Process capability (Cp & Cpk) calculator
Compare a supplied process mean and standard deviation with lower and upper specification limits, with the centering effect shown separately.
Lowest value allowed by the specification, in your measurement unit.
Highest value allowed by the specification, in the same unit.
Supplied mean for the process being assessed.
Supplied positive process standard deviation; this calculator does not estimate it.
The supplied mean is closer to the upper specification limit than to the lower limit.
- Potential capability (Cp)
- 1
- Upper capability (Cpu)
- 0.666667
- Lower capability (Cpl)
- 1.333333
- Specification width
- 12
- Six-sigma process spread
- 12
- Specification midpoint
- 14
- Mean offset from midpoint
- +2
Specification band and process span
The purple span shows mean ±3 standard deviations. Labels and numeric results carry the comparison without relying on position or color.
Computed from the supplied mean and standard deviation. Process stability, normality, sample uncertainty and acceptance requirements are not tested.
Included
- Cp, Cpk, Cpu and Cpl from supplied summary statistics
- Two-sided lower and upper specification limits
- Specification midpoint, width and six-standard-deviation process spread
- A mean outside the limits, including a meaningful negative Cpk
Not included
- Raw-data analysis or estimation of the mean and standard deviation
- Tests of process stability, statistical control or distribution shape
- Sample size, confidence intervals or sampling uncertainty
- A pass/fail, acceptance, certification or production-release decision
What this means
Cp compares the distance between the two specification limits with a six-standard-deviation process spread. It describes potential capability only; it does not account for where the process mean sits inside that specification band.
Cpk uses the smaller of the upper and lower one-sided indices. It therefore reflects both spread and centering. When the supplied mean lies outside a specification limit, the index on that side—and Cpk—becomes negative.
The arithmetic assumes the supplied mean and standard deviation describe a process you consider stable and approximately normal. This calculator does not test those conditions, estimate uncertainty or decide whether any capability value is acceptable for your product.
Formula & worked example
Cp = (USL − LSL) ÷ (6 × standard deviation) Cpu = (USL − mean) ÷ (3 × standard deviation) Cpl = (mean − LSL) ÷ (3 × standard deviation) Cpk = smaller of Cpu and Cpl mean offset = mean − specification midpoint
LSL 8, USL 20, process mean 16 and supplied standard deviation 2
- Cp: (20 − 8) ÷ (6 × 2)
- 1.00
- Cpu: (20 − 16) ÷ (3 × 2)
- 0.67
- Cpl: (16 − 8) ÷ (3 × 2)
- 1.33
Cpk is 0.67 because the upper side is closer to the mean. This is a computed index from the supplied summary statistics, not an acceptance decision.
How this calculation works
The calculation follows the formulas, definitions and assumptions explained on this page. The references below support the method and any stated boundaries.
Official sources
- NIST/SEMATECH — What is process capability? — Cp, Cpk and one-sided capability equations, with stability and distribution context
- NIST/SEMATECH — Assessing process capability — Difference between potential capability and capability after process centering is considered
- ASQ — Process capability — Practitioner context for stable processes, distribution assumptions and capability analysis