Cp Calculator
Compare specification width with short-term process spread.
What this calculator does
Direct calculation. The page states that Cp ignores centring and links to the Cpk calculator, which does not.
Inputs and what they mean
- Upper specification limit
- — number value.
- Lower specification limit
- — number value.
- Within-subgroup standard deviation
- — Within-subgroup (short-term) standard deviation, estimated from the variation inside subgroups — for example R-bar ÷ d2..
How to use it
- Enter your own figures — the calculator never fills in a rate, price or benchmark for you.
- Press Calculate to see the result.
- Read the formula, variables, assumptions and source below the result before you rely on it.
Formula
Cp = (USL − LSL) ÷ (6σ_within)
Worked example
Specification 9.5 to 10.5 with a within-subgroup sigma of 0.12
Potential capability, before any allowance for centring.
Reading the result
The headline figure is the main answer. Any breakdown underneath shows the parts that make it up, so you can check the working and see what changes when you adjust an input.
Limitations and assumptions
Results depend entirely on the figures you enter and are rounded for display. They are for general information and education, not professional advice.
Reference: National Institute of Standards and Technology — NIST/SEMATECH e-Handbook of Statistical Methods
Last reviewed:
Common questions
Formula, source and verification
Specification width divided by six within-subgroup standard deviations.
The question it answers: How does the process perform over the long run, and what sigma level does its defect rate imply?
The formula
Cp = (USL − LSL) ÷ (6σ_within)
- USL — Upper specification limit
- (measurement). Highest acceptable value.
- LSL — Lower specification limit
- (measurement). Lowest acceptable value.
- σ_within — Within-subgroup standard deviation
- (measurement). Short-term variation, estimated from inside subgroups (for example R̄ ÷ d₂).
Units: Specification and standard deviation in the same measurement unit; the index is dimensionless.
What kind of calculation this is
Deterministic formula. The same inputs always give the same answer. The maths is fixed and does not depend on judgement.
Method
Direct calculation. The page states that Cp ignores centring and links to the Cpk calculator, which does not.
Assumptions built into the result
- Statistical: The standard deviation supplied is a within-subgroup (short-term) estimate.
- Statistical: Capability indices are normally interpreted for a stable process whose measurements are approximately normal.
Figures this calculator will never guess for you
- No benchmark, target or 'world class' value is supplied or implied; the result describes only the figures entered.
- No minimum acceptable Cp is stated; a required capability is a customer or organisational target, not part of the formula.
- Normality and stability are stated as conditions, not assumed away.
Limitations
- Cp says nothing about where the mean sits — a badly centred process can have a high Cp and still produce defects.
- Meaningful only for a stable process; on an unstable process the estimate of sigma itself is not trustworthy.
- A capability index, an industry benchmark and a customer's required index are three different things.
Source and version
- Standard or reference
- Process capability index Cp — NIST/SEMATECH (NIST/SEMATECH e-Handbook of Statistical Methods, process capability indices: Cp = (USL − LSL) ÷ 6σ using within-subgroup variation.)
- Published source
- National Institute of Standards and Technology — e-Handbook
- Formula version
- Version 1
- Verification
- Reviewed against the cited source on
- How much weight the source carries
- Standards or government
- Applies to
- Currency
- The result is a ratio or index, so it does not depend on currency.
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