# Rolled Throughput Yield Calculator

> Multiply step yields to find the chance a unit passes every step.

Page: https://freecalculator.tech/tools/rolled-throughput-yield-calculator
Last reviewed: 2026-09-16

## Formula

RTY = Y₁ × Y₂ × … × Yₙ (each Y as a proportion), shown as a percentage

- 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..

## Inputs

- 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)

## Worked example: Four steps at 98%, 97%, 99% and 96%

The rolled yield falls well below the weakest single step.
1. Start with Step 1 yield: 98, Step 2 yield: 97, Step 3 yield (optional): 99, Step 4 yield (optional): 96.
2. Apply the method: RTY = Y₁ × Y₂ × … × Yₙ (each Y as a proportion), shown as a percentage.
3. The rolled yield falls well below the weakest single step.

## 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.

## 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.

## Sources

- American Society for Quality — https://asq.org/quality-resources/process-capability

## Cite this page

- APA: Free Calculator. (2026, September 16). Rolled Throughput Yield Calculator. https://freecalculator.tech/tools/rolled-throughput-yield-calculator
- MLA: "Rolled Throughput Yield Calculator." Free Calculator, 16 Sept. 2026, https://freecalculator.tech/tools/rolled-throughput-yield-calculator.
- Link: Rolled Throughput Yield Calculator — Free Calculator, https://freecalculator.tech/tools/rolled-throughput-yield-calculator