Mathematics & Conversions

Tolerance Compliance & Process Capability Calculator — Margin, Deviation, Cp and Cpk Validator

Tolerance Compliance & Process Capability Calculator — Margin, Deviation, Cp and Cpk Validator

Unit-aware inputs Deterministic calculation Engineering interpretation
Calculation workspace

Enter the known values and review the calculated result

Deterministic calculation
01
Parameters

Input parameters

Use consistent values and select the intended engineering units.

Evaluation mode

Nominal & tolerances

Measurement

Statistical parameters

02
Output

Results

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Engineering reference

Method, application and limitations

Review the calculation method, intended application and engineering assumptions before using the result in a design decision.

01
Method

Formula and calculation method

compliance status formula:

U = N + T+

L = N – T–

ΔU = U – X

ΔL = X – L

Compliance status = 1 when ΔU ≥ 0 and ΔL ≥ 0; otherwise Compliance status = 0

margin to nearest limit formula:

M = min(ΔU, ΔL) when the value is within limits

M = -min(|ΔU|, |ΔL|) when the value is outside limits

normalized deviation formula:

η = (X – N) / T+ when X ≥ N

η = (X – N) / T– when X < N

where:

  • N — Nominal value [—]
  • T+ — Upper tolerance [—]
  • T– — Lower tolerance [—]
  • X — Actual value [—]
  • U — Upper limit [—]
  • L — Lower limit [—]
  • ΔU — Distance to upper limit [—]
  • ΔL — Distance to lower limit [—]
  • M — Margin to nearest limit [—]
  • η — Normalized deviation [—]
02
Application

When to use this calculator

When to use this calculator:

  • Checking whether a measured part dimension is inside asymmetric upper and lower tolerance limits.
  • Calculating the remaining margin between an actual measurement and the nearest tolerance boundary.
  • Comparing actual deviation from nominal value against different upper and lower tolerances.
  • Evaluating process capability when process mean and standard deviation are available.
  • Estimating defect probability from process mean, standard deviation and tolerance limits.
03
Decision support

How to interpret the result

Compliance status is defined as a binary result: 1 means the actual value is inside the tolerance limits, and 0 means the actual value is outside at least one limit.

Margin to nearest limit is defined as the distance from the actual value to the closest tolerance boundary. A positive margin means the value is inside limits, and a negative margin means the value is outside limits.

Normalized deviation is defined as the deviation from nominal value divided by the applicable tolerance side. Values above nominal use the upper tolerance, and values below nominal use the lower tolerance.

  • Safe — in measurement mode, the actual value is within limits and absolute normalized deviation is ≤ 0.9; in process mode, the actual value is within limits and Cpk ≥ 1.33.
  • Warning — in measurement mode, the actual value is within limits and absolute normalized deviation is > 0.9; in process mode, the actual value is within limits and 1 ≤ Cpk < 1.33.
  • Unsafe — the actual value is outside the tolerance limits, or in process mode Cpk < 1.
  • Invalid — required numeric inputs are missing or invalid, tolerance values are not greater than zero, process mode is selected without valid standard deviation and process mean, or the evaluation mode is not measurement or process capability.

The result is used to decide whether the measured value passes tolerance compliance and, in process mode, whether the process has sufficient capability margin.

04
Worked case

Calculation example

Example:

A user checks a measured shaft dimension against an asymmetric tolerance range before accepting the part.

  • N — Nominal value = 50.00
  • T+ — Upper tolerance = 0.10
  • T– — Lower tolerance = 0.05
  • X — Actual value = 50.07
  • Mode = Measurement

U = 50.10, L = 49.95, ΔU = 0.03, ΔL = 0.12, M = 0.03, η = 0.700, Compliance status = 1.

05
Model boundaries

Assumptions and limitations

  • The upper limit is calculated as nominal value plus upper tolerance.
  • The lower limit is calculated as nominal value minus lower tolerance.
  • Upper and lower tolerances must be greater than zero.
  • Measurement mode evaluates the actual value against tolerance limits and normalized deviation.
  • Process capability mode requires standard deviation greater than zero and a finite process mean.
  • Process capability mode calculates Cp, Cpk, distance to limit and defect probability from the tolerance span, process mean and standard deviation.
06
Questions

Frequently asked questions

How to calculate compliance status?
Compliance status is calculated by comparing the actual value with the upper and lower limits. The result is compliant when the actual value is not above the upper limit and not below the lower limit.
What affects margin to nearest limit the most?
Margin to nearest limit depends on the actual value, nominal value, upper tolerance and lower tolerance. Moving the actual value closer to either tolerance boundary decreases the margin.
When is the normalized deviation formula not valid?
The normalized deviation formula is not valid when the nominal value is not finite, the actual value is not finite, the upper tolerance is not greater than zero, or the lower tolerance is not greater than zero.
Can this calculator be used for process capability?
It can be used for process capability when process mode is selected and both standard deviation greater than zero and process mean are provided. In process mode, capability is evaluated using Cp, Cpk, distance to limit and defect probability.
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Engineering notice. Verify input data, assumptions, applicable standards and required safety factors before using results for design release or safety-critical decisions.