Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes Calculator

✖Outer Semi Major Axis of Elliptical Ring is half of the length of the chord of the outer ellipse which passing through both foci of the outer ellipse of the Elliptical Ring.ⓘ Outer Semi Major Axis of Elliptical Ring [a_Outer]			+10% -10%
✖Outer Linear Eccentricity of Elliptical Ring is the distance from center of the Elliptical Ring to any of the foci of the outer ellipse.ⓘ Outer Linear Eccentricity of Elliptical Ring [c_Outer]			+10% -10%
✖Inner Semi Major Axis of Elliptical Ring is half of the length of the chord of the inner ellipse which passing through both foci of the inner ellipse of the Elliptical Ring.ⓘ Inner Semi Major Axis of Elliptical Ring [a_Inner]			+10% -10%
✖Inner Linear Eccentricity of Elliptical Ring is the distance from center of the Elliptical Ring to any of the foci of the inner ellipse.ⓘ Inner Linear Eccentricity of Elliptical Ring [c_Inner]			+10% -10%

✖Area of Elliptical Ring is the total quantity of plane enclosed between the outer and inner elliptical boundary edges of the Elliptical Ring.ⓘ Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes [A]

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Formula

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Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes

Formula

`"A" = pi*((sqrt("a"_{"Outer"}^2-"c"_{"Outer"}^2)*"a"_{"Outer"})-(sqrt("a"_{"Inner"}^2-"c"_{"Inner"}^2)*"a"_{"Inner"}))`

Example

`"124.9979m²"=pi*((sqrt(("10m")^2-("6m")^2)*"10m")-(sqrt(("7m")^2-("4m")^2)*"7m"))`

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Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Elliptical Ring = pi*((sqrt(Outer Semi Major Axis of Elliptical Ring^2-Outer Linear Eccentricity of Elliptical Ring^2)*Outer Semi Major Axis of Elliptical Ring)-(sqrt(Inner Semi Major Axis of Elliptical Ring^2-Inner Linear Eccentricity of Elliptical Ring^2)*Inner Semi Major Axis of Elliptical Ring))
A = pi*((sqrt(a_Outer^2-c_Outer^2)*a_Outer)-(sqrt(a_Inner^2-c_Inner^2)*a_Inner))
This formula uses 1 Constants, 1 Functions, 5 Variables

Constants Used

pi - Archimedes' constant Value Taken As 3.14159265358979323846264338327950288

Functions Used

sqrt - A square root function is a function that takes a non-negative number as an input and returns the square root of the given input number., sqrt(Number)

Variables Used

Area of Elliptical Ring - (Measured in Square Meter) - Area of Elliptical Ring is the total quantity of plane enclosed between the outer and inner elliptical boundary edges of the Elliptical Ring.
Outer Semi Major Axis of Elliptical Ring - (Measured in Meter) - Outer Semi Major Axis of Elliptical Ring is half of the length of the chord of the outer ellipse which passing through both foci of the outer ellipse of the Elliptical Ring.
Outer Linear Eccentricity of Elliptical Ring - (Measured in Meter) - Outer Linear Eccentricity of Elliptical Ring is the distance from center of the Elliptical Ring to any of the foci of the outer ellipse.
Inner Semi Major Axis of Elliptical Ring - (Measured in Meter) - Inner Semi Major Axis of Elliptical Ring is half of the length of the chord of the inner ellipse which passing through both foci of the inner ellipse of the Elliptical Ring.
Inner Linear Eccentricity of Elliptical Ring - (Measured in Meter) - Inner Linear Eccentricity of Elliptical Ring is the distance from center of the Elliptical Ring to any of the foci of the inner ellipse.

STEP 1: Convert Input(s) to Base Unit

Outer Semi Major Axis of Elliptical Ring: 10 Meter --> 10 Meter No Conversion Required
Outer Linear Eccentricity of Elliptical Ring: 6 Meter --> 6 Meter No Conversion Required
Inner Semi Major Axis of Elliptical Ring: 7 Meter --> 7 Meter No Conversion Required
Inner Linear Eccentricity of Elliptical Ring: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = pi*((sqrt(a_Outer^2-c_Outer^2)*a_Outer)-(sqrt(a_Inner^2-c_Inner^2)*a_Inner)) --> pi*((sqrt(10^2-6^2)*10)-(sqrt(7^2-4^2)*7))

Evaluating ... ...

