Percent Error = | (Experimental Value - Theoretical Value) / Theoretical Value | * 100%
Where:
* Experimental Value: The value you obtained through your experiment or measurement.
* Theoretical Value: The accepted or true value, often found in textbooks or scientific literature.
* | |: These are absolute value bars. The result is always positive, as we're only interested in the magnitude of the error, not its direction.
Example:
Let's say you experimentally determined the acceleration due to gravity (g) to be 9.5 m/s². The accepted value for g is approximately 9.8 m/s². The percent error would be:
Percent Error = | (9.5 m/s² - 9.8 m/s²) / 9.8 m/s² | * 100%
= | -0.3 m/s² / 9.8 m/s² | * 100%
≈ 3.06%
This means your experimental value was approximately 3.06% different from the accepted value.
Important Considerations:
* Significant Figures: Pay attention to significant figures in your calculations and final answer. The number of significant figures in your percent error should generally match the least number of significant figures in your experimental and theoretical values.
* Units: Make sure your experimental and theoretical values use the same units before performing the calculation.
* Error Propagation: If your experimental value is derived from multiple measurements, you need to consider error propagation to accurately assess the overall uncertainty in your result. This is a more advanced topic involving techniques like adding errors in quadrature.
In short, the formula is straightforward, but understanding the context and potential sources of error is crucial for interpreting the results meaningfully.