Uncertainty Calculator
Calculate absolute, relative, and percentage uncertainty for measurements
Calculation Results:
Standard Notation:
Relative Uncertainty:
Percentage Uncertainty: %
How to Calculate Uncertainty
In physics and chemistry, uncertainty refers to the range of possible values within which the true value of a measurement lies. Since no measurement is perfectly precise, we use uncertainty to express the degree of confidence in our data.
1. Absolute Uncertainty
This is the actual range of error in your measurement. For example, if you use a ruler with millimeter markings, the absolute uncertainty is often considered ±0.5 mm or ±1 mm, depending on the experimental protocol.
2. Relative Uncertainty
Relative uncertainty shows how large the error is in comparison to the total measurement. It is a ratio with no units. The formula is:
3. Percentage Uncertainty
This is simply the relative uncertainty expressed as a percentage. It helps in understanding the significance of the error relative to the size of the measurement.
Practical Example
Imagine you measure the length of a table to be 150 cm using a tape measure that has an accuracy of ±0.2 cm.
- Measured Value: 150 cm
- Absolute Uncertainty: 0.2 cm
- Relative Uncertainty: 0.2 / 150 = 0.00133
- Percentage Uncertainty: 0.00133 × 100 = 0.133%
The final result would be reported as 150.0 ± 0.2 cm.