Cp and Cpk Calculator
Process capability indices from the specification limits, the mean and the standard deviation.
Results
Cpk
1.0667
Cp
1.3333
Percentage
20.00
%
What this tool does
Cp measures whether the process spread fits the tolerance; Cpk measures whether it fits and is centred. The third result is how far off centre the process is, as a percentage of the half-tolerance.
Formula
Cp = (USL − LSL) ÷ 6σ · Cpk = min(USL−µ, µ−LSL) ÷ 3σ
Variables
| Symbol | Meaning | Unit |
|---|---|---|
usl | Upper specification limit | — |
lsl | Lower specification limit | — |
mu | Process mean | — |
sg | Standard deviation | — |
CPK | Cpk | — |
CP | Cp | — |
K | Percentage | % |
Worked example
- Upper specification limit10.1
- Lower specification limit9.9
- Process mean10.02
- Standard deviation0.025
- Cpk1.0667
- Cp1.3333
- Percentage20.00 %
Limitations
- For work that must comply with a standard or be signed off, check the result against the applicable code and have it reviewed by a qualified engineer.
- Standard deviation and variance are calculated for a sample (dividing by n − 1). For a full population, divide by n instead.
- The result is an estimate based only on the values you type. Real situations often include factors this calculator does not know about.
Frequently asked questions
Why are Cp and Cpk different?
Cp only asks whether the spread fits inside the tolerance; Cpk also asks whether it is centred. A process can be tight enough and still produce scrap because it is running towards one limit. When Cpk is much lower than Cp, the fix is usually to re-centre the process, not to reduce its variation.