# Cp Calculator

> Compare specification width with short-term process spread.

Page: https://freecalculator.tech/tools/cp-calculator
Last reviewed: 2026-09-16

## Formula

Cp = (USL − LSL) ÷ (6σ_within)

- Cp = (USL − LSL) ÷ (6σ_within).
- Inputs used: Upper specification limit, Lower specification limit, Within-subgroup 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.; Within-subgroup standard deviation is required..

## Inputs

- Upper specification limit
- Lower specification limit
- Within-subgroup standard deviation

## Worked example: Specification 9.5 to 10.5 with a within-subgroup sigma of 0.12

Potential capability, before any allowance for centring.
1. Start with Upper specification limit: 10.5, Lower specification limit: 9.5, Within-subgroup standard deviation: 0.12.
2. Apply the method: Cp = (USL − LSL) ÷ (6σ_within).
3. Potential capability, before any allowance for centring.

## Common questions

### Where does this formula come from?

NIST/SEMATECH e-Handbook of Statistical Methods, process capability indices: Cp = (USL − LSL) ÷ 6σ using within-subgroup variation. See the source link on this page.

### What kind of calculation is this?

Specification width divided by six within-subgroup standard deviations. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.

### What are its limits?

Cp says nothing about where the mean sits — a badly centred process can have a high Cp and still produce defects. Meaningful only for a stable process; on an unstable process the estimate of sigma itself is not trustworthy. A capability index, an industry benchmark and a customer's required index are three different things.

### How do I use the Cp Calculator?

Enter the required values for Upper specification limit, Lower specification limit, Within-subgroup 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 Cp Calculator use?

Cp = (USL − LSL) ÷ (6σ_within) 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 Cp 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 cp calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.

## Sources

- National Institute of Standards and Technology — https://www.itl.nist.gov/div898/handbook/pmc/section1/pmc16.htm

## Cite this page

- APA: Free Calculator. (2026, September 16). Cp Calculator. https://freecalculator.tech/tools/cp-calculator
- MLA: "Cp Calculator." Free Calculator, 16 Sept. 2026, https://freecalculator.tech/tools/cp-calculator.
- Link: Cp Calculator — Free Calculator, https://freecalculator.tech/tools/cp-calculator