semi-major Axis; 2 units Semi-minor Axis0.979796 Eccentricity
10 units Semi-major Axis; 3 units Semi-minor Axis0.953939 Eccentricity
10 units Semi-major Axis; 4 units Semi-minor Axis0.916515 Eccentricity
10 units Semi-major Axis; 5 units Semi-minor Axis0.866025 Eccentricity
10 units Semi-major Axis; 8 units Semi-minor Axis0.6 Eccentricity
10 units Semi-major Axis; 10 units Semi-minor Axis0 Eccentricity
12 units Semi-major Axis; 0.5 units Semi-minor Axis0.999132 Eccentricity
12 units Semi-major Axis; 1 units Semi-minor Axis0.996522 Eccentricity
12 units Semi-major Axis; 2 units Semi-minor Axis0.986013 Eccentricity
12 units Semi-major Axis; 3 units Semi-minor Axis0.968246 Eccentricity
12 units Semi-major Axis; 4 units Semi-minor Axis0.942809 Eccentricity
12 units Semi-major Axis; 5 units Semi-minor Axis0.909059 Eccentricity
12 units Semi-major Axis; 8 units Semi-minor Axis0.745356 Eccentricity
12 units Semi-major Axis; 10 units Semi-minor Axis0.552771 Eccentricity
12 units Semi-major Axis; 12 units Semi-minor Axis0 Eccentricity
15 units Semi-major Axis; 0.5 units Semi-minor Axis0.999444 Eccentricity
15 units Semi-major Axis; 1 units Semi-minor Axis0.997775 Eccentricity
15 units Semi-major Axis; 2 units Semi-minor Axis0.991071 Eccentricity
15 units Semi-major Axis; 3 units Semi-minor Axis0.979796 Eccentricity
15 units Semi-major Axis; 4 units Semi-minor Axis0.963789 Eccentricity
15 units Semi-major Axis; 5 units Semi-minor Axis0.942809 Eccentricity
15 units Semi-major Axis; 8 units Semi-minor Axis0.845905 Eccentricity
15 units Semi-major Axis; 10 units Semi-minor Axis0.745356 Eccentricity
15 units Semi-major Axis; 12 units Semi-minor Axis0.6 Eccentricity
15 units Semi-major Axis; 15 units Semi-minor Axis0 Eccentricity
20 units Semi-major Axis; 0.5 units Semi-minor Axis0.999687 Eccentricity
20 units Semi-major Axis; 1 units Semi-minor Axis0.998749 Eccentricity
20 units Semi-major Axis; 2 units Semi-minor Axis0.994987 Eccentricity
20 units Semi-major Axis; 3 units Semi-minor Axis0.988686 Eccentricity
20 units Semi-major Axis; 4 units Semi-minor Axis0.979796 Eccentricity
20 units Semi-major Axis; 5 units Semi-minor Axis0.968246 Eccentricity
20 units Semi-major Axis; 8 units Semi-minor Axis0.916515 Eccentricity
20 units Semi-major Axis; 10 units Semi-minor Axis0.866025 Eccentricity
20 units Semi-major Axis; 12 units Semi-minor Axis0.8 Eccentricity
20 units Semi-major Axis; 15 units Semi-minor Axis0.661438 Eccentricity
20 units Semi-major Axis; 20 units Semi-minor Axis0 Eccentricity
25 units Semi-major Axis; 0.5 units Semi-minor Axis0.9998 Eccentricity
25 units Semi-major Axis; 1 units Semi-minor Axis0.9992 Eccentricity
25 units Semi-major Axis; 2 units Semi-minor Axis0.996795 Eccentricity
25 units Semi-major Axis; 3 units Semi-minor Axis0.992774 Eccentricity
25 units Semi-major Axis; 4 units Semi-minor Axis0.987117 Eccentricity
25 units Semi-major Axis; 5 units Semi-minor Axis0.979796 Eccentricity
25 units Semi-major Axis; 8 units Semi-minor Axis0.947418 Eccentricity
25 units Semi-major Axis; 10 units Semi-minor Axis0.916515 Eccentricity
25 units Semi-major Axis; 12 units Semi-minor Axis0.877268 Eccentricity
25 units Semi-major Axis; 15 units Semi-minor Axis0.8 Eccentricity
25 units Semi-major Axis; 20 units Semi-minor Axis0.6 Eccentricity
25 units Semi-major Axis; 25 units Semi-minor Axis0 Eccentricity
30 units Semi-major Axis; 0.5 units Semi-minor Axis0.999861 Eccentricity
30 units Semi-major Axis; 1 units Semi-minor Axis0.999444 Eccentricity
