TATITIC CALCULATOR
Error Propagation
A precise tool.
What is the Error Propagation & How does it work?
Error propagation quantifies how uncertainties in measured variables affect the uncertainty of a derived result.
When variables are independent, the combined variance is obtained by summing the squares of each partialβderivative term multiplied by its respective uncertainty.
For common operations such as multiplication, the relative uncertainties add in quadrature, allowing quick estimation of the final error.
Delta z = sqrt{left(frac{partial f}{partial x}Delta xright)^2 + left(frac{partial f}{partial y}Delta yright)^2}
Ξz = propagated uncertainty
Parameters
Result
β
Frequently Asked Questions
What is error propagation?
Error propagation quantifies how uncertainties in measured variables affect the uncertainty of a derived result.
How do I calculate combined variance for independent variables?
Sum the squares of each partial-derivative term multiplied by its respective uncertainty to obtain the combined variance.
What happens to relative uncertainties in multiplication?
Relative uncertainties add in quadrature when multiplying variables, allowing quick estimation of the final error.
Can you explain how to use this calculator?
Input the partial derivatives and uncertainties of your measured variables to calculate the propagated uncertainty of your derived result.
What is the formula for error propagation in addition?
For addition, the absolute uncertainties add directly: Ξz = Ξx + Ξy.
How does this calculator handle dependent variables?
This calculator assumes independent variables. For dependent variables, a different approach is needed, typically involving covariance terms.
What are the units of the propagated uncertainty?
The units of the propagated uncertainty are the same as the units of the derived result.
Results are for informational purposes only and do not constitute professional advice.