A = 124.997881628032

STEP 3: Convert Result to Output's Unit

124.997881628032 Square Meter --> No Conversion Required

FINAL ANSWER

124.997881628032 ≈ 124.9979 Square Meter <-- Area of Elliptical Ring

(Calculation completed in 00.020 seconds)

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< 4 Area of Elliptical Ring Calculators

Area of Elliptical Ring given Linear Eccentricities and Semi Minor Axes

Go Area of Elliptical Ring = pi*((sqrt(Outer Semi Minor Axis of Elliptical Ring^2+Outer Linear Eccentricity of Elliptical Ring^2)*Outer Semi Minor Axis of Elliptical Ring)-(sqrt(Inner Semi Minor Axis of Elliptical Ring^2+Inner Linear Eccentricity of Elliptical Ring^2)*Inner Semi Minor Axis of Elliptical Ring))

Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes

Go Area of Elliptical Ring = pi*((sqrt(Outer Semi Major Axis of Elliptical Ring^2-Outer Linear Eccentricity of Elliptical Ring^2)*Outer Semi Major Axis of Elliptical Ring)-(sqrt(Inner Semi Major Axis of Elliptical Ring^2-Inner Linear Eccentricity of Elliptical Ring^2)*Inner Semi Major Axis of Elliptical Ring))

Area of Elliptical Ring given Width and Outer Semi Axes

Go Area of Elliptical Ring = pi*((Outer Semi Major Axis of Elliptical Ring*Outer Semi Minor Axis of Elliptical Ring)-((Outer Semi Major Axis of Elliptical Ring-Ring Width of Elliptical Ring)*(Outer Semi Minor Axis of Elliptical Ring-Ring Width of Elliptical Ring)))

Area of Elliptical Ring

Go Area of Elliptical Ring = pi*((Outer Semi Major Axis of Elliptical Ring*Outer Semi Minor Axis of Elliptical Ring)-(Inner Semi Major Axis of Elliptical Ring*Inner Semi Minor Axis of Elliptical Ring))

Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes Formula

What is an Elliptical Ring?

An Elliptical Ring is an ellipse in which another smaller ellipse is removed from the center, such that the difference of inner and outer semi axes (semi major axes and semi minor axes) are equal. That difference is called the width of the Elliptical Ring.

What is an Ellipse?

An Ellipse is basically a conic section. If we cut a right circular cone using a plane at an angle greater than the semi angle of cone. Geometrically an Ellipse is the collection of all points in a plane such that the sum of the distances to them from two fixed points is a constant. Those fixed points are the foci of the Ellipse. The largest chord of the Ellipse is the major axis and the chord which passing through the center and perpendicular to the major axis is the minor axis of the ellipse. Circle is a special case of Ellipse in which both foci coincide at the center and so both major and minor axes become equal in length which is called the diameter of the circle.

How to Calculate Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes?

Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes calculator uses Area of Elliptical Ring = pi*((sqrt(Outer Semi Major Axis of Elliptical Ring^2-Outer Linear Eccentricity of Elliptical Ring^2)*Outer Semi Major Axis of Elliptical Ring)-(sqrt(Inner Semi Major Axis of Elliptical Ring^2-Inner Linear Eccentricity of Elliptical Ring^2)*Inner Semi Major Axis of Elliptical Ring)) to calculate the Area of Elliptical Ring, Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes formula is defined as the total quantity of plane enclosed between the outer and inner elliptical boundary edges of the Elliptical Ring and calculated using the linear eccentricities and semi-major axes of the Elliptical Ring. Area of Elliptical Ring is denoted by A symbol.

How to calculate Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes using this online calculator? To use this online calculator for Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes, enter Outer Semi Major Axis of Elliptical Ring (a_Outer), Outer Linear Eccentricity of Elliptical Ring (c_Outer), Inner Semi Major Axis of Elliptical Ring (a_Inner) & Inner Linear Eccentricity of Elliptical Ring (c_Inner) and hit the calculate button. Here is how the Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes calculation can be explained with given input values -> 124.9979 = pi*((sqrt(10^2-6^2)*10)-(sqrt(7^2-4^2)*7)).

