Error Propagation Calculator
Calculate the uncertainty of a result based on the uncertainties of the input variables using standard error propagation formulas.
Published by:
isCalculator Editorial Team
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How to use this tool?
How to Use the Error Propagation Calculator
This calculator computes the result of an operation on up to three measured values (A, B, C) and their uncertainties (σA, σB, σC), then propagates the errors to give the final uncertainty.
- Enter values and uncertainties – Fill in the numeric fields for each variable. Uncertainties must be non-negative numbers. Units (e.g., m, kg) are optional but recommended for clarity.
- Select an operation – Choose from:
- A + B + C (addition)
- A - B - C (subtraction)
- A × B × C (multiplication)
- A ÷ B ÷ C (division)
- A^B (power, where A is base and B is exponent)
- Click "Calculate" – The result will appear as
value ± uncertaintywith the unit (if provided). A formula explanation is shown below the result. - Check for errors – If inputs are invalid (e.g., division by zero, negative base with non-integer exponent), an error message will appear. Correct the inputs and recalculate.
Note: All values are treated as real numbers. Use consistent units (metric, imperial, etc.) for meaningful results. The calculator uses standard error propagation formulas: for addition/subtraction, uncertainties add in quadrature; for multiplication/division/power, relative uncertainties combine.
Previous Results
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Frequently Asked Questions
Error propagation is the process of determining the uncertainty of a result based on the uncertainties of the input variables used in a calculation.
The calculator supports addition, subtraction, multiplication, division, and power (A^B) operations.
For addition/subtraction, the uncertainty is the square root of the sum of squares of individual uncertainties. For multiplication/division, relative uncertainties are combined. For power, a more complex formula involving natural log is used.
