TUR & TAR calculator
Enter a tolerance, your expanded measurement uncertainty, and the reference standard accuracy to get your test uncertainty ratio (TUR) and test accuracy ratio (TAR), both as X:1, checked against the 4:1 rule of thumb. It also shows why TUR, built on your full measurement uncertainty, is the more complete number modern ISO/IEC 17025 practice leans on. Everything runs in your browser.
Your numbers
The specification limit you judge against, as a half-width (±).
Your full measurement uncertainty at 95% (k = 2), as a ± value in the same units. Not just the standard.
The reference standard accuracy or maximum permissible error, as a ± value in the same units. Optional; leave blank to compute TUR only.
Result
TUR = tolerance half-width ÷ expanded uncertainty U (k = 2), the ANSI/NCSL Z540.3 form. TAR = tolerance half-width ÷ reference standard accuracy. Both are ratios, not probabilities of false accept.
TUR and TAR, in plain terms
What TUR is
The test uncertainty ratio is the tolerance divided by the expanded measurement uncertainty at k = 2. The ANSI/NCSL Z540.3 Handbook writes it as the span of the tolerance over twice the 95% expanded uncertainty of the measurement, which is the same as the tolerance half-width divided by U. A TUR of 4:1 means the tolerance is four times your measurement uncertainty. The key word is measurement: U rolls up every contributor to the calibration, the reference standard, repeatability, instrument resolution, the environment, and the item under test, into one number. That is why TUR is the ratio used in modern decision-risk work.
What TAR is
The test accuracy ratio is the older ratio: the tolerance divided by the accuracy of the reference standard alone. It answers a narrower question, how much better is the standard than the thing it is checking. TAR is easy to read off a datasheet, since you only need the standard accuracy, and it was the common ratio for decades. Its weakness is exactly what it leaves out: everything about the measurement other than the standard. A gage block set can be very accurate, but if your comparator, operator, and temperature add uncertainty, TAR will not see it.
Why TUR is preferred
Because TAR ignores most of the measurement, it almost always looks better than the measurement really is. You can have a comfortable 5:1 TAR and a marginal 3:1 TUR at the same time, on the same setup, once you fold in repeatability and conditions. The decision you actually make, pass or fail against the spec, depends on the full uncertainty, so the full uncertainty is what should drive the ratio. ANSI/NCSL Z540.3 and ILAC-G8 both frame conformity decisions around measurement uncertainty, and the Z540.3 default treats a TUR of 4:1 or better as one accepted way to keep consumer risk low. When TUR and TAR disagree, trust the TUR.
The 4:1 rule of thumb and its heritage
The 4:1 target is old. It traces to military and quality practice, including MIL-STD-45662A, where the collective uncertainty of the standards was to be no more than 25% of the tolerance, which is a 4:1 ratio. It carried into ANSI/NCSL Z540.3 as a convenient bar for keeping the probability of a false accept low without a full risk analysis. It is a rule of thumb, not a law. ISO/IEC 17025 does not require any particular ratio; it requires that you have a documented decision rule and apply it. When the TUR falls below 4:1, the usual moves are to reduce uncertainty, widen the tolerance if the application allows, or apply a guard band that tightens the acceptance limit so the false-accept risk stays controlled. And remember that neither ratio is itself a probability. For the specific consumer risk on a given reading, a JCGM 106 conformance-probability analysis is the rigorous tool.
Common questions
What is the difference between TUR and TAR?
Both compare your tolerance to the quality of the measurement, as a ratio like 4:1. The test uncertainty ratio (TUR) divides the tolerance by the full expanded measurement uncertainty at k = 2, which includes the reference standard plus repeatability, resolution, the environment, and the item under test. The test accuracy ratio (TAR) divides the tolerance by only the reference standard accuracy. TUR is the stricter and more complete number, because a real measurement carries more uncertainty than the standard alone.
What is the TUR formula?
TUR = tolerance, as a plus or minus half-width, divided by the expanded measurement uncertainty at k = 2. With a spec of plus or minus 1.0 and U = 0.2, TUR = 1.0 / 0.2 = 5:1. Some sources write the same ratio as the full tolerance span divided by 2U, which gives the same number. This calculator uses the half-width convention, and its full-span toggle does the halving for you.
What TUR or TAR do I need?
The long-standing rule of thumb is 4:1: the tolerance should be at least four times the measurement uncertainty (TUR) or four times the standard accuracy (TAR). It comes from older military and quality practice and is carried forward in ANSI/NCSL Z540.3, where a TUR of 4:1 or better is one accepted way to meet the standard consumer-risk limit. ISO/IEC 17025 does not fix a ratio. Below 4:1, laboratories commonly apply a guard band so the false-accept risk stays controlled.
Why is TUR preferred over TAR?
TAR only looks at the reference standard accuracy, so it can make a measurement look better than it really is. A calibration also carries uncertainty from repeatability, instrument resolution, temperature and other conditions, and the item being measured. TUR rolls all of that into one expanded uncertainty, so it reflects the real risk of the decision. That is why modern guidance, including ANSI/NCSL Z540.3 and ILAC-G8, works in terms of measurement uncertainty rather than the standard accuracy alone.
Do I enter the tolerance as a half-width or the full span?
Either. Use the toggle. In symmetric mode you enter the tolerance as a plus or minus half-width, for example 1.0 for a spec of plus or minus 1.0. In full-span mode you enter the whole width from the lower to the upper specification limit, and the tool halves it to a half-width for the ratio. Enter the expanded uncertainty and the standard accuracy as plus or minus values in the same units, so every quantity is on the same basis.
What should I do if my TUR is below 4:1?
A TUR below 4:1 does not automatically fail the measurement, but it means uncertainty is eating into the tolerance, so a pass or fail right at the limit is less certain. The common responses are to reduce the measurement uncertainty with a better standard, more averaging, or tighter conditions, to widen the tolerance if the application allows, or to apply a guard band that tightens the acceptance limit so the false-accept risk stays controlled. The guard band and decision rule calculator works this through.
Does ISO/IEC 17025 require a specific TUR or TAR?
No. ISO/IEC 17025:2017 does not set a numeric ratio. What it requires, when you report a statement of conformity, is a documented decision rule (clause 7.1.3) that is applied consistently (clause 7.8.6). TUR and the 4:1 rule of thumb are common inputs to that decision rule, not a mandate on their own. The ratio helps you reason about risk; the decision rule and the conformity statement are owned by your laboratory.
Is TUR or TAR a probability of false accept?
No. Both are simple ratios, not risk probabilities. A TUR of 4:1 is associated with a low consumer risk under common assumptions, which is why it became a rule of thumb, but the actual probability of a false accept depends on where the measured value sits and how your process is distributed. For that specific decision risk, use a JCGM 106 conformance-probability analysis rather than reading a number off the ratio.
This calculator computes transparent ratios, TUR and TAR, from the numbers you enter. A ratio is not a probability of false accept, does not set your laboratory risk policy, and does not replace ISO/IEC 17025, ANSI/NCSL Z540.3, or ILAC-G8. Review any decision against your own quality system before you use it.
Keep the uncertainty with the record
Axiospec keeps every calibration, uncertainty, and certificate in one tamper-evident ledger built for ISO/IEC 17025, with a test uncertainty ratio on each instrument. See it on real calibration data, no signup.