Short Answer
Resolution, accuracy, and uncertainty are often used as synonyms in casual technical writing. In metrology, they answer three different questions. Confusing them leads to overreported precision, misleading specifications, and incorrect conformance decisions. This reference page explains the definitions, standards, reporting rules, worked examples, and common pitfalls so you can use each term correctly.
Rule Statement: Three Different Questions
Resolution is the smallest change in a quantity that produces a perceptible change in indication (VIM §4.14). Accuracy is closeness of agreement between a measured quantity value and a true quantity value (VIM §4.1). Measurement uncertainty is a non-negative parameter characterizing the dispersion of quantity values attributed to a measurand (VIM §2.26).
Practical rule: resolution is a property of the instrument or display; accuracy is a qualitative closeness to truth; uncertainty is a quantitative property of the measurement result. When reporting, the expanded uncertainty U determines the last significant digit. A result should be written as x ± U with a stated coverage factor k, often k = 2 for approximately 95% coverage.
Resolution shows how finely you can read; accuracy describes how close you are; uncertainty says how much you should trust the number.
Convention Comparison Table
| Concept | VIM clause | Core definition | Typical quantification | What it depends on |
|---|---|---|---|---|
| Resolution | 4.14 | Smallest change causing perceptible indication change | Last displayed digit; 0.01 mm; 0.1 mg | Sensor, display, scale, electronics |
| Accuracy | 4.1 | Closeness to true value | Error limits; ±0.02 mm | Calibration, bias, systematic effects |
| Measurement uncertainty | 2.26 | Dispersion of values attributed to measurand | u_c, U; 12.34 ±0.04 mm | Random and systematic components, model, calibration |
| Precision | 4.3 | Closeness of agreement among repeated measurements | s, repeatability limit | Random variation, operator, environment |
| Error | 4.4 | Measured value minus reference value | Bias; +0.03 mm | True value, systematic effects |
Table note: Precision is not accuracy. A precise instrument can be consistently biased. Uncertainty combines both random and systematic contributions, though not all systematic effects are always known.
Worked Examples
Example 1: Digital caliper with 0.01 mm resolution
A caliper displays 0.01 mm. Its calibration certificate gives expanded uncertainty U = 0.03 mm (k = 2), so standard uncertainty from calibration is u_cal = 0.015 mm. Ten repeated readings on a gauge block have standard deviation s = 0.01 mm, taken as u_rep = 0.01 mm. Combined standard uncertainty:
u_c = sqrt(0.015² + 0.01²) = sqrt(0.000225 + 0.0001) = sqrt(0.000325) ≈ 0.018 mm.
Expanded uncertainty: U = k u_c = 2 × 0.018 = 0.036 mm, rounded to 0.04 mm. If the mean reading is 12.34 mm, report 12.34 ± 0.04 mm. The resolution is 0.01 mm, but the uncertainty is 0.04 mm. The hundredths digit is already affected by uncertainty.
Example 2: Analytical balance with 0.1 mg resolution
An analytical balance reads to 0.1 mg. Calibration gives U = 0.05 mg (k = 2), so u_cal = 0.025 mg. Repeatability standard deviation is s = 0.08 mg. Then u_c = sqrt(0.025² + 0.08²) ≈ 0.084 mg. Expanded U = 2 × 0.084 ≈ 0.17 mg, rounded to 0.2 mg. For a mass reading of 10.2345 g (10234.5 mg), report 10.2345 g ±0.0002 g. The resolution is 0.0001 g; the uncertainty is 0.0002 g. Reporting additional digits would overstate knowledge.
Example 3: Rounding to match uncertainty
Suppose a result is 2.3456 m with U = 0.037 m. Round U to one significant digit: 0.04 m. Round the value to the same decimal place: 2.35 m. Report 2.35 ±0.04 m (k = 2). If two significant digits are desired for U, use 0.037 m and report 2.346 ±0.037 m. Consistency matters more than dogmatic digit counts.
Counter-Examples
- Resolution equals accuracy fallacy. A balance with 0.001 g resolution but no calibration reads 10.123 g for a 10.000 g standard. The resolution is high; the accuracy is poor; the uncertainty is dominated by bias.
- Using resolution as uncertainty. A caliper with 0.01 mm resolution may have repeatability and calibration uncertainty totaling 0.05 mm. Reporting ±0.01 mm understates the doubt.
