TAR and TUR calculator

Test accuracy ratio and test uncertainty ratio, calculated separately because they are different quantities. Companion to the three-wire and pre-plate pitch diameter calculators.

Calculation aid. Not a compliance determination. This page performs arithmetic on values you supply. It does not determine whether any decision rule, uncertainty budget, or acceptance decision satisfies ANSI/NCSL Z540.3, ISO/IEC 17025, or any other standard, and it does not constitute a statement of conformity. Selecting a guardband method here is not the same as having a documented decision rule. Walden Gage Distribution & Calibration Services is not an accredited calibration laboratory; calibration is managed through ISO/IEC 17025 accredited partner laboratories. Uncertainty budgets, decision rules, and acceptance decisions remain the responsibility of the user and their accredited laboratory. No warranty of any kind is made as to accuracy, completeness, or fitness for a particular purpose, and no liability is accepted for any loss or damage arising from use of this page. Version 1.0 · All values computed from user input · Last reviewed August 2026

Measurement and tolerance

Identification, optional

Item or characteristic

Work order or record reference

Date

Printed with the results so the sheet can be attached to a calibration record. Not stored anywhere.

Unit under test tolerance

Units

Label only. Every value on this page must be entered in this same unit.

Nominal value, optional

Upper tolerance limit

Signed deviation from nominal.

Lower tolerance limit

Signed. Enter 0 for a minus-zero unilateral gage tolerance.

Display decimals

Tolerances are entered as separate upper and lower limits rather than a symmetric plus-or-minus, because thread and plug gage tolerances are frequently unilateral. Both ratios below are computed on the tolerance span, so unilateral and asymmetric tolerances need no special handling.

TAR — test accuracy ratio

Reference standard accuracy specification

Upper accuracy limit

Lower accuracy limit

The published accuracy specification of the reference standard alone, as signed limits. For a symmetric spec, enter the plus figure and its negative.

What TAR leaves out TAR accounts for exactly one contributor: the published accuracy specification of the reference standard. It ignores repeatability, resolution, thermal effects, operator reproducibility, fixturing, and every other contributor to the uncertainty of the measurement. Two labs using the same standard on the same part can produce very different measurement uncertainties and identical TAR figures. TAR is calculated here because it is still widely used and still requested, not because it is interchangeable with TUR.

TUR — test uncertainty ratio

Per the definition in ANSI/NCSL Z540.3: the span of the tolerance divided by twice the 95% expanded uncertainty of the measurement process.

Uncertainty budget

Contributor	Value	Distribution	Divisor	u_i

Enter each value as a half-width (semi-range) for rectangular and triangular distributions, and as the stated uncertainty for normal. The divisor is applied automatically. Root-sum-square combination assumes the contributors are independent; correlated contributors are not handled here.

Guardbanding

Options

Apply guardband to

Both limits Upper limit only Lower limit only

Show guardbands even when TUR is 4:1 or better

Formulas and standards framing

Formulas

Tolerance span	`span = UL − LL`
Half-span	`T = span / 2`
TAR	`span_UUT / span_standard`
Standard uncertainty of a contributor	`u_i = value_i / divisor_i`
Divisors	`normal k=2 → 2 normal k=1 → 1 rectangular → √3 triangular → √6`
Combined standard uncertainty	`u_c = √( Σ u_i² )`
Expanded uncertainty	`U = k · u_c`, k = 2, approximately 95%
TUR	`span_UUT / (2 U)`
Percentage contribution	`u_i² / u_c²` variances sum, so variance shares total 100%
Guardband, root-difference-of-squares	`√( U² − (T/4)² )`
Guardband, subtract expanded uncertainty	`U`

The root-difference-of-squares guardband is defined only where U > T/4, which is the same thing as TUR below 4:1. At or above 4:1 the radicand is zero or negative and the method yields no guardband. That is a property of the method, not a fault in the calculation.

Standards framing

ANSI/NCSL Z540.3. The requirement at clause 5.3(b) is stated in terms of risk: the probability of false accept arising from calibration tests must not exceed 2%, and must be documented. A test uncertainty ratio of at least 4:1 is specified for the case where estimating that probability is not practical. The 4:1 ratio is the fallback provision, not the primary requirement. It is common to see this stated the other way round.

ISO/IEC 17025:2017. No fixed ratio is mandated anywhere in the standard. Where a statement of conformity is given, a decision rule must be documented and agreed with the customer, and measurement uncertainty must be taken into account. A 4:1 TUR is one possible basis for a decision rule, not a requirement of 17025.

This tool does not tell you what your decision rule should be. It computes ratios and guardbands from values you supply. Whether a given ratio, method, or guardband is appropriate is a determination for you and your accredited laboratory, documented in your quality system.

Deliberately not computed

False accept risk. Estimating the probability of false accept requires an assumed a priori distribution for the population of units under test and an end-of-period reliability estimate. Both materially change the answer and neither can be known by this page. A PFA figure resting on assumptions invented by a web tool would look more authoritative than it is, in precisely the setting where that does the most harm. If your decision rule relies on the 2% risk provision, that calculation belongs with your accredited laboratory.

Also not computed: degrees of freedom and effective degrees of freedom, coverage factors other than k = 2, correlation between contributors, and any determination of whether a decision rule satisfies a standard.