Rolled Throughput Yield Calculator
Multiply step yields to find the chance a unit passes every step.
In short
Multiply step yields to find the chance a unit passes every step.
Formula: RTY = Y₁ × Y₂ × … × Yₙ (each Y as a proportion), shown as a percentage
What this calculator does
Product of the entered step yields. Steps left blank are excluded and the page says how many were included. The normalised yield is the nth root of the product.
Use it to turn Step 1 yield, Step 2 yield, Step 3 yield (optional), Step 4 yield (optional), and the other shown inputs into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this professional & industry calculation.
Inputs and what they mean
- Step 1 yield
- — First pass yield of this step, as a percentage..
- Step 2 yield
- — First pass yield of this step, as a percentage..
- Step 3 yield (optional)
- — Leave blank to exclude this step. A step entered as 0 is included and makes the rolled yield zero..
- Step 4 yield (optional)
- — Leave blank to exclude this step. A step entered as 0 is included and makes the rolled yield zero..
- Step 5 yield (optional)
- — Leave blank to exclude this step. A step entered as 0 is included and makes the rolled yield zero..
- Step 6 yield (optional)
- — Leave blank to exclude this step. A step entered as 0 is included and makes the rolled yield zero..
- Step 7 yield (optional)
- — Leave blank to exclude this step. A step entered as 0 is included and makes the rolled yield zero..
- Step 8 yield (optional)
- — Leave blank to exclude this step. A step entered as 0 is included and makes the rolled yield zero..
How to use it
- Enter your own figures — the calculator never fills in a rate, price or benchmark for you.
- Press Calculate to see the result.
- Read the formula, variables, assumptions and source below the result before you rely on it.
Formula
RTY = Y₁ × Y₂ × … × Yₙ (each Y as a proportion), shown as a percentage.
Inputs used: Step 1 yield, Step 2 yield, Step 3 yield (optional), Step 4 yield (optional), Step 5 yield (optional), Step 6 yield (optional), Step 7 yield (optional), Step 8 yield (optional).
Edge handling: Step 1 yield is required.; Step 1 yield cannot be negative.; Step 1 yield must be no more than 100.; Step 2 yield is required.; Step 2 yield cannot be negative..
Worked example
Four steps at 98%, 97%, 99% and 96%
- Start with Step 1 yield: 98, Step 2 yield: 97, Step 3 yield (optional): 99, Step 4 yield (optional): 96.
- Apply the method: RTY = Y₁ × Y₂ × … × Yₙ (each Y as a proportion), shown as a percentage.
- The rolled yield falls well below the weakest single step.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
- Inputs outside the supported range are rejected rather than forced into a result.
- The result depends on the values you enter for this rolled throughput yield calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Reference: American Society for Quality — Process capability and defect rate measures
Last reviewed:
Common questions
Where does this formula come from?
ASQ quality resources, yield measures: rolled throughput yield multiplies the first pass yields of the steps in sequence. See the source link on this page.
What kind of calculation is this?
The product of the first pass yields of every step in sequence, with the normalised yield as the geometric mean step yield. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.
What are its limits?
Multiplying step yields assumes the steps are measured on the same flow; a step measured on a different sample will distort the result. Excluding a step understates the rolled yield of the full process. Arithmetic over the counts entered — it cannot tell whether the inspection behind them was complete or consistent.
How do I use the Rolled Throughput Yield Calculator?
Enter the required values for Step 1 yield, Step 2 yield, Step 3 yield (optional), Step 4 yield (optional), Step 5 yield (optional), and the other fields shown. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the Rolled Throughput Yield Calculator use?
RTY = Y₁ × Y₂ × … × Yₙ (each Y as a proportion), shown as a percentage The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.
Can the Rolled Throughput Yield Calculator be used for exact decisions?
Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.
Formula, source and verification
The product of the first pass yields of every step in sequence, with the normalised yield as the geometric mean step yield.
The question it answers: How much of our output is right first time, and how much survives every step?
The formula
RTY = Y₁ × Y₂ × … × Yₙ (each Y as a proportion), shown as a percentage
- Yᵢ — Step yield
- (%). First pass yield of step i.
- n — Steps
- (count). Number of steps entered.
Units: Percentages in; percentage out.
What kind of calculation this is
Deterministic formula. The same inputs always give the same answer. The maths is fixed and does not depend on judgement.
Method
Product of the entered step yields. Steps left blank are excluded and the page says how many were included. The normalised yield is the nth root of the product.
Assumptions built into the result
- Operational: Each step yield is a first pass yield for the same units flowing through the sequence.
Figures this calculator will never guess for you
- No benchmark, target or 'world class' value is supplied or implied; the result describes only the figures entered.
- No yield is assumed for a step left blank — it is excluded, not treated as 100%.
- No independence correction or sampling model is applied beyond multiplying the entered yields.
Limitations
- Multiplying step yields assumes the steps are measured on the same flow; a step measured on a different sample will distort the result.
- Excluding a step understates the rolled yield of the full process.
- Arithmetic over the counts entered — it cannot tell whether the inspection behind them was complete or consistent.
Source and version
- Standard or reference
- Rolled throughput yield — ASQ (ASQ quality resources, yield measures: rolled throughput yield multiplies the first pass yields of the steps in sequence.)
- Published source
- American Society for Quality — Quality resources
- Formula version
- Version 1
- Verification
- Reviewed against the cited source on
- How much weight the source carries
- Standards or government
- Applies to
- Currency
- The result is a ratio or index, so it does not depend on currency.
Cite this page
Free Calculator. (2026, September 16). Rolled Throughput Yield Calculator. https://freecalculator.tech/tools/rolled-throughput-yield-calculator
"Rolled Throughput Yield Calculator." Free Calculator, 16 Sept. 2026, https://freecalculator.tech/tools/rolled-throughput-yield-calculator.
Rolled Throughput Yield Calculator — Free Calculator, https://freecalculator.tech/tools/rolled-throughput-yield-calculator
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