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Test uncertainty ratio (TUR) calculator

Compare the tolerance of the unit under test with the expanded measurement uncertainty of the calibration process. Use the same unit for every value.

TUR = (upper limit − lower limit) / (2 × U) = ±tolerance / U.

Example: ±0.02 mm tolerance and U = 0.004 mm gives TUR = 0.02 / 0.004 = 5:1.

How is the tolerance specified?± toleranceLower and upper limits

Use positive tolerance and uncertainty values. Limits may be negative or zero; the upper limit must exceed the lower limit. Use a decimal point, for example 0.004.

± tolerance

Tolerance (positive ± value)

Lower and upper limits

Lower limitUpper limit

Expanded measurement uncertainty U (k=2) Calculate TUR

TUR:

Enter your values, then calculate.

4:1 is a common rule of thumb. ANSI/NCSL Z540.3 uses TUR ≥ 4:1 as a way to keep false acceptance low when calculating that risk is impractical. It does not establish a specific false-acceptance probability for every measurement. Below 4:1, consider guard-banding or a better reference; U should include the whole calibration process.

A 4:1 TUR is not a requirement of ISO 9001 or IATF 16949. This ratio does not decide whether an individual result passes; your decision rule and measurement procedure still apply.

NASA guidance on measurement decision risk and Z540.3

Questions about TUR

Which uncertainty should I enter?

Enter expanded measurement uncertainty U with coverage factor k=2 for the calibration process, in the same unit as the tolerance. Do not enter standard uncertainty or only the reference instrument specification.

Can tolerance limits be negative?

Yes. Lower and upper limits may be negative or zero. Their difference must be positive, and U must be positive.

Is 4:1 required by ISO 9001 or IATF 16949?

No. It is a common rule of thumb. Below 4:1, consider guard-banding or a better reference and apply the decision rule appropriate to your measurement.

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