Check whether a process can hold its tolerance. Enter the upper and lower specification limits and either paste your measurements or type the mean and standard deviation. You get Cp, Cpk, Pp, Ppk, Cpm, the expected parts per million out of spec and a histogram with the limits drawn in.
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Specification limits
Leave empty for a one-sided lower spec
Leave empty for a one-sided upper spec
Process data
Input
Separate with commas, spaces or new lines.
Consecutive values are grouped to estimate within-subgroup σ
For Cp/Cpk. Empty = use the overall s
Enter your values to see the result.
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How to use the Process Capability (Cpk) Calculator
Enter the specification limits USL and LSL (leave one empty for a one-sided spec).
Paste your measurements in the order they were made, or switch to mean and standard deviation.
Pick the subgroup size if your data was collected in subgroups (for example 5 parts every hour).
Read Cpk and Ppk, the expected ppm out of spec and the histogram.
Compare with the reference table: 1.33 is a common minimum, 1.67 for critical features.
Capability index formulas
Index
Formula
Uses
Cp
(USL − LSL) ÷ 6σwithin
Potential capability if perfectly centered
Cpu, Cpl
(USL − x̄) ÷ 3σ, (x̄ − LSL) ÷ 3σ
Capability toward each limit
Cpk
min(Cpu, Cpl)
Actual short-term capability
Pp, Ppk
Same as Cp, Cpk with overall s
Long-term performance
Cpm
(USL − LSL) ÷ 6√(s² + (x̄ − T)²)
Penalises being off target
Within-subgroup σ is estimated from short-term variation. For individual readings it is the average moving range divided by d₂ = 1.128; for subgroups it is the average range R̄ divided by d₂ (1.128 for n = 2, 1.693 for 3, 2.059 for 4, 2.326 for 5, 2.534 for 6, 2.704 for 7, 2.847 for 8, 2.970 for 9, 3.078 for 10). The overall s is the ordinary sample standard deviation of all values.
Cpk, sigma level and defect rate
Cpk
Distance to nearest limit
Out of spec (centered, two-sided)
Typical verdict
0.67
2σ
≈ 45,500 ppm (4.55%)
Not capable
1.00
3σ
≈ 2,700 ppm
Not capable / bare minimum
1.33
4σ
≈ 63 ppm
Capable (common minimum)
1.50
4.5σ
≈ 6.8 ppm
Good
1.67
5σ
≈ 0.57 ppm
Excellent, critical features
2.00
6σ
≈ 0.002 ppm
Six Sigma level
Tips for a meaningful capability study
Make sure the process is stable first (use a control chart). Capability of an out-of-control process does not predict the future.
Keep the time order of your data so the moving range or subgroup ranges reflect true short-term variation.
Check the measurement system. Gauge variation adds to the observed spread and lowers Cpk; a gauge R&R study tells you how much.
Improve centering first: if Cp is high but Cpk low, adjusting the mean is usually the cheapest fix.
Frequently asked questions
What is the Cpk formula?
Cpk = min[(USL − mean) ÷ 3σ, (mean − LSL) ÷ 3σ], where σ is the within-subgroup (short-term) standard deviation. It measures how many three-sigma widths fit between the mean and the nearest specification limit.
What is the difference between Cp and Cpk?
Cp = (USL − LSL) ÷ 6σ compares the tolerance width with the process spread but ignores where the process is centered. Cpk also accounts for centering. If Cp is much larger than Cpk, moving the mean to the middle of the tolerance would improve capability without reducing variation.
What is the difference between Cpk and Ppk?
Both use the same formula, but Cpk uses the within-subgroup standard deviation (short-term variation, estimated from ranges), while Ppk uses the overall standard deviation of all data (long-term performance, including shifts between subgroups). Ppk is usually equal to or lower than Cpk.
What is a good Cpk value?
Cpk below 1.0 means the process produces out-of-spec parts. 1.33 (a 4σ distance to the nearest limit) is a widely used minimum, 1.67 is common for safety or critical characteristics, and 2.0 corresponds to Six Sigma quality.
How many measurements do I need?
At least 25 to 30 for a rough estimate, and 100 or more (for example 25 subgroups of 4 or 5) for a reliable capability study. With few data points the confidence interval for Cpk is wide.
How is ppm out of spec calculated?
Assuming a normal distribution, ppm = 1,000,000 × [P(Z > (USL − mean) ÷ s) + P(Z < (LSL − mean) ÷ s)]. A centered process with Cpk 1.33 gives about 63 ppm; with Cpk 1.0, about 2,700 ppm.
Does the data have to be normal?
The indices and ppm estimates assume an approximately normal, stable process. Check the histogram: skewed or bimodal data, or a process that is not in statistical control, can make Cpk misleading. Non-normal data needs a transformation or a non-normal capability method.
Are all the tools on FreeToolCabin tested for quality and accuracy?
Yes! Every tool on our site undergoes automated Q/A testing in real browser environments to ensure high precision, correct output, and zero errors. If you happen to spot a bug or have a suggestion, please contact us at [email protected] and our team will review it right away.