Compute absolute and relative uncertainty from single measurements with known error or from repeated measurements using the range method.
Last updated: March 2026
| Instrument | Typical Uncertainty | Notes |
|---|---|---|
| Digital Scale (0.1g precision) | ±0.05g | Half of smallest division |
| Ruler (1mm marks) | ±0.5mm | Half of smallest division |
| Graduated Cylinder (10mL) | ±0.5mL | Read from meniscus |
| Thermometer (1°C marks) | ±0.5°C | Interpolate between marks |
| Caliper (0.05mm precision) | ±0.025mm | Check zero before use |
| Burette (0.1mL marks) | ±0.05mL | Parallax error is main source |
Absolute uncertainty (also called absolute error) represents the margin of error in a measurement, expressed in the same units as the measurement itself. It quantifies how much the measured value might differ from the true value due to limitations in measuring instruments, methodology, or natural variation.
When you report a measurement with absolute uncertainty, you write it as: Value ± Uncertainty. For example, if you measure a length as 10.2 cm with an uncertainty of 0.3 cm, you would report it as 10.2 ± 0.3 cm. This means the true value likely lies between 9.9 cm and 10.5 cm.
Relative uncertainty expresses the uncertainty as a percentage of the measured value:Relative Uncertainty (%) = (Absolute Uncertainty / Mean Value) × 100. This is useful for comparing the precision of different measurements or determining which measurement contributes most to uncertainty in derived quantities.
When you have a single measurement and know the instrument's uncertainty (from specifications or calibration):
When you take multiple measurements of the same quantity:
Note: For more precise uncertainty estimates with many measurements, use standard deviation instead of the range method.
Calculate uncertainty from repeated mass measurements:
Absolute uncertainty is expressed in the same units as the measurement (e.g., ±0.3 cm), while relative uncertainty is expressed as a percentage (e.g., 2.94%). Relative uncertainty is useful for comparing precision across different scales.
The uncertainty should typically be reported to 1 or 2 significant figures, and the measured value should be rounded to match the decimal place of the uncertainty. For example: 10.24 ± 0.15, not 10.2400 ± 0.1500.
The range method is a quick estimate suitable for small datasets (3-10 measurements). For larger datasets or when higher precision is needed, use standard deviation or standard error of the mean.
No, uncertainty is always a positive value. The ± symbol indicates the measurement could be higher or lower by that amount, but the uncertainty value itself is positive.
When adding/subtracting measurements, add absolute uncertainties. When multiplying/dividing, add relative uncertainties. For complex formulas, use propagation of uncertainty formulas.
Large variation in repeated measurements suggests systematic errors, poor technique, or an unstable system. Investigate the source of variation before reporting results.
Yes, the range method typically gives larger uncertainty than statistical methods (standard deviation), making it a conservative choice that's less likely to underestimate true uncertainty.
Uncertainty intervals are similar to confidence intervals. The ± range represents where we expect the true value to lie. For statistical rigor, use standard error and specify confidence levels (e.g., 95% CI).