# Area of an elliptical sector Calculator

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

angle θ0
angle θ1
 same unit as θ0
semimajor axis a
semiminor axis b

area of sector S
length of arc L
 $\normal Elliptical\ Sector\\(1)\ area:\\\hspace{20} S=F(\theta_1)-F(\theta_0)\\\hspace{20} F(\theta)= {\large\frac{ab}{2}}\left[\theta-tan^{\small-1}\left({\large\frac{(b-a)sin2\theta}{b+a+(b-a)cos2\theta}}\right)\right]\\\hspace{20} r(\theta)^2={\large\frac{a^2b^2}{b^2cos^2\theta+a^2sin^2\theta}}\\\vspace{5}(2)\ elliptical\ arch :\\\hspace{20} L=aE({\large\frac{x(\theta_0)}{a}},k)-aE({\large\frac{x(\theta_1)}{a}},k)\\\hspace{20} x(\theta)=r(\theta)cos\theta,\ k=\sqrt{1-({\large\frac{b}{a}})^2},\hspace{20} a\ge b,\hspace{10}\frac{\pi}{2}\ge \theta\ge 0\\\hspace{20} E(x,k):\ 2nd\ incomplete\ elliptic\ integral\\$

Sending completion

To improve this 'Area of an elliptical sector Calculator', please fill in questionnaire.
Male or Female ?
Male Female
Age
Under 20 years old 20 years old level 30 years old level
40 years old level 50 years old level 60 years old level or over
Occupation
Elementary school/ Junior high-school student
High-school/ University/ Grad student A homemaker An office worker / A public employee
Self-employed people An engineer A teacher / A researcher
A retired people Others
Useful?
Very Useful A little Not at All
Purpose of use?