Quality & Metrology calculator

Process Capability Cpk Calculator

Compare the mean with both specification limits using within variation and your required Cpk.

What this calculator does

  • Compare the mean with both specification limits using within variation and your required Cpk.

Formula used

  • Upper index = (upper limit − mean) ÷ (3 × within SD)
  • Lower index = (mean − lower limit) ÷ (3 × within SD)
  • Cpk = minimum of the upper and lower indices
  • Nearest clearance = min(upper limit − mean, mean − lower limit)
  • Index margin = calculated index − required index

Inputs explained

  • Lower Specification Limit: Lower drawing or customer limit for the measured characteristic.
  • Upper Specification Limit: Upper drawing or customer limit for the same characteristic.
  • Process Mean: Average measurement from the matching study population.
  • Within Standard Deviation: Within-process SD from the matching rational-subgroup analysis.
  • Required Cpk: Minimum index specified by your customer or quality plan.

How to use the result

  • Best suited to less Nearest-Limit Clearance, more Nearest-Limit clearance.
  • Normal capability interpretation needs an appropriate distribution and adequate measurement quality. A point index has sampling uncertainty and does not itself establish process stability.

Current U.S. benchmarks

  • U.S. manufacturing runs at 75.7% of capacity (Federal Reserve, Aug 2026). New factory orders are up 8.5% year over year (Census).

Common questions

  • Why can the index be negative? The distance to a limit becomes negative when the mean lies beyond it. Keeping that sign identifies a mean outside specification.
  • Is the required index always 1.33? No. Enter the requirement agreed for this characteristic. Example targets are illustrative, not acceptance rules.
  • Which variation estimate should I use? Use a defensible within-process SD from the same study. An overall SD includes between-subgroup changes and belongs in Ppk.
  • Do both limits need to be present? Yes. This calculator evaluates a two-sided specification. Use the appropriate one-sided index when only one limit is specified.

Related guides

Last reviewed 2026-10-06.