Measurement quality
What is measurement uncertainty?
Measurement uncertainty describes the estimated range around a reported value. It communicates that an experimental measurement is not perfectly exact.
Reporting format
Plus-or-minus notation
Measurement notationmeasured value ± absolute uncertainty
The measured value and absolute uncertainty should normally use the same unit.
Relative uncertainty
Compare uncertainty to the measurement
Relative uncertaintyabsolute uncertainty ÷ |measured value|
Relative uncertainty expresses the uncertainty as a fraction of the measurement size.
Percentage form
Percentage uncertainty formula
Percentage uncertaintyrelative uncertainty × 100%
Worked example
Calculate uncertainty for 50 ± 2
- Measured value = 50.
- Absolute uncertainty = 2.
- Relative uncertainty = 2 ÷ 50 = 0.04.
- Percentage uncertainty = 4%.
- Measurement range = 48 to 52.
Interpretation
What does a lower uncertainty mean?
A lower relative or percentage uncertainty indicates that the uncertainty is small compared with the measured value. This often suggests greater measurement precision.
Uncertainty should still be interpreted in relation to the instrument, experimental method, sample size, and research question.
Scientific reporting
Report uncertainty clearly
- Include the correct measurement unit.
- Use consistent decimal places.
- State how the uncertainty was estimated.
- Add error bars when uncertainty is shown on a graph.
- Discuss important sources of uncertainty in the lab report discussion.
Model assumptions
Calculator assumptions and limitations
- The calculation assumes measured values and uncertainty use the same unit.
- Reported uncertainty should come from appropriate experimental methods.
- The calculator does not identify systematic measurement errors.
- Instrument calibration and sampling quality are not evaluated.
- Results depend entirely on the accuracy of the entered values.
Continue your analysis
Report and interpret measurement uncertainty
Round measured results appropriately with the significant figures guide, and explain uncertainty with the lab report discussion guide.
Present repeated measurements using the scientific tables and graphs guide, or compare a measured result with an accepted value using the percent error calculator.
Questions and answers
Measurement uncertainty FAQ
What is absolute uncertainty?
Absolute uncertainty is the plus-or-minus amount attached to a measured value and is normally written in the same unit as the measurement.
How is relative uncertainty calculated?
Relative uncertainty equals absolute uncertainty divided by the absolute measured value.
How is percentage uncertainty calculated?
Percentage uncertainty equals relative uncertainty multiplied by 100 percent.
Why can the measured value not be zero?
Relative and percentage uncertainty require division by the measured value, so they are undefined when the measured value is zero.