How to use this calculator
- Choose dimension count. Select how many dimensions are in the stack.
- Set directions. Mark each dimension as adding to or subtracting from the final stack.
- Enter nominal sizes. Use the drawing nominal for each dimension.
- Enter tolerances. Enter bilateral plus/minus tolerances as positive values.
- Compare limits. Use worst-case limits for guaranteed fit; treat RSS as statistical only.
How it works
The nominal stack is the signed sum of each dimension:
S = +/-D1 +/-D2 +/-D3 ...
Tolerances widen that nominal value. Worst case adds every tolerance:
T_wc = t1 + t2 + t3 ....
RSS stack-up treats independent tolerances statistically:
T_rss = sqrt(t1^2 + t2^2 + t3^2 ...). The calculator reports both
min and max limits so the difference between guaranteed worst case and statistical
RSS is visible.
Worked example
Verified against the live calculator
With default inputs, the nominal stack is 50 + 25 - 20 = 55 mm.
Worst-case tolerance is 0.10 + 0.05 + 0.08 = 0.23 mm, so limits are
54.77 mm to 55.23 mm.
RSS tolerance is sqrt(0.10^2 + 0.05^2 + 0.08^2) = 0.1375 mm, giving
statistical limits of about 54.8625 mm to 55.1375 mm.
RSS is narrower because it does not assume every dimension hits the bad limit at once.
Frequently asked questions
What is tolerance stack-up?
Tolerance stack-up adds the effect of multiple part dimensions and tolerances on a final gap, location or assembly condition. Signed dimensions add or subtract from the nominal stack; tolerances widen the possible limits.
What is worst-case tolerance stack-up?
Worst-case stack-up adds every plus/minus tolerance: T_wc = t1 + t2 + ... . It assumes every dimension lands at its least favorable limit at the same time, so it is conservative and appropriate for guaranteed interchangeability.
What is RSS tolerance stack-up?
RSS, or root-sum-square, is T_rss = sqrt(t1^2 + t2^2 + ...). It assumes independent, centered variation and gives a statistical estimate instead of a guaranteed limit.
When should I use RSS instead of worst case?
Use RSS only when the dimensions are independent, processes are centered and variation is statistically controlled. Use worst case for hard functional limits, safety-critical fits or when process capability is unknown.
How do the plus and minus signs work?
Use plus for dimensions that increase the final stack and minus for dimensions that reduce it. Tolerances are always entered as positive plus/minus values.
Does this replace GD&T analysis?
No. It is a one-dimensional size stack. Datum shift, position tolerance, profile, orientation, bonus tolerance and 3D variation require a geometric tolerance analysis.
Method & assumptions
- One-dimensional linear stack only; angular, radial and 3D effects are not included.
- Each tolerance is treated as a symmetric plus/minus tolerance.
- RSS assumes independent, centered variation; verify process capability before using it for design release.
- GD&T position, bonus tolerance, datum shift, runout and profile require separate geometric analysis.