Cp Calculator
Compare specification width with short-term process spread.
In short
Compare specification width with short-term process spread.
Formula: Cp = (USL − LSL) ÷ (6σ_within)
What this calculator does
Direct calculation. The page states that Cp ignores centring and links to the Cpk calculator, which does not.
Use it to turn Upper specification limit, Lower specification limit, Within-subgroup standard deviation into a checked result you can compare, copy, or rerun with different assumptions.
The page shows the formula, a numeric worked example, and the assumptions that affect this professional & industry calculation.
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).
Inputs used: Upper specification limit, Lower specification limit, Within-subgroup standard deviation.
Edge handling: Upper specification limit is required.; Upper specification limit must be no more than 1000000000000.; Lower specification limit is required.; Lower specification limit must be no more than 1000000000000.; Within-subgroup standard deviation is required..
Worked example
Specification 9.5 to 10.5 with a within-subgroup sigma of 0.12
- Start with Upper specification limit: 10.5, Lower specification limit: 9.5, Within-subgroup standard deviation: 0.12.
- Apply the method: Cp = (USL − LSL) ÷ (6σ_within).
- 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
- Inputs outside the supported range are rejected rather than forced into a result.
- The result depends on the values you enter for this cp calculator; it does not supply missing rates, rules, prices, dates, or assumptions for you.
Reference: National Institute of Standards and Technology — NIST/SEMATECH e-Handbook of Statistical Methods
Last reviewed:
Common questions
Where does this formula come from?
NIST/SEMATECH e-Handbook of Statistical Methods, process capability indices: Cp = (USL − LSL) ÷ 6σ using within-subgroup variation. See the source link on this page.
What kind of calculation is this?
Specification width divided by six within-subgroup standard deviations. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.
What are its limits?
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.
How do I use the Cp Calculator?
Enter the required values for Upper specification limit, Lower specification limit, Within-subgroup standard deviation. The calculator applies the formula on this page and shows the main result with any supporting breakdown so you can check the arithmetic.
What formula does the Cp Calculator use?
Cp = (USL − LSL) ÷ (6σ_within) The visible formula section above lists the calculation path and the edge cases the page handles, so the result can be checked without relying on the form alone. Check the formula, example, and limitations on this page before using the result for a real professional & industry decision.
Can the Cp Calculator be used for exact decisions?
Use it as a calculation aid, not as a substitute for checking the underlying rule, contract, policy, or professional advice that applies to your situation. When a result depends on local rules, personal details, prices, or dates, enter those values yourself and confirm them before acting.
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.
Cite this page
Free Calculator. (2026, September 16). Cp Calculator. https://freecalculator.tech/tools/cp-calculator
"Cp Calculator." Free Calculator, 16 Sept. 2026, https://freecalculator.tech/tools/cp-calculator.
Cp Calculator — Free Calculator, https://freecalculator.tech/tools/cp-calculator
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