What Is Absolute Uncertainty?
Absolute uncertainty (absolute error) is the magnitude of the difference between the measured value and the true value, or half the range of a set of repeated measurements. It is expressed in the same units as the measurement and indicates the possible range within which the true value lies.
For a single measurement, absolute uncertainty is often estimated from the precision of the measuring instrument (typically half the smallest division). For multiple measurements, it can be calculated from the range or standard deviation of the readings.
Formulas
Types of Uncertainty
| Type | Definition | Example |
|---|---|---|
| Absolute | Difference in same units | ± 0.5 cm |
| Relative | Fraction of the value | ± 0.02 |
| Percentage | Relative × 100 | ± 2.0% |
Uncertainty Propagation Rules
- Addition/Subtraction: Add absolute uncertainties: Δ(A±B) = ΔA + ΔB
- Multiplication/Division: Add relative uncertainties: Δ(AB)/AB = ΔA/A + ΔB/B
- Powers: Multiply relative uncertainty by the exponent: Δ(A^n)/A^n = n×ΔA/A
- Constants: Multiplying by a constant multiplies absolute uncertainty by that constant.
Frequently Asked Questions
What is the difference between error and uncertainty?
Error is the difference between measured and true values (which we often don't know exactly). Uncertainty is the estimated range within which the true value is expected to lie. In modern metrology, "uncertainty" is preferred because it acknowledges our incomplete knowledge.
How do I report measurements with uncertainty?
Use the format: value ± uncertainty (units). For example, 25.3 ± 0.2 cm. The uncertainty should have 1-2 significant figures, and the measurement should be rounded to match the uncertainty's decimal place.
Why is uncertainty important in science?
Uncertainty quantifies the reliability of measurements. Without it, we cannot compare results, determine if two measurements agree, or assess whether a result is consistent with a theoretical prediction. All scientific measurements must include uncertainty to be meaningful.