- Overstating significant figures. Reporting 12.34567 ±0.05 mm contradicts the uncertainty. Digits beyond the hundredths place are not meaningful.
- Confusing error and uncertainty. Error is a single difference from a reference value. Uncertainty is a range of plausible values. Calibration can reduce systematic error, but uncertainty remains.
- Ignoring k. An expanded uncertainty U = 0.2 mg without a coverage factor is incomplete. State k and the coverage probability when possible.
Standards Citation
These definitions and practices are standardized:
- ISO/IEC Guide 99:2007 (VIM) §4.14 defines resolution; §4.1 defines accuracy; §2.26 defines measurement uncertainty; §4.3 defines precision.
- ISO/IEC Guide 98-3:2008 (GUM) provides the framework for evaluating and expressing uncertainty, including Type A and Type B evaluation and combined standard uncertainty.
- NIST Technical Note 1297 gives practical guidance for uncertainty statements; see §2.2 and Appendix A for Type A/B evaluation.
- ASTM E29-22a addresses significant digits and rounding for test data and conformance; see §6 for rounding rules and comparison to specifications.
- ISO 80000-1:2009 Clause 7 covers quantities, units, and rounding conventions, including rules for significant digits.
When a specification says accuracy ±0.02 mm, it usually means maximum permissible error or an accuracy class, not a full uncertainty budget. The measurement uncertainty must be evaluated for the actual measurement process.
Common Mistakes
- Equating resolution with accuracy or uncertainty.
- Reporting every displayed digit even when uncertainty is larger.
- Rounding intermediate uncertainty components before combining them.
- Using expanded uncertainty without stating k or coverage.
- Ignoring calibration status, drift, or environmental effects.
- Treating precision as proof of accuracy.
- Mixing standard deviation, standard uncertainty, and expanded uncertainty.
- Assuming more resolution automatically improves measurement quality.
Quick Reference Table
| Concept | Question it answers | Example | Reporting notation |
|---|---|---|---|
| Resolution | How finely can the instrument indicate change? | 0.01 mm caliper | Not usually reported as uncertainty |
| Accuracy | How close is the result to the true value? | ±0.02 mm specification | Error limits or qualitative statement |
| Uncertainty | How much doubt is associated with the result? | U = 0.04 mm, k = 2 | 12.34 ±0.04 mm |
| Precision | How close are repeated measurements to each other? | s = 0.01 mm | Standard deviation or repeatability limit |
| Error | How far is the result from a reference value? | +0.03 mm bias | Correction or error statement |
Related Rules
For further precision and rounding reference, see Accuracy vs Precision, Significant Figures, Measurement Uncertainty, Error Propagation, Rounding Rules, ASTM E29, GUM Guide, and Why Sig Figs Are an Approximation. These articles explain the conventions behind the significant figures calculator and help you avoid double rounding, over-precision, and reporting errors.
Sources & Further Reading
- ISO/IEC Guide 99:2007, International Vocabulary of Metrology — Basic and General Concepts and Associated Terms (VIM), clauses 2.26, 4.1, 4.3, 4.14.
- ISO/IEC Guide 98-3:2008, Guide to the Expression of Uncertainty in Measurement (GUM).
- NIST Technical Note 1297, Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results.
- ASTM E29-22a, Standard Practice for Using Significant Digits in Test Data to Determine Conformance with Specifications.
- ISO 80000-1:2009, Quantities and units — Part 1: General, Clause 7.
FAQ
Is resolution the same as accuracy?
No. Resolution is the smallest detectable change. Accuracy is closeness to a true value. A high-resolution device can still be inaccurate if it is biased or uncalibrated.
Does higher resolution always mean better measurement?
No. Higher resolution can help detect smaller changes, but accuracy and uncertainty depend on calibration, repeatability, environmental control, and the measurement model. A lower-resolution calibrated instrument may produce a more accurate result.
How do I decide how many significant figures to report?
Use the uncertainty. Round U to one or two significant digits, then round the measured value to the same decimal place. For example, 12.345 ±0.04 mm becomes 12.35 ±0.04 mm. State k for expanded uncertainty.
What is the difference between uncertainty and error?
Error is the difference between a measured value and a reference value. Uncertainty is a quantified dispersion of values that could reasonably be attributed to the measurand. Error is a realized difference; uncertainty describes doubt about the result.
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