Instrument accuracy calculator: % of reading, % of full scale and counts
Turn a datasheet accuracy such as ±(0.1 % of reading + 0.05 % of full scale + 2 counts) into the absolute error at your reading, and see how it grows as the reading falls.
The specification
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At one reading
±0.095 °C
0.025 from reading + 0.05 from full scale + 0.02 from counts
That is 0.38 % of the reading, and 0.095 % of full scale.
Read as a rectangular distribution, the standard uncertainty is 0.05485 °C.
Across the range
| Reading | Error (±) | % of reading |
|---|---|---|
| 10 °C | 0.08 °C | 0.8 % |
| 25 °C | 0.095 °C | 0.38 % |
| 50 °C | 0.12 °C | 0.24 % |
| 75 °C | 0.145 °C | 0.193 % |
| 100 °C | 0.17 °C | 0.17 % |
The percent-of-full-scale and counts terms do not shrink with the reading, so the relative error is largest at the bottom of the range. If you will mostly use the instrument at 10 % of its range, that row, not the last one, is the accuracy you have.
How the calculation works
- 01The error at a reading x is the sum of the terms the specification contains: (a/100)·|x| for a percent-of-reading term, (b/100)·FS for a percent-of-full-scale term, and c × (value of one count) for a counts term.
- 02The percent-of-full-scale and counts terms do not depend on the reading, so the relative error rises as the reading falls. The table steps through 10, 25, 50, 75 and 100 % of full scale to show it.
- 03A limit of ±e read as a rectangular distribution gives a standard uncertainty u = e/√3, the usual Type B treatment of a datasheet accuracy statement in an uncertainty budget.
Limitations
- It evaluates the specification as stated. It cannot tell whether the manufacturer's conditions (temperature range, warm-up, calibration interval) apply to your use.
- A datasheet accuracy describes the instrument, not a calibration. After calibration the uncertainty on the certificate, not this figure, is the one to use.
- The rectangular treatment is a convention. If a specification is quoted at a stated confidence level, use that instead.
Frequently asked questions
- What does ±0.1 % of reading + 2 counts mean?
- The error limit is 0.1 % of whatever the instrument is reading plus 2 steps of its last displayed digit. On a 25.00 reading with 0.01 resolution that is 0.025 + 0.02 = 0.045.
- What is the difference between % of reading and % of full scale?
- Percent of reading scales with the value being measured, so the error shrinks towards zero with the reading. Percent of full scale is a fixed amount across the whole range, so at 10 % of range it is ten times larger relative to the reading than at full scale.
- How do I use a datasheet accuracy in an uncertainty budget?
- Convert the limit to a standard uncertainty by dividing by √3 (rectangular distribution), then combine it with the other components. The calculator shows that figure for the reading you enter.
- Why is my accuracy worse at low readings?
- Because the fixed terms, full scale and counts, do not get smaller as the reading does. An instrument specified at ±0.5 % of full scale is ±5 % of a reading that is one-tenth of full scale.
Need the reasoning, not just the number?
Ask ValiTrac AI and see the standards evidence and the engine calculation behind the answer.
Ask ValiTrac AIRead the theory
Accuracy vs precision in measurement
Precision is about scatter; accuracy is about closeness to the true value. An instrument can be precise and wrong, or accurate on average and noisy.
Resolution as an uncertainty component
A digital display of resolution d contributes a rectangular term of half-width d/2, so u = d/(2√3) ≈ 0.29 d. For a 0.1 °C logger that is 0.029 °C.
Tolerance versus uncertainty
Tolerance is what you require of the instrument; uncertainty is how well the calibration could measure it. A conformity statement needs both.
What is a decision rule and why every certificate needs one
A decision rule states how measurement uncertainty is accounted for in declaring pass or fail: simple acceptance, guard banding or a non-binary statement.
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