Area of Elliptical Segment Calculator

✖Major Axis of Elliptical Segment is the chord passing through both the foci of the Ellipse from which the Elliptical Segment is cut.ⓘ Major Axis of Elliptical Segment [2a]			+10% -10%
✖Minor Axis of Elliptical Segment is the length of the longest chord which is perpendicular to the line joining the foci of the Ellipse from which the Elliptical Segment is cut.ⓘ Minor Axis of Elliptical Segment [2b]			+10% -10%
✖Height of Elliptical Segment is the maximum vertical distance from the base edge to the curved edge of the Elliptical Segment.ⓘ Height of Elliptical Segment [h]			+10% -10%

✖Area of Elliptical Segment is the total quantity of plane enclosed by the boundary of the Elliptical Segment.ⓘ Area of Elliptical Segment [A]

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Formula

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Area of Elliptical Segment

Formula

`"A" = (("2a"*"2b")/4)*(arccos(1-((2*"h")/"2a"))-(1-((2*"h")/"2a"))*sqrt(((4*"h")/"2a")-((4*"h"^2)/("2a"^2))))`

Example

`"26.83771m²"=(("20m"*"12m")/4)*(arccos(1-((2*"4m")/"20m"))-(1-((2*"4m")/"20m"))*sqrt(((4*"4m")/"20m")-((4*("4m")^2)/(("20m")^2))))`

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Area of Elliptical Segment Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Elliptical Segment = ((Major Axis of Elliptical Segment*Minor Axis of Elliptical Segment)/4)*(arccos(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))-(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))*sqrt(((4*Height of Elliptical Segment)/Major Axis of Elliptical Segment)-((4*Height of Elliptical Segment^2)/(Major Axis of Elliptical Segment^2))))
A = ((2a*2b)/4)*(arccos(1-((2*h)/2a))-(1-((2*h)/2a))*sqrt(((4*h)/2a)-((4*h^2)/(2a^2))))
This formula uses 3 Functions, 4 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
arccos - Arccosine function, is the inverse function of the cosine function.It is the function that takes a ratio as an input and returns the angle whose cosine is equal to that ratio., arccos(Number)
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 Segment - (Measured in Square Meter) - Area of Elliptical Segment is the total quantity of plane enclosed by the boundary of the Elliptical Segment.
Major Axis of Elliptical Segment - (Measured in Meter) - Major Axis of Elliptical Segment is the chord passing through both the foci of the Ellipse from which the Elliptical Segment is cut.
Minor Axis of Elliptical Segment - (Measured in Meter) - Minor Axis of Elliptical Segment is the length of the longest chord which is perpendicular to the line joining the foci of the Ellipse from which the Elliptical Segment is cut.
Height of Elliptical Segment - (Measured in Meter) - Height of Elliptical Segment is the maximum vertical distance from the base edge to the curved edge of the Elliptical Segment.

STEP 1: Convert Input(s) to Base Unit

Major Axis of Elliptical Segment: 20 Meter --> 20 Meter No Conversion Required
Minor Axis of Elliptical Segment: 12 Meter --> 12 Meter No Conversion Required
Height of Elliptical Segment: 4 Meter --> 4 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A = ((2a*2b)/4)*(arccos(1-((2*h)/2a))-(1-((2*h)/2a))*sqrt(((4*h)/2a)-((4*h^2)/(2a^2)))) --> ((20*12)/4)*(arccos(1-((2*4)/20))-(1-((2*4)/20))*sqrt(((4*4)/20)-((4*4^2)/(20^2))))

Evaluating ... ...

