Process Capability Calculator (Cp, Cpk, PPM)
By Santaji GadepatilinUpdated November 4, 2026
Process capability compares the spread of a process with the tolerance it has to meet. This process capability calculator returns Cp (potential capability), Cpk (actual capability, allowing for an off-centre mean) and the expected parts per million outside the specification limits, assuming a normal distribution.
How to use the process capability calculator
Enter the upper and lower specification limits, the process mean and the process standard deviation. The calculator returns Cp, the one-sided indices Cpu and Cpl, Cpk (the smaller of the two) and the expected fraction outside the limits in parts per million. Collect at least 25 subgroups from a stable process before trusting the result.
Process capability formulas
Cp = (USL − LSL) ÷ 6σ · Cpu = (USL − x̄) ÷ 3σ · Cpl = (x̄ − LSL) ÷ 3σ · Cpk = min(Cpu, Cpl)
ppm = [Φ(−3 Cpu) + Φ(−3 Cpl)] × 10⁶
Example
A shaft diameter specified 10.00 ± 0.05 mm (USL 10.05, LSL 9.95), with mean 10.01 mm and σ = 0.012 mm:
- Cp = 0.10 ÷ (6 × 0.012) = 1.389
- Cpu = (10.05 − 10.01) ÷ (3 × 0.012) = 1.111, Cpl = (10.01 − 9.95) ÷ 0.036 = 1.667
- Cpk = min(1.111, 1.667) = 1.111
- Expected out of tolerance = [Φ(−3.333) + Φ(−5.000)] × 10⁶ = 429.3 ppm
Centring the process at 10.00 mm would raise Cpk to 1.389 without reducing the variation.
Cpk and expected defects (centred process)
| Cpk | Distance to nearest limit | Out of spec (ppm) | Yield |
|---|---|---|---|
| 0.50 | 1.5σ | 133,614.4 | 86.63856% |
| 0.67 | 2.0σ | 44,431.2 | 95.55688% |
| 1.00 | 3.0σ | 2,699.8 | 99.73002% |
| 1.33 | 4.0σ | 66.1 | 99.99339% |
| 1.50 | 4.5σ | 6.8 | 99.99932% |
| 1.67 | 5.0σ | 0.5 | 99.99995% |
| 2.00 | 6.0σ | 0.002 | 100.00000% |
Notes
- Capability only means something for a process in statistical control.
- Six sigma quality with a 1.5σ long-term shift corresponds to 3.4 defects per million — see the six sigma calculator.
Frequently asked questions
What is the difference between Cp and Cpk?
Cp = (USL − LSL) ÷ 6σ compares the tolerance width with the process spread and ignores where the process is centred. Cpk = min(USL − x̄, x̄ − LSL) ÷ 3σ also accounts for an off-centre mean, so Cpk ≤ Cp, and they are equal only when the process is centred.
What is a good Cpk value?
1.33 is the usual minimum for an established process (about 63 ppm out of tolerance when centred), 1.67 for new or safety-critical characteristics, and 2.0 corresponds to six sigma quality.
What is the difference between Cpk and Ppk?
Cpk uses the short-term, within-subgroup standard deviation (from a control chart, R̄/d₂); Ppk uses the overall standard deviation of all data. Ppk reflects what the customer actually receives.
Does Cpk assume a normal distribution?
The ppm estimate does. Check normality with a histogram or probability plot first; skewed data (such as flatness or runout) need a transformation or a non-normal capability method.