Tolerance Stackup Calculator
Estimate tolerance stackup for your project with our free calculator. Get accurate material quantities, costs, and specifications.
Reviewed by Abdullah, Technical Content Specialist
Formula
RSS Stackup = sqrt(t1² + t2² + t3² + ... + tn²)
The RSS (Root Sum of Squares) method calculates the statistical tolerance stackup by taking the square root of the sum of the squares of each individual tolerance. This assumes part dimensions follow a normal distribution and tolerances are independent. For worst-case, simply sum all tolerances. For statistical analysis, multiply RSS by Z/3 where Z is the Z-score for the desired confidence level.
Worked Examples
Example 1: Three-Part Linear Assembly
Problem:Three parts with nominal dimensions 25mm, 30mm, and 15mm have tolerances of 0.10mm, 0.15mm, and 0.08mm respectively. Find the RSS stackup.
Solution:Nominal total = 25 + 30 + 15 = 70mm\nWorst-case = 0.10 + 0.15 + 0.08 = 0.33mm\nRSS = sqrt(0.10² + 0.15² + 0.08²) = sqrt(0.01 + 0.0225 + 0.0064) = sqrt(0.0389) = 0.1972mm
Result:RSS stackup = 0.1972mm, assembly range = 69.8028mm to 70.1972mm
Example 2: Five-Component Stack
Problem:Five components each with a nominal dimension of 10mm and individual tolerances of 0.05mm. Compare worst-case and RSS.
Solution:Nominal total = 5 x 10 = 50mm\nWorst-case = 5 x 0.05 = 0.25mm\nRSS = sqrt(5 x 0.05²) = sqrt(5 x 0.0025) = sqrt(0.0125) = 0.1118mm\nReduction = (1 - 0.1118/0.25) x 100 = 55.3%
Result:RSS is 55.3% tighter than worst-case: 0.1118mm vs 0.25mm
Frequently Asked Questions
What is tolerance stackup analysis?
Tolerance stackup analysis is the process of calculating the cumulative effect of individual part tolerances on an overall assembly dimension. When multiple parts are assembled together, each part contributes its own tolerance variation, and these variations can add up to produce a total assembly variation that may exceed acceptable limits. Engineers use stackup analysis during the design phase to ensure that assembled components will fit and function correctly.
What is the difference between worst-case and RSS stackup?
Worst-case (arithmetic) stackup assumes every part is simultaneously at its maximum or minimum tolerance limit, which is extremely unlikely in real production. RSS (Root Sum of Squares) stackup uses a statistical approach, calculating the square root of the sum of squared tolerances. RSS typically yields a stackup 40-60% smaller than worst-case because it accounts for the statistical probability that not all parts will be at their extremes simultaneously. RSS assumes a normal distribution of part dimensions.
How does the confidence level affect statistical tolerance stackup?
The confidence level determines what percentage of assemblies will fall within the calculated tolerance range. A 99.73% confidence (3-sigma) means only 2,700 out of 1 million assemblies might fall outside limits. Higher confidence levels like 99.99% (approximately 3.89-sigma) produce wider tolerance bands but fewer rejects. The statistical stackup equals the RSS value multiplied by the Z-score divided by 3. For most manufacturing, 99.73% (3-sigma) provides a good balance between tight tolerances and acceptable reject rates.
References
Reviewed by Abdullah, Technical Content Specialist · Editorial policy