Root Sum Square (RSS) Calculator
Combine independent tolerances, uncertainties, errors, or other contributors using root sum square. Add as many terms as needed and see which terms dominate the total.
| Label | Value |
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Contribution breakdown
| Term | Value | Squared value | % of variance | Contribution |
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RSS formula
When should RSS be used?
RSS is a useful engineering tool because it gives a realistic estimate of combined variation when multiple independent part or drawing tolerances contribute to an assembly, without assuming every feature reaches its worst-case limit in the same direction at the same time.
Mathematically, independent variances add, which is why the combined spread is found by root-sum-squaring the individual values.
The RSS result is a statistical estimate, not a guaranteed bound. A drawing tolerance only defines the allowable range; it does not define how parts are distributed within that range. Therefore, a confidence level cannot be assigned to an RSS stack unless the underlying process distributions are known or assumed.
What does percent contribution mean?
Each term's percent contribution is its squared value divided by the total sum of squares. This shows how much that term contributes to the combined variance and makes dominant contributors easy to identify.
Can values be negative?
Yes. Because each term is squared, positive and negative inputs of the same magnitude make the same contribution to RSS. In tolerance and uncertainty applications, users will usually enter magnitudes.