Enter the values and their respective errors into the calculator to determine the propagated error when these values are combined.
Propagated Error Formula
The following formula is used to calculate the propagated error.
PE = √(E_A^2 + E_B^2)
Variables:
- PE is the propagated error
- E_A is the error in value A
- E_B is the error in value B
To calculate the propagated error, square the errors of each value, sum them, and then take the square root of the total.
What is a Propagated Error?
Propagated error refers to the uncertainty in a result caused by the uncertainty in the measurements that contribute to that result. It is a measure of how errors in the input values can affect the final calculated value. Understanding propagated error is crucial in fields such as physics, engineering, and statistics, where precision is important and measurements are often accompanied by some degree of uncertainty.
How to Calculate Propagated Error?
The following steps outline how to calculate the Propagated Error.
- First, determine the error in value A (E_A).
- Next, determine the error in value B (E_B).
- Use the formula PE = √(E_A^2 + E_B^2) to calculate the propagated error (PE).
- Finally, enter the errors into the calculator to verify the propagated error.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Error in value A (E_A) = 0.2
Error in value B (E_B) = 0.3
