Cpk vs Ppk Calculator: Both Indices From the Same Data

How the math works

Cpk and Ppk share the same formula shape. The only difference is which estimate of sigma goes in the denominator, and that difference is the whole point of comparing them.

• Mean: x̄ = Σx / N, across all readings.
• Within sigma (short-term): σ_w = R̄ / d₂, where R̄ is the average subgroup range and d₂ is the standard constant for your subgroup size (n=2: 1.128, n=3: 1.693, n=4: 2.059, n=5: 2.326, n=6: 2.534, n=7: 2.704, n=8: 2.847, n=9: 2.970, n=10: 3.078).
• Overall sigma (long-term): σ_o = the sample standard deviation of all readings (N−1 denominator).
• Cp = (USL − LSL) / 6σ_w and Cpk = min[(USL − x̄) / 3σ_w, (x̄ − LSL) / 3σ_w]
• Pp = (USL − LSL) / 6σ_o and Ppk = min[(USL − x̄) / 3σ_o, (x̄ − LSL) / 3σ_o]

With a one-sided spec, only the defined side is reported and Cp and Pp are suppressed, since they need the full tolerance width. Because σ_w ignores everything that happens between subgroups and σ_o includes it, Cpk answers "what could this process hold if it stayed stable?" while Ppk answers "what did it actually deliver?"

Worked example: 25 shaft diameters

A machining cell measures 5 shafts per hour for 5 hours: 25 diameters in subgroups of 5, against a spec of 9.95 to 10.05 mm. The mean lands at 10.002. The average subgroup range is 0.026, so within sigma is 0.026 / 2.326 = 0.0112. The overall standard deviation of all 25 readings is 0.0135.

• Cp = 0.10 / (6 × 0.0112) = 1.49
• Cpk = (10.05 − 10.002) / (3 × 0.0112) = 1.43
• Pp = 0.10 / (6 × 0.0135) = 1.23
• Ppk = (10.05 − 10.002) / (3 × 0.0135) = 1.19

The read: short-term, this process is comfortably capable (Cpk 1.43). But Ppk sits well below Cpk, which means the mean is drifting between hourly subgroups, and that drift, not the machine's inherent precision, is what to fix first. Hit "Load example" above to run these exact numbers through the calculator.

FAQ

What is the difference between Cpk and Ppk?

Cpk uses within-subgroup (short-term) variation, estimated from the average subgroup range, so it describes what the process is capable of when it is stable. Ppk uses overall (long-term) variation, the standard deviation of every reading pooled together, so it describes how the process actually performed, including drift and shifts between subgroups. Same formula shape, different sigma.

Why is my Ppk lower than my Cpk?

Because overall variation includes everything that happens between subgroups: tool wear, setup differences, material lot changes, shift-to-shift drift. Within-subgroup variation does not see any of that. When the process mean moves around over time, overall sigma grows, and Ppk drops below Cpk. A large gap is a signal that stability, not inherent capability, is your problem.

What is a good Cpk value?

A common minimum for existing processes is 1.33, which corresponds to a 4 sigma spread inside the closest specification limit. Many customers require 1.67 for new processes or safety-critical characteristics. A Cpk of 1.00 means the process spread just barely fits, with no margin for drift.

Can I calculate Cpk with a one-sided specification?

Yes. With only an upper limit, Cpk is (USL minus the mean) divided by 3 sigma. With only a lower limit, it is (the mean minus LSL) divided by 3 sigma. Cp and Pp are not defined for one-sided specs because they need the full tolerance width. This calculator handles both cases: leave the unused limit blank.

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