FigureCheck
Absolute, relative and percentage uncertainty
Calculate absolute, relative, and percentage uncertainty with formulas, units, and a worked scientific example.
Absolute uncertainty has the same unit as the measurement. Relative uncertainty is absolute uncertainty divided by the magnitude of the measured value, and percentage uncertainty is that ratio multiplied by 100%.
The three forms
Write a result as value plus or minus absolute uncertainty. Divide the absolute uncertainty by the absolute value of the measurement to obtain relative uncertainty. Multiply by 100 to express the same ratio as a percentage. Relative and percentage uncertainty have no physical unit.
When each form is useful
Absolute uncertainty belongs beside a reported measurement and on an error bar. Percentage uncertainty makes measurements with different scales or units easier to compare. A percentage is undefined when the measured value is zero, so report the absolute uncertainty and explain the situation instead.
Worked example: timing an oscillation
For T = 2.40 plus or minus 0.06 s, the relative uncertainty is 0.06 / 2.40 = 0.025. The percentage uncertainty is 2.5%. A clear report is T = (2.40 plus or minus 0.06) s, or 2.5% uncertainty.
Common mistakes to avoid
- Giving absolute uncertainty without its unit
- Dividing by the uncertainty instead of the measured value
- Reporting many unsupported decimal places
Open an editable example and apply the idea to a real graph.
Sources and further reading
These links support the scientific principles summarized above. Always follow the reporting rules required by your course, laboratory, journal, or field.