Semi Major Axis of Ellipse given Area and Eccentricity Calculator

✖Area of Ellipse is the total quantity of plane enclosed by the boundary of the Ellipse.ⓘ Area of Ellipse [A]			+10% -10%
✖Eccentricity of Ellipse is the ratio of the linear eccentricity to the semi major axis of the Ellipse.ⓘ Eccentricity of Ellipse [e]			+10% -10%

✖Semi Major Axis of Ellipse is half of the chord passing through both the foci of the Ellipse.ⓘ Semi Major Axis of Ellipse given Area and Eccentricity [a]

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Semi Major Axis of Ellipse given Area and Eccentricity Solution

STEP 0: Pre-Calculation Summary

Formula Used

Semi Major Axis of Ellipse = sqrt(Area of Ellipse/(pi*sqrt(1-Eccentricity of Ellipse^2)))
a = sqrt(A/(pi*sqrt(1-e^2)))
This formula uses 1 Constants, 1 Functions, 3 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

Semi Major Axis of Ellipse - (Measured in Meter) - Semi Major Axis of Ellipse is half of the chord passing through both the foci of the Ellipse.
Area of Ellipse - (Measured in Square Meter) - Area of Ellipse is the total quantity of plane enclosed by the boundary of the Ellipse.
Eccentricity of Ellipse - (Measured in Meter) - Eccentricity of Ellipse is the ratio of the linear eccentricity to the semi major axis of the Ellipse.

STEP 1: Convert Input(s) to Base Unit

Area of Ellipse: 190 Square Meter --> 190 Square Meter No Conversion Required
Eccentricity of Ellipse: 0.8 Meter --> 0.8 Meter No Conversion Required

STEP 2: Evaluate Formula

Substituting Input Values in Formula

a = sqrt(A/(pi*sqrt(1-e^2))) --> sqrt(190/(pi*sqrt(1-0.8^2)))

Evaluating ... ...

a = 10.0398272208673

STEP 3: Convert Result to Output's Unit

10.0398272208673 Meter --> No Conversion Required

FINAL ANSWER

10.0398272208673 ≈ 10.03983 Meter <-- Semi Major Axis of Ellipse

(Calculation completed in 00.004 seconds)

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Created by Dhruv Walia

Indian Institute of Technology, Indian School of Mines, DHANBAD (IIT ISM), Dhanbad, Jharkhand

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< Major Axis of Ellipse Calculators

Semi Major Axis of Ellipse given Linear Eccentricity and Semi Minor Axis

LaTeX Go Semi Major Axis of Ellipse = sqrt(Semi Minor Axis of Ellipse^2+Linear Eccentricity of Ellipse^2)

Semi Major Axis of Ellipse given Area and Semi Minor Axis

LaTeX Go Semi Major Axis of Ellipse = Area of Ellipse/(pi*Semi Minor Axis of Ellipse)

Major Axis of Ellipse given Area and Minor Axis

LaTeX Go Major Axis of Ellipse = (4*Area of Ellipse)/(pi*Minor Axis of Ellipse)

Major Axis of Ellipse

LaTeX Go Major Axis of Ellipse = 2*Semi Major Axis of Ellipse

Semi Major Axis of Ellipse given Area and Eccentricity Formula

LaTeX Go

Semi Major Axis of Ellipse = sqrt(Area of Ellipse/(pi*sqrt(1-Eccentricity of Ellipse^2)))
a = sqrt(A/(pi*sqrt(1-e^2)))

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 Semi Major Axis of Ellipse given Area and Eccentricity?

Semi Major Axis of Ellipse given Area and Eccentricity calculator uses Semi Major Axis of Ellipse = sqrt(Area of Ellipse/(pi*sqrt(1-Eccentricity of Ellipse^2))) to calculate the Semi Major Axis of Ellipse, The Semi Major Axis of Ellipse given Area and Eccentricity formula is defined as half of the length of the chord which passes through both foci of the Ellipse and is calculated using the area and eccentricity of the Ellipse. Semi Major Axis of Ellipse is denoted by a symbol.

How to calculate Semi Major Axis of Ellipse given Area and Eccentricity using this online calculator? To use this online calculator for Semi Major Axis of Ellipse given Area and Eccentricity, enter Area of Ellipse (A) & Eccentricity of Ellipse (e) and hit the calculate button. Here is how the Semi Major Axis of Ellipse given Area and Eccentricity calculation can be explained with given input values -> 10.03983 = sqrt(190/(pi*sqrt(1-0.8^2))).

FAQ

What is Semi Major Axis of Ellipse given Area and Eccentricity?

The Semi Major Axis of Ellipse given Area and Eccentricity formula is defined as half of the length of the chord which passes through both foci of the Ellipse and is calculated using the area and eccentricity of the Ellipse and is represented as a = sqrt(A/(pi*sqrt(1-e^2))) or Semi Major Axis of Ellipse = sqrt(Area of Ellipse/(pi*sqrt(1-Eccentricity of Ellipse^2))). Area of Ellipse is the total quantity of plane enclosed by the boundary of the Ellipse & Eccentricity of Ellipse is the ratio of the linear eccentricity to the semi major axis of the Ellipse.

How to calculate Semi Major Axis of Ellipse given Area and Eccentricity?

The Semi Major Axis of Ellipse given Area and Eccentricity formula is defined as half of the length of the chord which passes through both foci of the Ellipse and is calculated using the area and eccentricity of the Ellipse is calculated using Semi Major Axis of Ellipse = sqrt(Area of Ellipse/(pi*sqrt(1-Eccentricity of Ellipse^2))). To calculate Semi Major Axis of Ellipse given Area and Eccentricity, you need Area of Ellipse (A) & Eccentricity of Ellipse (e). With our tool, you need to enter the respective value for Area of Ellipse & Eccentricity of Ellipse 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 Semi Major Axis of Ellipse?

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

Semi Major Axis of Ellipse = sqrt(Semi Minor Axis of Ellipse^2+Linear Eccentricity of Ellipse^2)
Semi Major Axis of Ellipse = Area of Ellipse/(pi*Semi Minor Axis of Ellipse)
Semi Major Axis of Ellipse = Major Axis of Ellipse/2

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