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Ellipse perimeter calculator

Estimate the perimeter of an ellipse from its two semi-axes (Ramanujan's formula).

Related tools

All Geometry tools →
Ellipse area calculatorCompute the area of an ellipse from its semi-major and semi-minor axes.Perimeter calculatorCompute the perimeter of a rectangle, square, circle or triangle.Regular polygon perimeter calculatorCompute the perimeter of a regular polygon from its number of sides and side length.Equilateral triangle calculatorCompute the area, height and perimeter of an equilateral triangle from its side.Triangle area calculator (Heron's formula)Compute a triangle's area from the length of its three sides.Rectangle diagonal calculatorCompute the diagonal, area and perimeter of a rectangle.Volume of an ellipsoid calculatorThe volume of an ellipsoid from its three semi-axes: V = 4⁄3·π·a·b·c. It also reports the surface area (Thomsen's approximation) — set all three axes equal and it becomes a sphere. Useful for eggs, tanks, planets and any squashed sphere.Rectangle calculatorEvery property of a rectangle from any two you know. Pick what you have — length & width, area & a side, perimeter & a side, or diagonal & a side — and it returns the length, width, area, perimeter and diagonal, using A = l·w, P = 2(l+w) and d = √(l²+w²).

Enter Semi-major axis (a), Semi-minor axis (b) and the Ellipse perimeter calculator works out Perimeter straight away. For instance, with Semi-major axis (a) = 5 and Semi-minor axis (b) = 3 it returns Perimeter = 25.527.

How to use it

  1. Enter your values: Semi-major axis (a), Semi-minor axis (b).
  2. Read the result instantly: Perimeter.

Frequently asked questions

What does the Ellipse perimeter calculator actually compute?

It takes Semi-major axis (a) and Semi-minor axis (b) and derives Perimeter from them. The calculation is live as you type, so the result updates on every change.

What information do I need to provide?

2 values: Semi-major axis (a) and Semi-minor axis (b). Nothing else is required — no account, no file upload.

Can you show a worked example?

With Semi-major axis (a) = 5 and Semi-minor axis (b) = 3, the calculator returns Perimeter = 25.527. Those figures come from running this exact tool, so you can reproduce them by entering the same values.

What happens if I enter larger values?

It moves a lot. Using Semi-major axis (a) = 10 and Semi-minor axis (b) = 6 instead, Perimeter goes from 25.527 to 51.054 — which is why it is worth testing a few scenarios rather than trusting a single figure.

What does it give for smaller values?

Scaled down to Semi-major axis (a) = 3 and Semi-minor axis (b) = 2, Perimeter comes out at 15.865. The relationship is worth checking at both ends before you rely on a single result.

When would I actually use this?

Homework and site work alike: how much paint a wall takes, how much water a tank holds, whether a corner is square — and, on the coordinate side, the slope between two points, the distance across a plan, the midpoint of a span.

What is the most common mistake?

Mixing units inside one shape. Entering a length in centimetres and a width in metres gives an area wrong by a factor of a hundred, and the result looks perfectly plausible.

What is the difference between the Ellipse perimeter calculator and the Ellipse area calculator?

This one returns Perimeter; the Ellipse area calculator returns Area. That is the whole difference — open the one whose figure you need.

Is there a tool for the next step?

Perimeter calculator is the closest one after this: Compute the perimeter of a rectangle, square, circle or triangle.

What else is worth having open alongside it?

Regular polygon perimeter calculator and Equilateral triangle calculator — they come up in the same task often enough to be worth a second tab.

Further reading

All guides →
How-toHow to Find the Area of a Triangle: Base × Height and Heron's FormulaTwo reliable ways to find a triangle's area: half base times height when you know the height, and Heron's formula when you only know the three sides.ExplainerThe Flat Pattern of a Cone Is a Sector, Not a CircleRoll a 50 mm cone 80 mm tall and its pattern is a 190.8° slice of a 94 mm circle. Flatten a nearly cylindrical lampshade and the pattern radius runs to 839 mm — the shallower the taper, the further away the apex.How-toHow to Find the Distance Between Two PointsUse the distance formula d = √((x₂−x₁)² + (y₂−y₁)²) to measure the straight-line distance between two points on a plane, with a worked example and the midpoint too.How-toHow to Calculate the Slope of a Line: Rise Over RunFind the slope of a line from two points with m = (y₂ − y₁) / (x₂ − x₁), and read what a positive, negative, zero, or undefined slope tells you.ExplainerThe Pythagorean Theorem ExplainedIn a right triangle, a² + b² = c². Here's what the formula means, a worked example, how to find any side, and where it's used in real life.How-toHow to Calculate VolumeVolume is the space inside a shape. Here's how to find it for boxes, cylinders and spheres, and why keeping your units consistent is the whole game.