Reviewed November 2026. Formulas are shown above the guide. Report an error or request a calculator.
What Cp and Cpk tell you
Process capability compares the spread of a process with the tolerance a drawing allows. Cp asks whether the process could fit inside the tolerance if it were perfectly centred: tolerance width divided by six standard deviations. Cpk also checks where the process actually sits, taking the nearer of the two limits. A process can have a good Cp and a poor Cpk simply because it runs off centre, and that is usually the cheapest problem to fix.
Worked example
A shaft diameter has limits of 9.90 to 10.10 mm. The process runs at a mean of 10.02 mm with a standard deviation of 0.025 mm.
| Index | Value |
|---|---|
| Cp (0.20 ÷ 0.15) | 1.33 |
| Cpu ((10.10 − 10.02) ÷ 0.075) | 1.07 |
| Cpl ((10.02 − 9.90) ÷ 0.075) | 1.60 |
| Cpk | 1.07 |
| Expected out of spec | about 690 ppm |
The spread is acceptable but the mean sits 0.02 mm high. Re-centring the process to 10.00 mm would raise Cpk to 1.33 without any new equipment.
Using the result correctly
- Check stability first. Capability only predicts the future if the process is in statistical control. Plot a control chart before quoting Cpk.
- Use enough data. At least 30 measurements, ideally 100 or more from several shifts, gives a reliable estimate.
- Normal data only. The ppm estimate assumes a normal distribution. Skewed characteristics such as flatness or runout need a different method.
Frequently asked questions
What is a good Cpk value?
1.33 is the common minimum for production, which means about 63 ppm out of spec for a centred process. 1.67 is often required for safety-critical or newly approved parts.
What is the difference between Cpk and Ppk?
Cpk uses short-term, within-subgroup variation; Ppk uses the overall standard deviation of all data. With a single set of pasted values this calculator gives the overall figure, which is effectively Ppk.
Can Cpk be negative?
Yes. A negative Cpk means the process mean lies outside the specification limits.
How many measurements do I need?
Thirty is a practical minimum; 100 or more across shifts and material lots gives a much more reliable estimate.