Ellipse Circumference Calculator

Created by Madhu Raman
Reviewed by Kenneth Alambra
Last updated: Jul 27, 2022

The ellipse circumference calculator helps you find the total perimeter around the ellipse, which is also referred to as the circumference of the ellipse. The ellipse circumference depends on the lengths of the semi-major and semi-minor axes. Read on to know more about how to find the circumference of an ellipse, and the formula to calculate it.

What is ellipse circumference?

The circumference of the ellipse is the total length of the boundary of the elliptical shape. In other words, we also refer to the perimeter of the ellipse as its circumference.

What is the formula for the circumference of the ellipse?

To calculate the ellipse circumference, we need to know the semi-major and semi-minor axes' lengths. Once we get these, we'd find the ellipse circumference using the following formula:

pπ(a+b)(1+3h10+43h)\small p \approx \pi (a+b) \left ( 1 + \frac {3h}{10 + \sqrt{4-3h}} \right )

where:
aa - Semi-major axis of the ellipse; and
bb - Semi-minor axis of the ellipse.

To find the value of hh in the above equation, we will use the following formula:

h=(ab)2(a+b)2\small h = \frac{(a-b)^2}{(a+b)^2}

Thus, using the above equations for ellipse circumference, we can find its approximate value.

How do I use the ellipse circumference calculator?

To find the ellipse circumference using our calculator, you need to do the following:

  1. Enter the value of the semi-major axis (a).
  2. Enter the value of the semi-minor axis (b).
  3. Voila! The tool will perform all the heavy computing to calculate the ellipse circumference and will display it as the result!

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FAQ

How do I find the circumference of an ellipse?

To find the circumference of an ellipse, we need to use the ellipse circumference equation, which is governed by the following steps:

  1. Find the values of the semi-major axis (a) and the semi-minor axis (b).
  2. Calculate the value of the variable h using the formula h = (a - b)²/(a + b)².
  3. Plug in the values of a, b and h in the formula for the circumference, given by this equation:
    Circumference = π × (a + b)[1 + (3 × h/(10 + √(4 - 3h)))].
  4. Tada! You now have the approximate value of the circumference of the ellipse!

Does ellipse have circumference?

Yes! We sometimes refer to the boundary of the ellipse as the circumference of the ellipse! Though the term circumference is usually associated with a circle, we also use it to refer to the ellipse's perimeter.

Madhu Raman
Ellipse with semiaxes, foci, center and vertices marked
(x - c₁)² / a² + (y - c₂)² / b² = 1
a
b
Circumference
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