Process Capability Cpk Calculator
Process capability indices Cp and Cpk quantify how well a process fits within its specification limits. Cp measures the ratio of the specification width to the process spread (6 sigma). Cpk adjusts for process centering. Enter the Upper Specification Limit (USL), Lower Specification Limit (LSL), process mean, and standard deviation (sigma) to calculate both indices and the estimated defect rate.
Cp and Cpk formulas
Cp = (USL - LSL) / (6 x sigma)
CPU = (USL - mean) / (3 x sigma)
CPL = (mean - LSL) / (3 x sigma)
Cpk = min(CPU, CPL)
Sigma level = Cpk x 3
Source: AIAG SPC Reference Manual, 4th Edition. These formulas are also documented in NIST/SEMATECH e-Handbook of Statistical Methods, Chapter 6.
Cpk interpretation guide
- Cpk below 1.00: Process is not capable; significant proportion of output will be outside specifications.
- Cpk 1.00 to 1.33: Marginally capable; process needs improvement or tighter control.
- Cpk 1.33 to 1.67: Capable; meets typical automotive and manufacturing requirements (AIAG target: 1.33 for existing processes).
- Cpk 1.67 and above: Highly capable; suitable for critical safety or medical device processes.
- Six Sigma target: Cpk of 1.50 (equivalent to 3.4 DPMO when process mean shifts up to 1.5 sigma).
Process capability: frequently asked questions
What is the Cpk formula?
Cpk = min((USL - mean) / (3 x sigma), (mean - LSL) / (3 x sigma)), where USL = Upper Specification Limit, LSL = Lower Specification Limit, mean = process average, and sigma = process standard deviation. Cpk measures how centered and spread the process is relative to the specification limits.
What is the difference between Cp and Cpk?
Cp = (USL - LSL) / (6 x sigma) measures whether the process spread fits within the specification window, ignoring centering. Cpk adjusts for process centering: if Cp = Cpk the process is perfectly centered. Cpk is always less than or equal to Cp.
What Cpk value is required for a capable process?
A Cpk of 1.00 means the process produces approximately 2,700 defects per million opportunities (3-sigma). A Cpk of 1.33 (4-sigma) is the typical minimum for a capable process in many industries. Six Sigma quality requires a Cpk of 1.50 or higher (process mean must be within 1.5 sigma of center to achieve 3.4 DPMO).
How many data points do I need to estimate sigma reliably?
A minimum of 30 measurements is recommended for an initial capability study. For a formal process capability study per AIAG SPC, at least 25 subgroups of 5 samples (125 total measurements) are preferred. With fewer than 20 data points, the sigma estimate has high uncertainty.
What is the Ppk vs Cpk distinction?
Cpk uses the within-subgroup (short-term) standard deviation estimated from a control chart (using the average range or moving range method). Ppk uses the overall (long-term) standard deviation from the full dataset. Cpk represents process potential; Ppk represents actual performance including all sources of variation.
Official sources
- NIST/SEMATECH e-Handbook of Statistical Methods: NIST Process Capability Indices.
- Automotive Industry Action Group (AIAG): AIAG SPC Reference Manual.
Reviewed by the CalculatorHub team, edited by James Graham, 14 June 2026. See our methodology.