30 units Semi-major Axis; 2 units Semi-minor Axis0.997775 Eccentricity
30 units Semi-major Axis; 3 units Semi-minor Axis0.994987 Eccentricity
30 units Semi-major Axis; 4 units Semi-minor Axis0.991071 Eccentricity
30 units Semi-major Axis; 5 units Semi-minor Axis0.986013 Eccentricity
30 units Semi-major Axis; 8 units Semi-minor Axis0.963789 Eccentricity
30 units Semi-major Axis; 10 units Semi-minor Axis0.942809 Eccentricity
30 units Semi-major Axis; 12 units Semi-minor Axis0.916515 Eccentricity
30 units Semi-major Axis; 15 units Semi-minor Axis0.866025 Eccentricity
30 units Semi-major Axis; 20 units Semi-minor Axis0.745356 Eccentricity
30 units Semi-major Axis; 25 units Semi-minor Axis0.552771 Eccentricity
30 units Semi-major Axis; 30 units Semi-minor Axis0 Eccentricity
40 units Semi-major Axis; 0.5 units Semi-minor Axis0.999922 Eccentricity
40 units Semi-major Axis; 1 units Semi-minor Axis0.999687 Eccentricity
40 units Semi-major Axis; 2 units Semi-minor Axis0.998749 Eccentricity
40 units Semi-major Axis; 3 units Semi-minor Axis0.997184 Eccentricity
40 units Semi-major Axis; 4 units Semi-minor Axis0.994987 Eccentricity
40 units Semi-major Axis; 5 units Semi-minor Axis0.992157 Eccentricity
40 units Semi-major Axis; 8 units Semi-minor Axis0.979796 Eccentricity
40 units Semi-major Axis; 10 units Semi-minor Axis0.968246 Eccentricity
40 units Semi-major Axis; 12 units Semi-minor Axis0.953939 Eccentricity
40 units Semi-major Axis; 15 units Semi-minor Axis0.927025 Eccentricity
40 units Semi-major Axis; 20 units Semi-minor Axis0.866025 Eccentricity
40 units Semi-major Axis; 25 units Semi-minor Axis0.780625 Eccentricity
40 units Semi-major Axis; 30 units Semi-minor Axis0.661438 Eccentricity
50 units Semi-major Axis; 0.5 units Semi-minor Axis0.99995 Eccentricity
50 units Semi-major Axis; 1 units Semi-minor Axis0.9998 Eccentricity
50 units Semi-major Axis; 2 units Semi-minor Axis0.9992 Eccentricity
50 units Semi-major Axis; 3 units Semi-minor Axis0.998198 Eccentricity
50 units Semi-major Axis; 4 units Semi-minor Axis0.996795 Eccentricity
50 units Semi-major Axis; 5 units Semi-minor Axis0.994987 Eccentricity
50 units Semi-major Axis; 8 units Semi-minor Axis0.987117 Eccentricity
50 units Semi-major Axis; 10 units Semi-minor Axis0.979796 Eccentricity
50 units Semi-major Axis; 12 units Semi-minor Axis0.970773 Eccentricity
50 units Semi-major Axis; 15 units Semi-minor Axis0.953939 Eccentricity
50 units Semi-major Axis; 20 units Semi-minor Axis0.916515 Eccentricity
50 units Semi-major Axis; 25 units Semi-minor Axis0.866025 Eccentricity
50 units Semi-major Axis; 30 units Semi-minor Axis0.8 Eccentricity

Frequently Asked Questions

Common questions about Ellipse Eccentricity from Semi-Axes, formulas, and typical use cases.

What does the Ellipse Eccentricity from Semi-Axes calculator do?

It helps with measuring how circular or elongated an ellipse is in geometry and orbital models.

What formula does the Ellipse Eccentricity from Semi-Axes calculator use?

Ellipse eccentricity e = √(1 - b²/a²), with a ≥ b ≥ 0.

What inputs are valid?

Semi-major axis a must be positive, and semi-minor axis b must satisfy 0 ≤ b ≤ a.

When would I use this?

measuring how circular or elongated an ellipse is in geometry and orbital models

Methodology and Review

This page combines a live calculator, precomputed reference values, and FAQ content from the same conversion definition to reduce mismatch between calculator output and lookup tables.

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