Area of an elliptical sector Calculator

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

Area of an elliptical sector
angle θ0
angle θ1
    1.    same unit as θ0
semimajor axis a
semiminor axis b

area of sector S
length of arc L
    Area of an elliptical sector
    [1-4] /4Disp-Num
    [1]  2022/02/26 00:11   30 years old level / High-school/ University/ Grad student / Useful /
    Purpose of use
    Calculation of ellipse segment after removal of triangle. Used for calculation of Hertzian contact pressure after removal of a segment.
    [2]  2017/07/17 13:18   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.
    Still getting my head round the arguments put forward, In order to make better use of them at the moment
    [3]  2014/12/06 02:22   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 ( I find that inputs of
    angle theta0 = -0.6 (rad)
    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.
    [4]  2014/04/01 15:37   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.


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