Process Capability Calculator
Paste measured values, or enter a mean and standard deviation, with the tolerance limits, to get Cp, Cpk and the predicted defect rate.
Tolerance a centered process of this spread can hold
| Target Cp | Total tolerance (6 x Cp x sigma) | As plus or minus |
|---|
Details
| Cpu (upper side) | |
| Cpl (lower side) | |
| Parts below the lower limit (ppm) | |
| Parts above the upper limit (ppm) | |
| Parts inside the limits | |
| Sigma level (3 x Cpk) | |
| 95% interval for the true mean (measured values) |
How it works
Cp compares the width of the tolerance with the width of the process: Cp = (USL − LSL) ÷ 6σ. Cpk also considers whether the process is centered: Cpk = the smaller of (USL − mean) ÷ 3σ and (mean − LSL) ÷ 3σ. Assuming the data are normally distributed (as in the Machinery’s Handbook chapter on statistical analysis), the fraction beyond each limit follows from the normal curve. From measured values the calculator uses the sample mean and the sample standard deviation (n − 1). The ideas are explained on the Statistical Tolerancing and Process Capability page.
Worked example
The preloaded sample is 20 measurements of a 25.000 ± 0.025 mm bore (limits 24.975 and 25.025). The mean is 25.0057 and the standard deviation 0.0043, so Cp = 0.050 ÷ (6 × 0.0043) = 1.92 and Cpk = (25.025 − 25.0057) ÷ (3 × 0.0043) = 1.49: capable, but off-center by 0.0057. About 4 parts per million are predicted outside the limits. A centered Cp of 1.33 uses 75% of the tolerance and gives about 63 ppm out; 1.67 gives about 0.57 ppm.
Things to know
The result is only as good as the data. Capability is for a stable process: plot the values in time order first and look for drift, steps or outliers. Twenty values are a rough estimate; 30 or more, from several short runs, is better.
The defect rate assumes a normal distribution. Flatness, runout, position and other values that cannot go below zero are not normal; use their one-sided capability (only the upper limit) or a method for non-normal data.
Cp and Cpk (short-term) use the standard deviation within a run; Pp and Ppk (long-term) use the overall standard deviation. This calculator uses the standard deviation you give it, so enter the one that matches the question.
Measurement error adds to the observed spread. If the gauge is not much better than the tolerance, the calculated capability is lower than the true one.
Common questions
What is a good Cpk?
A common minimum for an established process is 1.33, and 1.67 for critical characteristics, but the requirement is set by the customer or quality system.
Why is Cpk lower than Cp?
Because the mean is not in the middle of the tolerance. Cp ignores the position of the mean; Cpk does not. Centering the process lifts Cpk toward Cp.
Can Cpk be negative?
Yes, if the mean is outside the tolerance. Then most parts are out.
What do ppm and sigma level mean?
ppm is parts per million outside the limits. The sigma level here is 3 × Cpk: how many standard deviations the nearer limit is from the mean.
Sources
- Machinery’s Handbook, 31st edition, Industrial Press: “Statistical Analysis of Manufacturing Data” (normal distribution, sample mean and standard deviation, confidence intervals).
- AIAG, Statistical Process Control (SPC) Reference Manual; ISO 22514-2.
Last reviewed: October 22, 2026