Rolled Throughput Yield Calculator
Rolled throughput yield, or RTY, is the probability that a unit clears every step of a multi-step process with no defects anywhere. Because step yields multiply, a chain of seemingly healthy steps can produce a surprisingly low overall figure: this is the hidden factory of rework and scrap that final yield conceals. Enter the first pass yield of each step as a percentage and this calculator multiplies them, returning RTY as a percentage along with the total loss, so you can see the cumulative cost of imperfect steps.
Rolled throughput yield formula
RTY = Y1 * Y2 * Y3 * Y4 * Y5 (each yield as a decimal)
RTY (%) = RTY * 100
Total process loss (%) = 100 - RTY (%)
Each step yield is converted from a percentage to a decimal, then all are multiplied. A blank or 100 percent step contributes a factor of 1 and does not change the result.
Why RTY matters
- Step yields compound, so RTY is always at or below the lowest single-step yield.
- RTY exposes the hidden factory of rework that final yield hides.
- Improving the weakest step gives the largest gain in overall RTY.
- RTY is a core Six Sigma metric referenced in NIST statistical guidance.
- Use first pass yields, not final yields, for each step to keep RTY honest.
Rolled throughput yield: frequently asked questions
What is rolled throughput yield?
Rolled throughput yield (RTY) is the probability that a unit passes through every step of a multi-step process with no defects at any step. It equals the product of the first pass yields of each step.
How is rolled throughput yield calculated?
Multiply the first pass yield of each step together. With four steps at 95% each, RTY is 0.95 times 0.95 times 0.95 times 0.95, which equals about 81.5%. Enter each step yield as a percentage in this calculator.
Why is RTY lower than each individual yield?
Because defects compound. Even when each step looks strong, multiplying several yields below 100% gives a much smaller overall figure. This exposes the hidden factory: the cumulative loss invisible when steps are viewed alone.
What is the hidden factory?
The hidden factory is the rework, scrap, and lost capacity hidden inside a process that final yield does not reveal. RTY surfaces it by showing the true probability of a defect-free pass across all steps.
How many steps can I enter?
This calculator accepts up to five step yields. Leave a step blank or at 100 to exclude it. For processes with more steps, group steps or multiply intermediate RTY figures together.
Official sources
- U.S. National Institute of Standards and Technology: NIST/SEMATECH e-Handbook of Statistical Methods.
- U.S. National Institute of Standards and Technology: Manufacturing Extension Partnership.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.