A = 26.8377130800967

STEP 3: Convert Result to Output's Unit

26.8377130800967 Square Meter --> No Conversion Required

FINAL ANSWER

26.8377130800967 ≈ 26.83771 Square Meter <-- Area of Elliptical Segment

(Calculation completed in 00.020 seconds)

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Created by Mona Gladys

St Joseph's College (SJC), Bengaluru

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Walchand College of Engineering (WCE), Sangli

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< 5 Elliptical Segment Calculators

Area of Elliptical Segment

Go Area of Elliptical Segment = ((Major Axis of Elliptical Segment*Minor Axis of Elliptical Segment)/4)*(arccos(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))-(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))*sqrt(((4*Height of Elliptical Segment)/Major Axis of Elliptical Segment)-((4*Height of Elliptical Segment^2)/(Major Axis of Elliptical Segment^2))))

Semi Major Axis of Elliptical Segment

Go Semi Major Axis of Elliptical Segment = Major Axis of Elliptical Segment/2

Semi Minor Axis of Elliptical Segment

Go Semi Minor Axis of Elliptical Segment = Minor Axis of Elliptical Segment/2

Major Axis of Elliptical Segment

Go Major Axis of Elliptical Segment = 2*Semi Major Axis of Elliptical Segment

Minor Axis of Elliptical Segment

Go Minor Axis of Elliptical Segment = 2*Semi Minor Axis of Elliptical Segment

Area of Elliptical Segment Formula

What is an Elliptical Segment?

An Elliptical Segment is obtained by cutting an Ellipse along a chord of the Ellipse which is parallel to either the major axis or the minor axis of the Ellipse.

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 Segment?

Area of Elliptical Segment calculator uses Area of Elliptical Segment = ((Major Axis of Elliptical Segment*Minor Axis of Elliptical Segment)/4)*(arccos(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))-(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))*sqrt(((4*Height of Elliptical Segment)/Major Axis of Elliptical Segment)-((4*Height of Elliptical Segment^2)/(Major Axis of Elliptical Segment^2)))) to calculate the Area of Elliptical Segment, Area of Elliptical Segment formula is defined as the total quantity of plane enclosed by the boundary of the Elliptical Segment. Area of Elliptical Segment is denoted by A symbol.

How to calculate Area of Elliptical Segment using this online calculator? To use this online calculator for Area of Elliptical Segment, enter Major Axis of Elliptical Segment (2a), Minor Axis of Elliptical Segment (2b) & Height of Elliptical Segment (h) and hit the calculate button. Here is how the Area of Elliptical Segment calculation can be explained with given input values -> 26.83771 = ((20*12)/4)*(arccos(1-((2*4)/20))-(1-((2*4)/20))*sqrt(((4*4)/20)-((4*4^2)/(20^2)))).

FAQ

What is Area of Elliptical Segment?

Area of Elliptical Segment formula is defined as the total quantity of plane enclosed by the boundary of the Elliptical Segment and is represented as A = ((2a*2b)/4)*(arccos(1-((2*h)/2a))-(1-((2*h)/2a))*sqrt(((4*h)/2a)-((4*h^2)/(2a^2)))) or Area of Elliptical Segment = ((Major Axis of Elliptical Segment*Minor Axis of Elliptical Segment)/4)*(arccos(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))-(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))*sqrt(((4*Height of Elliptical Segment)/Major Axis of Elliptical Segment)-((4*Height of Elliptical Segment^2)/(Major Axis of Elliptical Segment^2)))). Major Axis of Elliptical Segment is the chord passing through both the foci of the Ellipse from which the Elliptical Segment is cut, Minor Axis of Elliptical Segment is the length of the longest chord which is perpendicular to the line joining the foci of the Ellipse from which the Elliptical Segment is cut & Height of Elliptical Segment is the maximum vertical distance from the base edge to the curved edge of the Elliptical Segment.

How to calculate Area of Elliptical Segment?

Area of Elliptical Segment formula is defined as the total quantity of plane enclosed by the boundary of the Elliptical Segment is calculated using Area of Elliptical Segment = ((Major Axis of Elliptical Segment*Minor Axis of Elliptical Segment)/4)*(arccos(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))-(1-((2*Height of Elliptical Segment)/Major Axis of Elliptical Segment))*sqrt(((4*Height of Elliptical Segment)/Major Axis of Elliptical Segment)-((4*Height of Elliptical Segment^2)/(Major Axis of Elliptical Segment^2)))). To calculate Area of Elliptical Segment, you need Major Axis of Elliptical Segment (2a), Minor Axis of Elliptical Segment (2b) & Height of Elliptical Segment (h). With our tool, you need to enter the respective value for Major Axis of Elliptical Segment, Minor Axis of Elliptical Segment & Height of Elliptical Segment and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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