Area of Elliptical Sector Calculator

✖Semi Major Axis of Elliptical Sector is half of the chord passing through both the foci of the Ellipse from which the Elliptical Sector is cut.ⓘ Semi Major Axis of Elliptical Sector [a_Sector]			+10% -10%
✖Semi Minor Axis of Elliptical Sector is half of the length of the longest chord which is perpendicular to the line joining the foci of the Ellipse from which the Elliptical Sector is cut.ⓘ Semi Minor Axis of Elliptical Sector [b_Sector]			+10% -10%
✖Angle of Elliptical Sector is the angle made by the linear edges of the sector at the center of the Elliptical Sector.ⓘ Angle of Elliptical Sector [∠_Sector]			+10% -10%
✖Second Leg Angle of Elliptical Sector is the angle made by the semi major axis on the right and the linear edge of the sector which is far from that semi major axis of the Elliptical Sector.ⓘ Second Leg Angle of Elliptical Sector [∠_Leg(2)]			+10% -10%
✖First Leg Angle of Elliptical Sector is the angle made by the semi major axis on the right and the linear edge of the sector which is adjacent to that semi major axis of the Elliptical Sector.ⓘ First Leg Angle of Elliptical Sector [∠_Leg(1)]			+10% -10%

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

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Area of Elliptical Sector Solution

STEP 0: Pre-Calculation Summary

Formula Used

Area of Elliptical Sector = ((Semi Major Axis of Elliptical Sector*Semi Minor Axis of Elliptical Sector)/2)*(Angle of Elliptical Sector-atan(((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*sin(2*Second Leg Angle of Elliptical Sector))/(Semi Major Axis of Elliptical Sector+Semi Minor Axis of Elliptical Sector+((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*cos(2*Second Leg Angle of Elliptical Sector))))+atan(((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*sin(2*First Leg Angle of Elliptical Sector))/(Semi Major Axis of Elliptical Sector+Semi Minor Axis of Elliptical Sector+((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*cos(2*First Leg Angle of Elliptical Sector)))))
A_Sec = ((a_Sector*b_Sector)/2)*(∠_Sector-atan(((b_Sector-a_Sector)*sin(2*∠_Leg(2)))/(a_Sector+b_Sector+((b_Sector-a_Sector)*cos(2*∠_Leg(2)))))+atan(((b_Sector-a_Sector)*sin(2*∠_Leg(1)))/(a_Sector+b_Sector+((b_Sector-a_Sector)*cos(2*∠_Leg(1))))))
This formula uses 4 Functions, 6 Variables

Functions Used

sin - Sine is a trigonometric function that describes the ratio of the length of the opposite side of a right triangle to the length of the hypotenuse., sin(Angle)
cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)
tan - The tangent of an angle is a trigonometric ratio of the length of the side opposite an angle to the length of the side adjacent to an angle in a right triangle., tan(Angle)
atan - Inverse tan is used to calculate the angle by applying the tangent ratio of the angle, which is the opposite side divided by the adjacent side of the right triangle., atan(Number)

Variables Used

Area of Elliptical Sector - (Measured in Square Meter) - Area of Elliptical Sector is the total quantity of plane enclosed by the boundary of the Elliptical Sector.
Semi Major Axis of Elliptical Sector - (Measured in Meter) - Semi Major Axis of Elliptical Sector is half of the chord passing through both the foci of the Ellipse from which the Elliptical Sector is cut.
Semi Minor Axis of Elliptical Sector - (Measured in Meter) - Semi Minor Axis of Elliptical Sector is half of the length of the longest chord which is perpendicular to the line joining the foci of the Ellipse from which the Elliptical Sector is cut.
Angle of Elliptical Sector - (Measured in Radian) - Angle of Elliptical Sector is the angle made by the linear edges of the sector at the center of the Elliptical Sector.
Second Leg Angle of Elliptical Sector - (Measured in Radian) - Second Leg Angle of Elliptical Sector is the angle made by the semi major axis on the right and the linear edge of the sector which is far from that semi major axis of the Elliptical Sector.
First Leg Angle of Elliptical Sector - (Measured in Radian) - First Leg Angle of Elliptical Sector is the angle made by the semi major axis on the right and the linear edge of the sector which is adjacent to that semi major axis of the Elliptical Sector.

