# Error propagation estimation

• I
• bznm
In summary, you can calculate the uncertainty on A by first determining the correlation between the uncertainties on M and N and the uncertainty on B. If this correlation is small, you can treat them as independent. The values of M and N are dependent on B, and their uncertainties can be estimated using relations such as ##log M=(0.755 \pm 0.059)*log B+(0.416\pm 0.024)##. The uncertainty on B, given by a software, is 0.0002. From there, you can use the 15% error assumption to estimate the uncertainty on A.

#### bznm

I have a physical quantity A defined as ##A=(74.5 B^2*(M+N))^{1/3}##

where B, M, N and relative uncertainties are given. And M and N are dependent on B.
Could you show me how to calculate and estimation for the uncertainty on A?

Thanks a lot

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You will need to know the correlation between the uncertainties on M and N and the uncertainties on B. If you think this is small, you can treat them as independent.

M and N are function of B (ie for example ##log M=(0.755 \pm 0.059)*log B+(0.416\pm 0.024)## The value of B is given by a software, and its uncertainty is 0.0002.
The values of M and N are extimated using relations like the one that I have just written, and it is assumed that the error is 15%.
How can I estimate the uncertainty on A?

## 1. What is error propagation estimation?

Error propagation estimation is a method used in scientific research to estimate the uncertainty or error associated with a calculated quantity that is based on a set of measured values. It takes into account the errors or uncertainties associated with each of the measured values and calculates the overall error of the final result.

## 2. Why is error propagation estimation important?

Error propagation estimation is important because it allows scientists to understand the accuracy and reliability of their experimental results. By taking into account the uncertainties associated with each measurement, it provides a more realistic representation of the true value of the quantity being measured.

## 3. How is error propagation estimation calculated?

Error propagation estimation is calculated using a mathematical formula that takes into account the uncertainties of each measured value and their respective relationships to the final calculated quantity. This formula is based on the principles of uncertainty propagation in mathematical operations.

## 4. What factors can affect error propagation estimation?

There are several factors that can affect error propagation estimation, including the precision and accuracy of the measuring instruments used, the skills of the experimenter, and the complexity of the mathematical operations involved in the calculation. Additionally, systematic errors such as instrument calibration errors, human error, and environmental factors can also impact the final error estimate.

## 5. How can error propagation estimation be minimized?

Error propagation estimation can be minimized by using high-quality measuring instruments, ensuring proper calibration and maintenance of equipment, and carefully controlling experimental conditions to minimize systematic errors. It is also important to properly document and analyze all sources of uncertainty in the measurement process to reduce overall error in the final result.