Area of an elliptical sector Calculator

Calculates the area and arc of an elliptical sector given two axes and two angles.

 angle θ0 degree radian angle θ1 same unit as θ0 semimajor axis a semiminor axis b 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit area of sector S length of arc L
 $\normal Elliptical\ Sector\\(1)\ area:\\\hspace{20} S=F(\theta_1)-F(\theta_0)\\\hspace{20} F(\theta)= {\large\frac{ab}{2}}\left[\theta-tan^{\small-1}\left({\large\frac{(b-a)sin2\theta}{b+a+(b-a)cos2\theta}}\right)\right]\\\hspace{20} r(\theta)^2={\large\frac{a^2b^2}{b^2cos^2\theta+a^2sin^2\theta}}\\\vspace{5}(2)\ elliptical\ arch :\\\hspace{20} L=aE({\large\frac{x(\theta_0)}{a}},k)-aE({\large\frac{x(\theta_1)}{a}},k)\\\hspace{20} x(\theta)=r(\theta)cos\theta,\ k=\sqrt{1-({\large\frac{b}{a}})^2},\hspace{20} a\ge b,\hspace{10}\frac{\pi}{2}\ge \theta\ge 0\\\hspace{20} E(x,k):\ 2nd\ incomplete\ elliptic\ integral\\$
Area of an elliptical sector
 [1-3] /3 Disp-Num5103050100200
[1]  2017/07/17 22:18   Male / 60 years old level or over / An engineer / Useful /
Purpose of use
To help me calculate the Hydraulic radius for Elliptical pipes when not in full flow.
Comment/Request
Still getting my head round the arguments put forward, In order to make better use of them at the moment
[2]  2014/12/06 11:22   Female / 20 years old level / High-school/ University/ Grad student / A little /
Bug report
Hi there,

When I compare the results of these formula to another derivation (http://math.stackexchange.com/questions/114371/deriving-the-area-of-a-sector-of-an-ellipse) I find that inputs of
angle theta1 = 0.8
semimajor axis a = 1100
semiminor axis b = 979

give different results. Your calculator returns 814,874.12267598 and the formula (a*b/2)(atan((a/b)*tan(theta1))-atan((a/b)*tan(theta0))) returns 753830.0.

Which one is wrong? Is it possible for you to post a derivation of your formulas?
from Keisan
Please refer to "The Area of Intersecting Ellipses (David Eberly)" on Related links.
[3]  2014/04/02 00:37   - / 50 years old level / An engineer / A little /
Purpose of use
I'm trying to calculate how much of the area of an ellipse I will block if I install a deflector plate across part of the opening. In addition to the information you provide, I need to know the chord length across L. I was looking for website that would do it, but it looks like I will have to do some real math myself.

Sending completion

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