# Process Capability Index (Cpk) Calculator

> Judge whether a process fits inside its specification limits and whether it is centred.

Page: https://freecalculator.tech/tools/cpk-calculator
Last reviewed: 2026-09-15

## Formula

Cp = (USL − LSL) ÷ (6σ); Cpk = min[(USL − μ) ÷ (3σ), (μ − LSL) ÷ (3σ)]

- Cp = (USL − LSL) ÷ (6σ); Cpk = min[(USL − μ) ÷ (3σ), (μ − LSL) ÷ (3σ)].
- Inputs used: Upper specification limit, Lower specification limit, Process mean, Process standard deviation.
- Edge handling: Upper specification limit is required.; Upper specification limit must be no more than 1000000000000.; Lower specification limit is required.; Lower specification limit must be no more than 1000000000000.; Process mean is required..

## Inputs

- Upper specification limit
- Lower specification limit
- Process mean
- Process standard deviation

## Worked example: Specification 9.5 to 10.5, mean 10, sigma 0.1

A centred process with capability well inside its limits.
1. Start with Upper specification limit: 10.5, Lower specification limit: 9.5, Process mean: 10, Process standard deviation: 0.1.
2. Apply the method: Cp = (USL − LSL) ÷ (6σ); Cpk = min[(USL − μ) ÷ (3σ), (μ − LSL) ÷ (3σ)].
3. A centred process with capability well inside its limits.

## Common questions

### Where does this formula come from?

NIST/SEMATECH e-Handbook of Statistical Methods, process capability indices. See the source link on this page.

### What kind of calculation is this?

Capability compares specification width with process spread; Cpk also accounts for how far the mean sits from centre. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.

### What are its limits?

Meaningless for a process that is not in control, or for strongly non-normal data. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.

### How do I use the Process Capability Index (Cpk) Calculator?

Enter the required values for Upper specification limit, Lower specification limit, Process mean, Process standard deviation. 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 Process Capability Index (Cpk) Calculator use?

Cp = (USL − LSL) ÷ (6σ); Cpk = min[(USL − μ) ÷ (3σ), (μ − LSL) ÷ (3σ)] 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 Process Capability Index (Cpk) 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 process capability index (cpk) calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.

## Sources

- NIST — https://www.itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm

## Cite this page

- APA: Free Calculator. (2026, September 15). Process Capability Index (Cpk) Calculator. https://freecalculator.tech/tools/cpk-calculator
- MLA: "Process Capability Index (Cpk) Calculator." Free Calculator, 15 Sept. 2026, https://freecalculator.tech/tools/cpk-calculator.
- Link: Process Capability Index (Cpk) Calculator — Free Calculator, https://freecalculator.tech/tools/cpk-calculator