Statistics and Data
Measurement Uncertainty Calculator
Measurement Uncertainty Calculator propagate independent standard uncertainties through addition, subtraction, multiplication, or division of two measured quantities.
Statistics and Data
Measurement Uncertainty Calculator
Propagate independent standard uncertainties through addition, subtraction, multiplication, or division of two measured quantities.
Formula
For sums or differences, u = sqrt(uA^2 + uB^2); for products or quotients, relative u = sqrt((uA/A)^2 + (uB/B)^2).
About the Measurement Uncertainty Calculator
Propagate independent standard uncertainties through addition, subtraction, multiplication, or division of two measured quantities.
How the Measurement Uncertainty Calculator Works
The selected operation determines whether absolute or relative root-sum-square propagation is used, and an entered coverage factor expands the combined standard uncertainty.
Formula
For sums or differences, u = sqrt(uA^2 + uB^2); for products or quotients, relative u = sqrt((uA/A)^2 + (uB/B)^2).
The calculation runs in your browser. Values are validated for required ranges, compatible units, and method-specific restrictions before results are displayed.
Required Inputs
- Measurement operation (required).
- Measured value A (required).
- Standard uncertainty of A (required).
- Measured value B (required).
- Standard uncertainty of B (required).
- Coverage factor k (required).
Results Reported
The result panel reports the final answer and the intermediate quantities needed to check the calculation:
- Calculated result
- Combined standard uncertainty
- Expanded uncertainty
- Relative standard uncertainty (%)
- Result with expanded uncertainty
Measurement Uncertainty Calculator Example
Select Example Data in the calculator to load this reproducible input set:
| Input | Example value |
|---|---|
| Measurement operation | addition |
| Measured value A | 12 |
| Standard uncertainty of A | 0.2 |
| Measured value B | 4 |
| Standard uncertainty of B | 0.1 |
| Coverage factor k | 2 |
How to Use the Calculator
- Confirm that the calculator title and formula match the quantity you need.
- Enter every required value using the unit shown with its field.
- Select Example Data to inspect a valid input set, or enter your own values and select Calculate.
- Review all reported values and the displayed formula before using the answer.
- Use Copy Result or Download CSV when you need a reusable record.
Accuracy and Limitations
Inputs must be independent standard uncertainties. Correlation, systematic bias, asymmetric distributions, nonlinear models, effective degrees of freedom, and Monte Carlo propagation are excluded.
Keep units consistent, use measurements that represent the actual situation, retain full precision during the calculation, and round only the final answer. Professional decisions may require current official rules, field measurements, laboratory methods, or specialist review.
Frequently Asked Questions
What does the Measurement Uncertainty Calculator calculate?
Propagate independent standard uncertainties through addition, subtraction, multiplication, or division of two measured quantities.
Which formula does the Measurement Uncertainty Calculator use?
For sums or differences, u = sqrt(uA^2 + uB^2); for products or quotients, relative u = sqrt((uA/A)^2 + (uB/B)^2). The selected operation determines whether absolute or relative root-sum-square propagation is used, and an entered coverage factor expands the combined standard uncertainty.
What should I check before using the Measurement Uncertainty Calculator result?
Inputs must be independent standard uncertainties. Correlation, systematic bias, asymmetric distributions, nonlinear models, effective degrees of freedom, and Monte Carlo propagation are excluded.