Free tool

Cp and Cpk calculator

Paste your measurements and enter the specification limits to get Cp, Cpk, Pp and Ppk step by step, with a histogram and a plain verdict on process capability.

Result

Distribution

What process capability (Cp, Cpk) tells you

Process capability indices sum up in one number how comfortably a process fits its tolerance. Cp compares the spread with the tolerance width; Cpk adds the position of the mean. Pp and Ppk do the same with the overall standard deviation of all the data and show how the process behaves in the long run.

The example in the calculator is 25 shaft diameters in production order (LSL 9.965 mm, USL 10.040 mm). The mean drifts slowly upwards, so Ppk (1.11) stays below Cpk (1.41): the process is capable in the short term, but the drift lowers its long-term performance. It is a typical case of why Cpk alone is not enough.

Things to watch

Order matters: within sigma comes from consecutive readings, so enter the data in production order.
The process should be stable: Cpk from a period with special causes (a broken tool, a material change) means little; check stability with a control chart first.
Normal distribution: the ppm estimate assumes normally distributed data and uses the overall standard deviation, so it is the expected out-of-spec rate on the Ppk basis, not the short-term (Cpk) one. Skewed characteristics (e.g. runout, flatness) need other methods.

Excel template

To run the same calculation in your own spreadsheet, download the Cp and Cpk template (Excel). All tools and templates are on the tools page.

From manual readings to automatic data

When measurements come straight from the machine, the gauge or the PLC, Cpk is calculated for every batch and drift shows the moment it starts. See our machine data collection and process monitoring pages.

Frequently asked questions

Common questions

How are Cp and Cpk calculated?

Cp = (USL − LSL) / 6σ and Cpk = min(USL − mean, mean − LSL) / 3σ, where σ is the within (short-term) standard deviation: the average moving range / 1.128 for individual readings, or the average range / d2 for subgroups. The calculator shows every step with your own data.

What is the difference between Cp and Cpk?

Cp only compares the spread with the tolerance and assumes the process is perfectly centred. Cpk also takes the position of the mean into account and is calculated against the nearer specification limit. Cpk is always equal to or lower than Cp; the gap shows how far off centre the process is.

What is the difference between Cpk and Ppk?

Cpk uses the within (short-term) standard deviation, Ppk the overall standard deviation of all the data. A Ppk clearly below Cpk means the mean drifts over time or batches differ.

What is a good Cpk value?

The widely used reference is Cpk ≥ 1.33; 1.67 is often required for critical characteristics and new processes. Below 1.00 the process is expected to make out-of-spec parts: either the spread does not fit the tolerance (Cp is below 1 too), or it fits but the mean sits too close to one limit (Cp above 1, Cpk below). These are industry conventions, not legal limits; the value that applies is in your customer's requirements.

How many measurements do I need?

The calculator works from 2 values, but a reliable figure usually needs at least 25–30 subgroups or around 100 measurements. Cpk from a small sample can mislead.