Process capability calculator
Enter your specification limits, process mean, and standard deviation, or paste a column of measurements, to get Cp, Cpk, Pp, Ppk, the sigma level, and the estimated ppm out of spec. Methods follow the AIAG SPC manual and everything runs in your browser.
Your numbers
Result
Cp = (USL − LSL) ÷ (6σ); Cpk = min((USL − mean), (mean − LSL)) ÷ (3σ). Pp and Ppk use the same formulas with the overall (long-term) σ, and the sigma level is 3 × Cpk.
Process capability, in plain terms
Cp and Cpk
Capability compares how much a process varies against how much room the specification gives it. Cp is the ratio of the tolerance width to the total process spread of six standard deviations: Cp = (USL − LSL) / (6σ). It assumes the process is centered, so it is a best case. Cpk brings in where the process actually sits: it is the distance from the mean to the nearer limit, divided by three standard deviations, Cpk = min((USL − mean)/(3σ), (mean − LSL)/(3σ)). Because it uses the nearer limit, Cpk is never larger than Cp, and the gap between them is a direct measure of how far off center the process is running.
Cp and Cpk versus Pp and Ppk
The AIAG SPC manual draws a clear line between capability and performance. Cp and Cpk use the within-subgroup standard deviation, the short-term spread estimated from a control chart as R-bar divided by d2 (or S-bar divided by c4). Pp and Ppk use the overall standard deviation, the ordinary sample standard deviation of every reading, which also captures drift and shifts between subgroups. Short-term capability is what the process could do on its best behavior; long-term performance is what it delivered over the whole run. This tool applies the exact same arithmetic and simply labels the result Cp/Cpk or Pp/Ppk according to which standard deviation you tell it you have.
Sigma level and ppm out of spec
The sigma level shown here is the distance from the process mean to the nearer specification limit, measured in standard deviations, which is exactly 3 times Cpk. A Cpk of 1.00 puts the nearer limit 3σ away, a 3 sigma process. To estimate the fraction out of spec, the tool fits a normal curve centered on your mean with your standard deviation, then adds the area beyond each limit: p_out = Φ((LSL − mean)/σ) + (1 − Φ((USL − mean)/σ)), where Φ is the standard normal cumulative distribution. Multiplying by one million gives the estimated ppm (or DPMO). Some Six Sigma tables add a 1.5σ long-term shift before quoting a sigma level; this tool does not add that shift for you, it only points out that the convention exists.
What capability does not tell you
Two assumptions sit under every capability index, and this calculator cannot check either one for you. First, the process must be stable and in statistical control, otherwise the mean and standard deviation are moving targets and a single number is misleading. Second, the numbers must be roughly normal, since the ppm estimate comes straight from the normal curve. There is a third trap that is easy to miss: capability indices include your measurement error. A noisy gage inflates the standard deviation and pulls Cpk down, so a genuinely capable process can look incapable when the real problem is the gage. Confirm the measurement system with a Gage R&R first, then read the capability numbers with confidence.
Common questions
What is the difference between Cp and Cpk?
Cp measures the potential capability: how the total spread of the process (6 sigma) compares to the width of the tolerance, ignoring where the process is centered. Cp = (USL - LSL) / (6 sigma). Cpk adds centering. It is the distance from the process mean to the nearer specification limit, in units of 3 sigma: Cpk = min((USL - mean)/(3 sigma), (mean - LSL)/(3 sigma)). Cp is always greater than or equal to Cpk, and they are equal only when the process is perfectly centered. A high Cp with a low Cpk means the spread is fine but the process is off center.
What Cpk is considered capable?
A widely used rule of thumb treats Cpk of 1.33 or higher as capable, 1.00 to 1.33 as marginal, and below 1.00 as not capable. Cpk of 1.33 corresponds to the nearer spec limit sitting 4 sigma from the mean; 1.67 is 5 sigma and is common for safety or high-reliability characteristics; 2.00 is the classic six sigma target. These are conventions, not a legal threshold. Your customer, drawing, or quality plan sets the value you actually have to meet.
What is the difference between Cp/Cpk and Pp/Ppk?
The formulas are identical. The difference is which standard deviation you feed in. Cp and Cpk use the within-subgroup (short-term) sigma, estimated from a control chart as R-bar divided by d2 or S-bar divided by c4. Pp and Ppk use the overall (long-term) sample standard deviation of all the individual readings. Short-term capability tells you what the process could do when it is behaving; long-term performance tells you what it actually delivered, including drift and shifts between subgroups. This tool applies whichever label you choose and reports both interpretations honestly.
How do you convert Cpk to a sigma level and ppm out of spec?
The sigma level reported here is the distance from the process mean to the nearer specification limit, which is exactly 3 times Cpk. A Cpk of 1.00 means the nearer limit is 3 sigma away, a 3 sigma process. The estimated parts per million out of spec come from a normal model: the tool sums the area of the normal curve beyond each specification limit, using the same Phi (standard normal cumulative distribution) as the conformance tool, and multiplies by one million. Note that some Six Sigma tables add a 1.5 sigma long-term shift before quoting a sigma level; this tool does not add that shift automatically, it only names it.
Do capability indices account for measurement error?
No. Cp, Cpk, Pp, and Ppk describe the spread and centering of your recorded numbers. They cannot tell how much of that spread is the process and how much is your gage. If the measurement system is noisy, a poor gage inflates the standard deviation and drags the indices down, so a truly capable process can look incapable. Run a Gage R&R first to confirm the measurement system is good enough, then trust the capability numbers. Axiospec includes an AIAG Gage R&R study, and there is a free Gage R&R calculator in these tools.
Can I calculate Cp and Cpk from a list of measurements?
Yes. Paste a column of individual readings and the tool computes the mean and the sample standard deviation (using n minus 1 in the denominator), then the indices. One caution: a single ungrouped column gives you the overall standard deviation, which is the Pp and Ppk basis. Strict Cp and Cpk want a within-subgroup sigma from subgrouped, in-control data (R-bar over d2). The tool flags this when you select the short-term label with pasted data, so you are never handed a within-subgroup number the data cannot support.
Does a good Cpk mean my process is in control?
Not on its own. Capability indices assume the process is stable and roughly normal. If the process is drifting or has special-cause shifts, a single Cpk is misleading, because the mean and standard deviation are moving targets. Confirm statistical control with a control chart and check that the distribution is approximately normal before you rely on the indices or the estimated ppm. This calculator computes the numbers; it does not verify that the assumptions behind them hold.
This calculator estimates process capability from the numbers you enter, assuming a stable, roughly normal process. It does not verify statistical control or normality, and it does not separate the measurement system error from the process, which requires a Gage R&R that is yours to run. It is an aid, not a substitute for the AIAG SPC manual or your own quality plan. Confirm the assumptions and review any capability decision against your customer requirements before you use it.
Capability is only as good as the data behind it
Axiospec keeps every calibration, as-found and as-left reading, and certificate in one tamper-evident ledger, so the numbers you feed a capability study are traceable and audit-ready. Start free, no credit card.
No signup and no credit card for the demo · Or compare plans, including a free option