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 commonly used to combine independent, uncorrelated contributors such as statistical tolerances, measurement uncertainties, and random error sources. It generally produces a smaller combined value than simply adding every magnitude together.
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.
RSS vs worst-case addition
Worst-case addition sums the absolute magnitudes of all contributors. RSS assumes the contributors are independent rather than all reaching their extremes in the same direction at the same time. Which method is appropriate depends on the engineering problem and its assumptions.