STEP 1: Convert Input(s) to Base Unit

Semi Major Axis of Elliptical Sector: 10 Meter --> 10 Meter No Conversion Required
Semi Minor Axis of Elliptical Sector: 6 Meter --> 6 Meter No Conversion Required
Angle of Elliptical Sector: 90 Degree --> 1.5707963267946 Radian (Check conversion here)
Second Leg Angle of Elliptical Sector: 120 Degree --> 2.0943951023928 Radian (Check conversion here)
First Leg Angle of Elliptical Sector: 30 Degree --> 0.5235987755982 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

A_Sec = ((a_Sector*b_Sector)/2)*(∠_Sector-atan(((b_Sector-a_Sector)*sin(2*∠_Leg(2)))/(a_Sector+b_Sector+((b_Sector-a_Sector)*cos(2*∠_Leg(2)))))+atan(((b_Sector-a_Sector)*sin(2*∠_Leg(1)))/(a_Sector+b_Sector+((b_Sector-a_Sector)*cos(2*∠_Leg(1)))))) --> ((10*6)/2)*(1.5707963267946-atan(((6-10)*sin(2*2.0943951023928))/(10+6+((6-10)*cos(2*2.0943951023928))))+atan(((6-10)*sin(2*0.5235987755982))/(10+6+((6-10)*cos(2*0.5235987755982)))))

Evaluating ... ...

A_Sec = 34.1432054805833

STEP 3: Convert Result to Output's Unit

34.1432054805833 Square Meter --> No Conversion Required

FINAL ANSWER

34.1432054805833 ≈ 34.14321 Square Meter <-- Area of Elliptical Sector

(Calculation completed in 00.012 seconds)

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St Joseph's College (SJC), Bengaluru

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Vellore Institute of Technology (VIT), Bhopal

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< Elliptical Sector Calculators

First Leg of Elliptical Sector

LaTeX Go First Leg of Elliptical Sector = sqrt((Semi Major Axis of Elliptical Sector^2*Semi Minor Axis of Elliptical Sector^2)/((Semi Major Axis of Elliptical Sector^2*sin(First Leg Angle of Elliptical Sector)^2)+(Semi Minor Axis of Elliptical Sector^2*cos(First Leg Angle of Elliptical Sector)^2)))

Second Leg Angle of Elliptical Sector

LaTeX Go Second Leg Angle of Elliptical Sector = Angle of Elliptical Sector+First Leg Angle of Elliptical Sector

First Leg Angle of Elliptical Sector

LaTeX Go First Leg Angle of Elliptical Sector = Second Leg Angle of Elliptical Sector-Angle of Elliptical Sector

Angle of Elliptical Sector

LaTeX Go Angle of Elliptical Sector = Second Leg Angle of Elliptical Sector-First Leg Angle of Elliptical Sector

Area of Elliptical Sector Formula

LaTeX Go

What is an Elliptical Sector?

An Elliptic Sector is a region bounded by an arc of an ellipse and line segments connecting the center of the ellipse and the endpoints of the arc. The angle made by those line segments is the angle of Elliptical Sector.

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 Sector?

Area of Elliptical Sector calculator uses Area of Elliptical Sector = ((Semi Major Axis of Elliptical Sector*Semi Minor Axis of Elliptical Sector)/2)*(Angle of Elliptical Sector-atan(((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*sin(2*Second Leg Angle of Elliptical Sector))/(Semi Major Axis of Elliptical Sector+Semi Minor Axis of Elliptical Sector+((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*cos(2*Second Leg Angle of Elliptical Sector))))+atan(((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*sin(2*First Leg Angle of Elliptical Sector))/(Semi Major Axis of Elliptical Sector+Semi Minor Axis of Elliptical Sector+((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*cos(2*First Leg Angle of Elliptical Sector))))) to calculate the Area of Elliptical Sector, Area of Elliptical Sector formula is defined as the total quantity of plane enclosed by the boundary of the Elliptical Sector. Area of Elliptical Sector is denoted by A_Sec symbol.