FAQ

What is Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes?

Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes formula is defined as the total quantity of plane enclosed between the outer and inner elliptical boundary edges of the Elliptical Ring and calculated using the linear eccentricities and semi-major axes of the Elliptical Ring and is represented as A = pi*((sqrt(a_Outer^2-c_Outer^2)*a_Outer)-(sqrt(a_Inner^2-c_Inner^2)*a_Inner)) or Area of Elliptical Ring = pi*((sqrt(Outer Semi Major Axis of Elliptical Ring^2-Outer Linear Eccentricity of Elliptical Ring^2)*Outer Semi Major Axis of Elliptical Ring)-(sqrt(Inner Semi Major Axis of Elliptical Ring^2-Inner Linear Eccentricity of Elliptical Ring^2)*Inner Semi Major Axis of Elliptical Ring)). Outer Semi Major Axis of Elliptical Ring is half of the length of the chord of the outer ellipse which passing through both foci of the outer ellipse of the Elliptical Ring, Outer Linear Eccentricity of Elliptical Ring is the distance from center of the Elliptical Ring to any of the foci of the outer ellipse, Inner Semi Major Axis of Elliptical Ring is half of the length of the chord of the inner ellipse which passing through both foci of the inner ellipse of the Elliptical Ring & Inner Linear Eccentricity of Elliptical Ring is the distance from center of the Elliptical Ring to any of the foci of the inner ellipse.

How to calculate Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes?

Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes formula is defined as the total quantity of plane enclosed between the outer and inner elliptical boundary edges of the Elliptical Ring and calculated using the linear eccentricities and semi-major axes of the Elliptical Ring is calculated using Area of Elliptical Ring = pi*((sqrt(Outer Semi Major Axis of Elliptical Ring^2-Outer Linear Eccentricity of Elliptical Ring^2)*Outer Semi Major Axis of Elliptical Ring)-(sqrt(Inner Semi Major Axis of Elliptical Ring^2-Inner Linear Eccentricity of Elliptical Ring^2)*Inner Semi Major Axis of Elliptical Ring)). To calculate Area of Elliptical Ring given Linear Eccentricities and Semi Major Axes, you need Outer Semi Major Axis of Elliptical Ring (a_Outer), Outer Linear Eccentricity of Elliptical Ring (c_Outer), Inner Semi Major Axis of Elliptical Ring (a_Inner) & Inner Linear Eccentricity of Elliptical Ring (c_Inner). With our tool, you need to enter the respective value for Outer Semi Major Axis of Elliptical Ring, Outer Linear Eccentricity of Elliptical Ring, Inner Semi Major Axis of Elliptical Ring & Inner Linear Eccentricity of Elliptical Ring and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

How many ways are there to calculate Area of Elliptical Ring?

In this formula, Area of Elliptical Ring uses Outer Semi Major Axis of Elliptical Ring, Outer Linear Eccentricity of Elliptical Ring, Inner Semi Major Axis of Elliptical Ring & Inner Linear Eccentricity of Elliptical Ring. We can use 3 other way(s) to calculate the same, which is/are as follows -

Area of Elliptical Ring = pi*((sqrt(Outer Semi Minor Axis of Elliptical Ring^2+Outer Linear Eccentricity of Elliptical Ring^2)*Outer Semi Minor Axis of Elliptical Ring)-(sqrt(Inner Semi Minor Axis of Elliptical Ring^2+Inner Linear Eccentricity of Elliptical Ring^2)*Inner Semi Minor Axis of Elliptical Ring))
Area of Elliptical Ring = pi*((Outer Semi Major Axis of Elliptical Ring*Outer Semi Minor Axis of Elliptical Ring)-((Outer Semi Major Axis of Elliptical Ring-Ring Width of Elliptical Ring)*(Outer Semi Minor Axis of Elliptical Ring-Ring Width of Elliptical Ring)))
Area of Elliptical Ring = pi*((Outer Semi Major Axis of Elliptical Ring*Outer Semi Minor Axis of Elliptical Ring)-(Inner Semi Major Axis of Elliptical Ring*Inner Semi Minor Axis of Elliptical Ring))

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