Quality & Metrology calculator

Process Capability Cp Calculator

Compare tolerance width with six within standard deviations and your required Cp index.

What this calculator does

  • Compare tolerance width with six within standard deviations and your required Cp index.

Formula used

  • Cp = tolerance width ÷ (6 × within standard deviation)
  • Six-sigma spread = 6 × standard deviation
  • Index margin = calculated index − required index
  • Tolerance used = six-sigma spread ÷ tolerance width × 100

Inputs explained

  • Tolerance Width: Upper specification minus lower specification, in consistent measurement units.
  • Within Standard Deviation: Within-process SD from the approved rational-subgroup analysis.
  • Required Cp: Minimum index specified by your customer or quality plan.

How to use the result

  • Best suited to a narrower tolerance reduces Cp, a wider tolerance raises cp.
  • Normal capability interpretation requires a suitable distribution and trustworthy measurements. This width-only index ignores centering and does not estimate a defect percentage.

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

  • Which standard deviation belongs here? Use a within-process estimate from a suitable subgroup analysis. Do not substitute a pooled overall SD without changing the index to Pp.
  • Does a high index guarantee good parts? No. The mean can lie near or outside a specification limit. This width comparison contains no information about centering.
  • Where does the required index come from? Enter the customer requirement or agreed quality-plan criterion. The calculator does not supply an acceptance threshold.
  • Can I convert inches to millimeters? Yes. Convert tolerance width and standard deviation together. Their ratio, and therefore the index, stays the same.

Last reviewed 2026-10-06.