# Calculating 1) weighted, 2) surface integrals of scalars in paraview
**URL:** https://discourse.paraview.org/t/calculating-1-weighted-2-surface-integrals-of-scalars-in-paraview/17505
**Category:** ParaView Support
**Created:** [April 2, 2026, 9:16am UTC](https://discourse.paraview.org/t/calculating-1-weighted-2-surface-integrals-of-scalars-in-paraview/17505 "2026-04-02T09:16:38Z")
**Posts on this page:** 2
**Page:** 1
### Author:  [@Fizikci](https://discourse.paraview.org/u/Fizikci)
#### Post date: [April 2, 2026, 9:16am UTC](https://discourse.paraview.org/t/calculating-1-weighted-2-surface-integrals-of-scalars-in-paraview/17505/1 "2026-04-02T09:16:38Z")
Hello ParaView community,
I am having deep troubles figuring out how to calculate this very specific operation:
weighted, surface integrals of scalars, that is \int \vec{\omega} T \,d\vec{A}, for example for temperature.
I am having trouble believing that the very generic “IntegrateVariables“ in ParaView actually performs cell area considering integrals. Because when I use **vectors** instead of **scalars** for the weight factor (such as \vec{\omega} = \rho\*\vec{v}) the result is also in 3D and for each direction I get an integrated value. This tells me that “IntegrateVariables” is not a true area/surface integral!
I am finding it hard to believe this because when I use **scalar** weights to compare my results from other tools (where I can control vector or scalar weighted area integrals), I get almost matching values. However as I said when I use **vector** weight factors, there is not even a comparable result, it literally just gives me a 3D result as if integration over the area is not calculating the integrand as \vec{\omega}\*d\vec{A} , where \vec{\omega} = \rho\*\vec{v} and d\vec{A} = [dx, dy, dz].
Could you please inform me if what I require is possible or not in ParaView? Why do I still get a 3D result after a supposedly weighted area integral operation on a vector?
Best regars,
Fizikci
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### Author:  [@Fizikci](https://discourse.paraview.org/u/Fizikci)
#### Post date: [April 7, 2026, 8:54am UTC](https://discourse.paraview.org/t/calculating-1-weighted-2-surface-integrals-of-scalars-in-paraview/17505/2 "2026-04-07T08:54:10Z")
Let me answer my own question so anyone who has come to the same issue can also find the answer. I am working with v6.0.1:
1. We need to extract the surfaces from the data –\> Filters/ **ExtractSurface**
2. Now we need the surface normals –\> Filters/ **SurfaceNormals**
3. Under the SurfaceNormals layer we calculate the variable of interest that will be mass-weighted, for example Temperature;
4. Perform the IntegrateVariables filter on this new mass-weighted variable, meaning calculate the surface integral on it. Obviously you need the surface you want to be active for this operation to make sense.
5. Calculate the weight factor omega as a new variable
6. Perform again the IntegrateVariables filter on omega
7. Divide the result of the first integral with the second one such that you have;