# Area of an elliptical sector Calculator

## Calculates the area and arc of an elliptical sector given two axes and two angles. angle θ0 degreeradian angle θ1 same unit as θ0 semimajor axis a semiminor axis b 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit area of sector S length of arc L
Area of an elliptical sector
 [1-4] /4 Disp-Num5103050100200  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.
  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.
Comment/Request
Still getting my head round the arguments put forward, In order to make better use of them at the moment
  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 (http://math.stackexchange.com/questions/114371/deriving-the-area-of-a-sector-of-an-ellipse) 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.
  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.  Thank you for your questionnaire.

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