Ellipse Circumference

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Ellipse Circumference Calculation:

  • r1 =

    Radius on the major axis

  • r2 =

    Radius on the minor axis

  • ~C =

    Approximate circumference of the ellipse

  •

    Choose the number of decimals to show in your answer. This is also known as significant figures. Select an appropriate amount of significant figures based on the precision of the input numbers.

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Ellipse Circumference Formula

An ellipse is a circle stretched along a single axis; this long axis is called the major axis and the shortest distance across the ellipse is called the minor axis. To calculate the circumference of an ellipse we can use the radius along each axis. This particular method is not a precise calculation but will provide a nice estimate so long as the major axis is not significantly longer than the minor axis.

C = 2π * √((r12 + r22) / 2)

Ellipse Perimeter Formula
Circumference Formula for an Ellipse

Ellipse Circumference Variables

Radius along the major axis and radius along the minor axis are two variables that can be used to calculate the circumference of an ellipse.

Radius 1 (r1)
Longest radius in the ellipse along the major axis.
Radius 2 (r2)
Shortest radius in the ellipse along the minor axis.
Circumference (c)
Distance completely around the perimeter of the ellipse.

Ellipse Circumference Solution

How to find the circumference of an ellipse with a radius of 7 along and major axis and a radius of 5 along the minor axis.

  • C = 2π * √((r12 + r22) / 2)
  • Formula to find the circumference of an ellipse
  • C = 2π * √((72 + 52) / 2)
  • Substitute in the radii values
  • C = 2π * √((49 + 25) / 2)
  • Square the radii values
  • C = 2π * √(74 / 2)
  • Addition inside brackets
  • C = 2π * √37
  • Division inside brackets
  • C = 2π * 6.083
  • Square root, rounded to three decimals
  • C = 2 * 3.14159 * 6.083
  • Use a value of 3.14159 as π
  • C = 38.22058394
  • final multiplication
  • approximately 38.221 linear units

An ellipse with a radius of 7 along the major axis and 5 along the minor axis will have a circumference of about 38.221.

Ellipse Circumference Example

Calculate the circumference of an ellispe that has a major axis of 24 inches and a minor axis of 18 inches. Note: the radius will be half the value of each axis.

  • C = 2π * √((r12 + r22) / 2)
  • C = 2π * √((122 + 92) / 2)
  • C = 2π * √((144 + 81) / 2)
  • C = 2π * √(225 / 2)
  • C = 2π * √(112.5)
  • C = 2 * 3.14159 * 10.607
  • ~66.646

An ellipse with a major axis of 24 inches and a minor axis of 18 inches will have a circumference of about 66.65 inches.

Want to find the ellipse area?

Ellipse area

Ellipse Perimeter Formula