How to calculate Area of Elliptical Sector using this online calculator? To use this online calculator for Area of Elliptical Sector, enter Semi Major Axis of Elliptical Sector (a_Sector), Semi Minor Axis of Elliptical Sector (b_Sector), Angle of Elliptical Sector (∠_Sector), Second Leg Angle of Elliptical Sector (∠_Leg(2)) & First Leg Angle of Elliptical Sector (∠_Leg(1)) and hit the calculate button. Here is how the Area of Elliptical Sector calculation can be explained with given input values -> 34.14321 = ((10*6)/2)*(1.5707963267946-atan(((6-10)*sin(2*2.0943951023928))/(10+6+((6-10)*cos(2*2.0943951023928))))+atan(((6-10)*sin(2*0.5235987755982))/(10+6+((6-10)*cos(2*0.5235987755982))))).

FAQ

What is Area of Elliptical Sector?

Area of Elliptical Sector formula is defined as the total quantity of plane enclosed by the boundary of the Elliptical Sector and is represented as A_Sec = ((a_Sector*b_Sector)/2)*(∠_Sector-atan(((b_Sector-a_Sector)*sin(2*∠_Leg(2)))/(a_Sector+b_Sector+((b_Sector-a_Sector)*cos(2*∠_Leg(2)))))+atan(((b_Sector-a_Sector)*sin(2*∠_Leg(1)))/(a_Sector+b_Sector+((b_Sector-a_Sector)*cos(2*∠_Leg(1)))))) or Area of Elliptical Sector = ((Semi Major Axis of Elliptical Sector*Semi Minor Axis of Elliptical Sector)/2)*(Angle of Elliptical Sector-atan(((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*sin(2*Second Leg Angle of Elliptical Sector))/(Semi Major Axis of Elliptical Sector+Semi Minor Axis of Elliptical Sector+((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*cos(2*Second Leg Angle of Elliptical Sector))))+atan(((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*sin(2*First Leg Angle of Elliptical Sector))/(Semi Major Axis of Elliptical Sector+Semi Minor Axis of Elliptical Sector+((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*cos(2*First Leg Angle of Elliptical Sector))))). Semi Major Axis of Elliptical Sector is half of the chord passing through both the foci of the Ellipse from which the Elliptical Sector is cut, Semi Minor Axis of Elliptical Sector is half of the length of the longest chord which is perpendicular to the line joining the foci of the Ellipse from which the Elliptical Sector is cut, Angle of Elliptical Sector is the angle made by the linear edges of the sector at the center of the Elliptical Sector, Second Leg Angle of Elliptical Sector is the angle made by the semi major axis on the right and the linear edge of the sector which is far from that semi major axis of the Elliptical Sector & First Leg Angle of Elliptical Sector is the angle made by the semi major axis on the right and the linear edge of the sector which is adjacent to that semi major axis of the Elliptical Sector.

How to calculate Area of Elliptical Sector?

Area of Elliptical Sector formula is defined as the total quantity of plane enclosed by the boundary of the Elliptical Sector is calculated using Area of Elliptical Sector = ((Semi Major Axis of Elliptical Sector*Semi Minor Axis of Elliptical Sector)/2)*(Angle of Elliptical Sector-atan(((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*sin(2*Second Leg Angle of Elliptical Sector))/(Semi Major Axis of Elliptical Sector+Semi Minor Axis of Elliptical Sector+((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*cos(2*Second Leg Angle of Elliptical Sector))))+atan(((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*sin(2*First Leg Angle of Elliptical Sector))/(Semi Major Axis of Elliptical Sector+Semi Minor Axis of Elliptical Sector+((Semi Minor Axis of Elliptical Sector-Semi Major Axis of Elliptical Sector)*cos(2*First Leg Angle of Elliptical Sector))))). To calculate Area of Elliptical Sector, you need Semi Major Axis of Elliptical Sector (a_Sector), Semi Minor Axis of Elliptical Sector (b_Sector), Angle of Elliptical Sector (∠_Sector), Second Leg Angle of Elliptical Sector (∠_Leg(2)) & First Leg Angle of Elliptical Sector (∠_Leg(1)). With our tool, you need to enter the respective value for Semi Major Axis of Elliptical Sector, Semi Minor Axis of Elliptical Sector, Angle of Elliptical Sector, Second Leg Angle of Elliptical Sector & First Leg Angle of Elliptical Sector 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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