Area of Ellipse given Eccentricity and Semi Minor Axis Solution

STEP 0: Pre-Calculation Summary
Formula Used
Area of Ellipse = (pi*Semi Minor Axis of Ellipse^2)/sqrt(1-Eccentricity of Ellipse^2)
A = (pi*b^2)/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
Area of Ellipse - (Measured in Square Meter) - Area of Ellipse is the total quantity of plane enclosed by the boundary of the Ellipse.
Semi Minor Axis of Ellipse - (Measured in Meter) - Semi Minor Axis of Ellipse is half of the length of the longest chord which is perpendicular to the line joining the foci 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
Semi Minor Axis of Ellipse: 6 Meter --> 6 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 = (pi*b^2)/sqrt(1-e^2) --> (pi*6^2)/sqrt(1-0.8^2)
Evaluating ... ...
A = 188.495559215388
STEP 3: Convert Result to Output's Unit
188.495559215388 Square Meter --> No Conversion Required
FINAL ANSWER
188.495559215388 188.4956 Square Meter <-- Area of Ellipse
(Calculation completed in 00.020 seconds)

Credits

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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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6 Area of Ellipse Calculators

Area of Ellipse given Linear Eccentricity and Semi Major Axis
​ Go Area of Ellipse = pi*Semi Major Axis of Ellipse*sqrt(Semi Major Axis of Ellipse^2-Linear Eccentricity of Ellipse^2)
Area of Ellipse given Linear Eccentricity and Semi Minor Axis
​ Go Area of Ellipse = pi*sqrt(Linear Eccentricity of Ellipse^2+Semi Minor Axis of Ellipse^2)*Semi Minor Axis of Ellipse
Area of Ellipse given Eccentricity and Semi Minor Axis
​ Go Area of Ellipse = (pi*Semi Minor Axis of Ellipse^2)/sqrt(1-Eccentricity of Ellipse^2)
Area of Ellipse given Eccentricity and Semi Major Axis
​ Go Area of Ellipse = pi*Semi Major Axis of Ellipse^2*sqrt(1-Eccentricity of Ellipse^2)
Area of Ellipse
​ Go Area of Ellipse = pi*Semi Major Axis of Ellipse*Semi Minor Axis of Ellipse
Area of Ellipse given Major and Minor Axes
​ Go Area of Ellipse = (pi/4)*Major Axis of Ellipse*Minor Axis of Ellipse

Area of Ellipse given Eccentricity and Semi Minor Axis Formula

Area of Ellipse = (pi*Semi Minor Axis of Ellipse^2)/sqrt(1-Eccentricity of Ellipse^2)
A = (pi*b^2)/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 Area of Ellipse given Eccentricity and Semi Minor Axis?

Area of Ellipse given Eccentricity and Semi Minor Axis calculator uses Area of Ellipse = (pi*Semi Minor Axis of Ellipse^2)/sqrt(1-Eccentricity of Ellipse^2) to calculate the Area of Ellipse, The Area of Ellipse given Eccentricity and Semi Minor Axis formula is defined as the total quantity of the plane enclosed by the boundary of the Ellipse, and calculated using the eccentricity and semi-minor axis of the Ellipse. Area of Ellipse is denoted by A symbol.

How to calculate Area of Ellipse given Eccentricity and Semi Minor Axis using this online calculator? To use this online calculator for Area of Ellipse given Eccentricity and Semi Minor Axis, enter Semi Minor Axis of Ellipse (b) & Eccentricity of Ellipse (e) and hit the calculate button. Here is how the Area of Ellipse given Eccentricity and Semi Minor Axis calculation can be explained with given input values -> 188.4956 = (pi*6^2)/sqrt(1-0.8^2).

FAQ

What is Area of Ellipse given Eccentricity and Semi Minor Axis?
The Area of Ellipse given Eccentricity and Semi Minor Axis formula is defined as the total quantity of the plane enclosed by the boundary of the Ellipse, and calculated using the eccentricity and semi-minor axis of the Ellipse and is represented as A = (pi*b^2)/sqrt(1-e^2) or Area of Ellipse = (pi*Semi Minor Axis of Ellipse^2)/sqrt(1-Eccentricity of Ellipse^2). Semi Minor Axis of Ellipse is half of the length of the longest chord which is perpendicular to the line joining the foci of the Ellipse & Eccentricity of Ellipse is the ratio of the linear eccentricity to the semi major axis of the Ellipse.
How to calculate Area of Ellipse given Eccentricity and Semi Minor Axis?
The Area of Ellipse given Eccentricity and Semi Minor Axis formula is defined as the total quantity of the plane enclosed by the boundary of the Ellipse, and calculated using the eccentricity and semi-minor axis of the Ellipse is calculated using Area of Ellipse = (pi*Semi Minor Axis of Ellipse^2)/sqrt(1-Eccentricity of Ellipse^2). To calculate Area of Ellipse given Eccentricity and Semi Minor Axis, you need Semi Minor Axis of Ellipse (b) & Eccentricity of Ellipse (e). With our tool, you need to enter the respective value for Semi Minor Axis 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 Area of Ellipse?
In this formula, Area of Ellipse uses Semi Minor Axis of Ellipse & Eccentricity of Ellipse. We can use 5 other way(s) to calculate the same, which is/are as follows -
  • Area of Ellipse = (pi/4)*Major Axis of Ellipse*Minor Axis of Ellipse
  • Area of Ellipse = pi*Semi Major Axis of Ellipse*Semi Minor Axis of Ellipse
  • Area of Ellipse = pi*Semi Major Axis of Ellipse*sqrt(Semi Major Axis of Ellipse^2-Linear Eccentricity of Ellipse^2)
  • Area of Ellipse = pi*sqrt(Linear Eccentricity of Ellipse^2+Semi Minor Axis of Ellipse^2)*Semi Minor Axis of Ellipse
  • Area of Ellipse = pi*Semi Major Axis of Ellipse^2*sqrt(1-Eccentricity of Ellipse^2)
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