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Tolerance Calculation in Mathcad


Tolerance Calculation in Mathcad

Hi all,

After doing so many complex design and engineering calculations, i am stuck with this simple plus minus calculation.

I have to do this addition and subtraction of dimenssions with tolerances, as shown in the attached image.

Request you to please help.

As i want similar representation of Tolerances in mathcad sheets.





Accepted Solutions

Re: Tolerance Calculation in Mathcad

Here is a sheet with an added unary minus which is a bit more explicit-friendly.

The drawback is the way you have to write your subtraction (either A + - D, or A + (-D)).


View solution in original post


Re: Tolerance Calculation in Mathcad

Hello Shashank,

hope this small routine will do. Add cells to the nested array Y as much as you need




This is a MC 15 sheet

Re: Tolerance Calculation in Mathcad

Another example to add along with Raiko's for your Mathcad toolbox. Also, a MC15 file but will convert to Prime.

I hope this helps.

Re: Tolerance Calculation in Mathcad


I tried various ideas for this approach.

Most of the applications, however, became too complex to make it useable for what I needed.

attached is a simple sheet with a few functions - hopefully they will give you some information about mathcads capabilities

If you make any useful modifications to these functions, I would be grateful if you could publish them here.



Re: Tolerance Calculation in Mathcad

Nice idea. Do you know why your inverse +/+ does not work as modificator placed in the unit field at the end of an evaluation? It should in my opinion but it keeps moaning about the argument is not a vector?

Working with tolerances is easy if you stay with addition and subtraction only, but going further your approach may fail because you assume you get the minimum/maximum value of any calculation by applying the minimum/maximum value of every variable involved. Unfortunately thats not true as the following simple example shows.


Furthermore it is not for sure that every calculation will end up in a symmetrical tolerance interval.

Re: Tolerance Calculation in Mathcad

Hmm, all these approaches only work OK if you just use addition and subtraction in your calculation. It may fail if using multiplication and/or divison or functions, absolute value, etc.

A more general (but also more cumbersome) appraoch can be found here:

Its in Prime2 format.


Re: Tolerance Calculation in Mathcad

I looked at the example in your sheet and think its wrong, too.

You get

but the correct result should be


considering that


While in this example you can get the correct result by making the calculation for ever combination of the extreme values of the variables, this must not be the case for every formula. So I think the most general solution would require a brute force calculation of a whole range for every variable and searching the min/max results as i did here(Prime2):

Attached is the file with the calculation of your formula (Prime3)

Re: Tolerance Calculation in Mathcad

Thank you all for your kind responses,

But what i need is actual tolerance representation and the logic behind upper and lower tolerance calculation while adding or subtracting parent dimenssion values.


Re: Tolerance Calculation in Mathcad

The best I could come up with:


Re: Tolerance Calculation in Mathcad

But the actual result of A-D should be 0.8 +0.4 -0.1

(where +0.4 is the upper tol & -0.1 is the lower tol)

as when we subtract parent dimenssions, their tolerances gets added in cross way

for example, tolerances of A-D will be calculated by following logic:

0.2 - (-0.2) upper tol of A(0.2) - Lower tol of D (-0.2)

-0.1- (0) Lower tol of A (-0.1) - Upper tol of D (0)