Laboratory Formula
Relative Uncertainty Formula
Shows measurement uncertainty relative to the measured magnitude.
Formula Summary
Relative Uncertainty
Shows measurement uncertainty relative to the measured magnitude.
- Category
- Laboratory
- Equation
- relative uncertainty = absolute uncertainty ÷ |measured value|
- Calculator
- Use Relative Uncertainty Calculator →
Equation
relative uncertainty = absolute uncertainty ÷ |measured value|
Variables
- absolute uncertainty = uncertainty in original units
- measured value = reported result
How to Use This Formula
- Identify the known values from the problem statement.
- Convert all values into compatible units.
- Substitute the values into the equation and calculate the result.
- Check that the final answer has the correct unit and meaning.
Explanation
Relative uncertainty expresses the size of measurement uncertainty compared with the measured value. It helps evaluate the precision of measurements regardless of the original units.
Worked Example
If a measurement is 50 cm with an uncertainty of 2 cm, the relative uncertainty is 2 ÷ 50 = 0.04.
Common Mistakes
- Using the wrong measured value as the denominator.
- Confusing absolute uncertainty with relative uncertainty.
- Forgetting to keep units consistent.
Applications
- Evaluating measurement precision.
- Reporting scientific experimental results.
- Comparing uncertainty between different measurements.
Related Formulas
Sample Standard Deviation
s = √(Σ(xᵢ − x̄)² ÷ (n − 1))
Measures the spread of sample observations around their mean.
Learn formula →Coefficient of Variation
CV = s ÷ x̄ × 100
Expresses variability relative to the mean as a percentage.
Learn formula →Percent Error
% error = |experimental − accepted| ÷ |accepted| × 100
Compares an experimental result with an accepted reference value.
Learn formula →Percent Difference
% difference = |A − B| ÷ ((|A| + |B|) ÷ 2) × 100
Compares two experimental values when neither is an accepted value.
Learn formula →