Convertools

Ellipse Perimeter (Ramanujan) from Semi-Axes

Approximate ellipse perimeter from semi-major and semi-minor axes using Ramanujan’s formula.

Author

Dr. Nadia Petrov

Math editorial contributor

Serbian biomedical engineer trained at Imperial College London, developing low-cost prosthetics for conflict zones

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 =

92.05245 units

Representative value from the Ellipse Perimeter (Ramanujan) from Semi-Axes reference table.

Reference Values

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

Browse all reference values

Ellipse Perimeter (Ramanujan) from Semi-Axes

Approximate ellipse perimeter from semi-major and semi-minor axes using Ramanujan’s formula.

Calculated Result

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Reference Table

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

Ellipse Perimeter (Ramanujan) from Semi-Axes Reference
ScenarioEllipse Perimeter
1 units Semi-major Axis; 0.5 units Semi-minor Axis4.844224 units
1 units Semi-major Axis; 1 units Semi-minor Axis6.283185 units
2 units Semi-major Axis; 0.5 units Semi-minor Axis8.57842 units
2 units Semi-major Axis; 1 units Semi-minor Axis9.688448 units
2 units Semi-major Axis; 2 units Semi-minor Axis12.566371 units
3 units Semi-major Axis; 0.5 units Semi-minor Axis12.450015 units
3 units Semi-major Axis; 1 units Semi-minor Axis13.364893 units
3 units Semi-major Axis; 2 units Semi-minor Axis15.86544 units
3 units Semi-major Axis; 3 units Semi-minor Axis18.849556 units
5 units Semi-major Axis; 0.5 units Semi-minor Axis20.319636 units
5 units Semi-major Axis; 1 units Semi-minor Axis21.010027 units
5 units Semi-major Axis; 2 units Semi-minor Axis23.013112 units
5 units Semi-major Axis; 3 units Semi-minor Axis25.526999 units
5 units Semi-major Axis; 4 units Semi-minor Axis28.361668 units
5 units Semi-major Axis; 5 units Semi-minor Axis31.415927 units
8 units Semi-major Axis; 0.5 units Semi-minor Axis32.227833 units
8 units Semi-major Axis; 1 units Semi-minor Axis32.744766 units
8 units Semi-major Axis; 2 units Semi-minor Axis34.313679 units
8 units Semi-major Axis; 3 units Semi-minor Axis36.366862 units
8 units Semi-major Axis; 4 units Semi-minor Axis38.753793 units
8 units Semi-major Axis; 5 units Semi-minor Axis41.386276 units
8 units Semi-major Axis; 8 units Semi-minor Axis50.265482 units
10 units Semi-major Axis; 0.5 units Semi-minor Axis40.19215 units
10 units Semi-major Axis; 1 units Semi-minor Axis40.639272 units
10 units Semi-major Axis; 2 units Semi-minor Axis42.020053 units
10 units Semi-major Axis; 3 units Semi-minor Axis43.859097 units
10 units Semi-major Axis; 4 units Semi-minor Axis46.026225 units
10 units Semi-major Axis; 5 units Semi-minor Axis48.442241 units
10 units Semi-major Axis; 8 units Semi-minor Axis56.723336 units
10 units Semi-major Axis; 10 units Semi-minor Axis62.831853 units
12 units Semi-major Axis; 0.5 units Semi-minor Axis48.166098 units
12 units Semi-major Axis; 1 units Semi-minor Axis48.562176 units
12 units Semi-major Axis; 2 units Semi-minor Axis49.800061 units
12 units Semi-major Axis; 3 units Semi-minor Axis51.470518 units
12 units Semi-major Axis; 4 units Semi-minor Axis53.459571 units
12 units Semi-major Axis; 5 units Semi-minor Axis55.695949 units
12 units Semi-major Axis; 8 units Semi-minor Axis63.461758 units
12 units Semi-major Axis; 10 units Semi-minor Axis69.257912 units
12 units Semi-major Axis; 12 units Semi-minor Axis75.398224 units
15 units Semi-major Axis; 0.5 units Semi-minor Axis60.137359 units
15 units Semi-major Axis; 1 units Semi-minor Axis60.478056 units
15 units Semi-major Axis; 2 units Semi-minor Axis61.555348 units
15 units Semi-major Axis; 3 units Semi-minor Axis63.03008 units
15 units Semi-major Axis; 4 units Semi-minor Axis64.80694 units
15 units Semi-major Axis; 5 units Semi-minor Axis66.824464 units
15 units Semi-major Axis; 8 units Semi-minor Axis73.93979 units
15 units Semi-major Axis; 10 units Semi-minor Axis79.327198 units
15 units Semi-major Axis; 12 units Semi-minor Axis85.085004 units
15 units Semi-major Axis; 15 units Semi-minor Axis94.24778 units
20 units Semi-major Axis; 0.5 units Semi-minor Axis80.104193 units
20 units Semi-major Axis; 1 units Semi-minor Axis80.384301 units
20 units Semi-major Axis; 2 units Semi-minor Axis81.278544 units
20 units Semi-major Axis; 3 units Semi-minor Axis82.521757 units
20 units Semi-major Axis; 4 units Semi-minor Axis84.040107 units
20 units Semi-major Axis; 5 units Semi-minor Axis85.784196 units
