Ellipse Area

Ellipse Area Calculation:

• r1 =

  Radius 1

  Radius along the major axis, the maximum radius

• r2 =

  Radius 2

  Radius along the minor axis, the minimum radius

•  A =

  Answer

  Area of the ellipse in square units

• -3 -2 -1 0 1 2 3 4 5 6 7 8 9

  Decimals

  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 Area Formula

An ellipse is a circle stretched symmetrically along an axis. This axis is called the major axis and will be the longest line across the ellipse through the center. Perpendicular to the major axis will be the minor axis, which will be the shortest line across an ellipse through the center

Area will be calculated almost identically to that of a circle except instead of squaring the radius we must multiply the radius along the major axis by the radius along the minor axis.

Ellipse Area Variables

To work out the area of an ellipse two radii must be known; the longest and shortest possible radii.

Radius 1 (r₁)

Radius along the major axis. The maximum possible radii in the ellipse, also called semi-major axis because it is half the major axis. Order of the radii input into the formula is not important so this chould be either radii.

Radius 2 (r₂)

Radius along the minor axis. The minimum possible radii in the ellipse, also called the semi-minor axis because it is half the minor axis. Order of the radii input into the formula is not important so this chould be either radii.

Area (A)

Total area of the ellipse measured in square units.

Ellipse Area Solution

Work out the area of an ellipse if the semi-major axis (r₁) is 5 and the semi-minor axis (r₂) is 3.

An ellipse with a semi-major axis of 5 and a semi-minor axis of 3 will have an area of about 47.12 square units.

Ellipse Area Example

What is the area of an ellipse if r₁ is 8 inches and r₂ is 6 inches? Use 3.14159 as π

An ellipse where r₁ is 8 inches and r₂ is 6 inches will have an area of about 150.8 square inches, or 972.901 square centimetres after conversion.