20 units Semi-major Axis; 8 units Semi-minor Axis92.05245 units
20 units Semi-major Axis; 10 units Semi-minor Axis96.884482 units
20 units Semi-major Axis; 12 units Semi-minor Axis102.107995 units
20 units Semi-major Axis; 15 units Semi-minor Axis110.517461 units
20 units Semi-major Axis; 20 units Semi-minor Axis125.663706 units
25 units Semi-major Axis; 0.5 units Semi-minor Axis100.080428 units
25 units Semi-major Axis; 1 units Semi-minor Axis100.321203 units
25 units Semi-major Axis; 2 units Semi-minor Axis101.091949 units
25 units Semi-major Axis; 3 units Semi-minor Axis102.173544 units
25 units Semi-major Axis; 4 units Semi-minor Axis103.506566 units
25 units Semi-major Axis; 5 units Semi-minor Axis105.050133 units
25 units Semi-major Axis; 8 units Semi-minor Axis110.673294 units
25 units Semi-major Axis; 10 units Semi-minor Axis115.065562 units
25 units Semi-major Axis; 12 units Semi-minor Axis119.854864 units
25 units Semi-major Axis; 15 units Semi-minor Axis127.634994 units
25 units Semi-major Axis; 20 units Semi-minor Axis141.808339 units
25 units Semi-major Axis; 25 units Semi-minor Axis157.079633 units
30 units Semi-major Axis; 0.5 units Semi-minor Axis120.061609 units
30 units Semi-major Axis; 1 units Semi-minor Axis120.274719 units
30 units Semi-major Axis; 2 units Semi-minor Axis120.956111 units
30 units Semi-major Axis; 3 units Semi-minor Axis121.917816 units
30 units Semi-major Axis; 4 units Semi-minor Axis123.110695 units
30 units Semi-major Axis; 5 units Semi-minor Axis124.500153 units
30 units Semi-major Axis; 8 units Semi-minor Axis129.613879 units
30 units Semi-major Axis; 10 units Semi-minor Axis133.648928 units
30 units Semi-major Axis; 12 units Semi-minor Axis138.078675 units
30 units Semi-major Axis; 15 units Semi-minor Axis145.326723 units
30 units Semi-major Axis; 20 units Semi-minor Axis158.654396 units
30 units Semi-major Axis; 25 units Semi-minor Axis173.14478 units
30 units Semi-major Axis; 30 units Semi-minor Axis188.495559 units
40 units Semi-major Axis; 0.5 units Semi-minor Axis160.031695 units
40 units Semi-major Axis; 1 units Semi-minor Axis160.208386 units
40 units Semi-major Axis; 2 units Semi-minor Axis160.768601 units
40 units Semi-major Axis; 3 units Semi-minor Axis161.563351 units
40 units Semi-major Axis; 4 units Semi-minor Axis162.557088 units
40 units Semi-major Axis; 5 units Semi-minor Axis163.72383 units
40 units Semi-major Axis; 8 units Semi-minor Axis168.080213 units
40 units Semi-major Axis; 10 units Semi-minor Axis171.568393 units
40 units Semi-major Axis; 12 units Semi-minor Axis175.43639 units
40 units Semi-major Axis; 15 units Semi-minor Axis181.834312 units
40 units Semi-major Axis; 20 units Semi-minor Axis193.768964 units
40 units Semi-major Axis; 25 units Semi-minor Axis206.93138 units
40 units Semi-major Axis; 30 units Semi-minor Axis221.034922 units
50 units Semi-major Axis; 0.5 units Semi-minor Axis200.007108 units
50 units Semi-major Axis; 1 units Semi-minor Axis200.160857 units
50 units Semi-major Axis; 2 units Semi-minor Axis200.642405 units
50 units Semi-major Axis; 3 units Semi-minor Axis201.325779 units
50 units Semi-major Axis; 4 units Semi-minor Axis202.183897 units
50 units Semi-major Axis; 5 units Semi-minor Axis203.196361 units
50 units Semi-major Axis; 8 units Semi-minor Axis207.013132 units
50 units Semi-major Axis; 10 units Semi-minor Axis210.100267 units
50 units Semi-major Axis; 12 units Semi-minor Axis213.547961 units
50 units Semi-major Axis; 15 units Semi-minor Axis219.295487 units
50 units Semi-major Axis; 20 units Semi-minor Axis230.131125 units
50 units Semi-major Axis; 25 units Semi-minor Axis242.211205 units
50 units Semi-major Axis; 30 units Semi-minor Axis255.269989 units

Frequently Asked Questions

Common questions about Ellipse Perimeter (Ramanujan) from Semi-Axes, formulas, and typical use cases.

What does the Ellipse Perimeter (Ramanujan) from Semi-Axes calculator do?

It helps with estimating ellipse perimeter for layout, design, and engineering approximations.

What formula does the Ellipse Perimeter (Ramanujan) from Semi-Axes calculator use?

Ramanujan approximation: P ≈ π(a+b)[1 + 3h/(10 + √(4-3h))], where h=((a-b)²/(a+b)²).

What inputs are valid?

Semi-axes must be non-negative, the semi-minor axis cannot exceed the semi-major axis, and not both can be zero.

When would I use this?

estimating ellipse perimeter for layout, design, and engineering approximations

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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