Understanding Relative Percent Error
Relative percent error serves as a quantitative measure to assess the accuracy of experimental results when compared to an accepted standard. This calculation helps scientists and researchers determine the precision of their measurements and observations. By expressing this deviation as a percentage, it offers a standardized way to evaluate the reliability of experimental data across various scientific disciplines.
Understanding Key Terms
To calculate relative percent error, two primary values are necessary: the actual value and the measured value. The “actual value,” also known as the true, theoretical, or accepted value, represents the correct or standard quantity that a measurement aims to achieve. This value is often derived from established scientific principles, known constants, or highly precise previous experiments.
The “measured value,” conversely, is the result obtained through an experiment, observation, or calculation performed in a laboratory or field setting. The difference between these two quantities forms the basis of “absolute error,” which indicates the magnitude of the discrepancy without considering its direction.
The Relative Percent Error Formula
The mathematical formula for calculating relative percent error provides a standardized way to express the accuracy of a measurement. It is derived by first finding the absolute difference between the measured value and the actual value. This difference is then divided by the actual value, which normalizes the error relative to the true quantity.
Finally, this ratio is multiplied by 100 to convert the result into a percentage. The formula is expressed as: Relative Percent Error = (|Measured Value – Actual Value| / Actual Value) × 100%. The absolute value signs ensure that the result is always a positive percentage, indicating the magnitude of the error.
Applying the Formula Step-by-Step
Consider a common laboratory scenario where a student measures the density of a known substance, such as water, at a specific temperature. The accepted density of water at 25°C is 0.997 g/mL. This represents the actual value for the calculation. If a student conducts an experiment and measures the density of water to be 1.015 g/mL, this becomes the measured value.
To apply the formula, follow these steps:
- Calculate the absolute difference between the measured and actual values: |1.015 g/mL – 0.997 g/mL|, which equals 0.018 g/mL.
- Divide this absolute error by the actual value: 0.018 g/mL / 0.997 g/mL, which yields approximately 0.01805.
- Multiply this result by 100 to express it as a percentage: 0.01805 × 100 = 1.81%.
- Therefore, the relative percent error for this measurement is 1.81%.
Interpreting Your Results
Once the relative percent error is calculated, understanding what the resulting percentage signifies is important. A lower relative percent error indicates that the measured value is very close to the actual value, suggesting higher accuracy in the experiment or measurement. Conversely, a higher relative percent error indicates a greater deviation from the actual value, implying less accuracy. For instance, a 1% error suggests a measurement is very close to the true value, while a 15% error indicates a substantial difference.
The sign of the difference before taking the absolute value can also provide additional information. If the measured value was higher than the actual value, the initial difference would be positive, indicating an overestimation. If the measured value was lower, the difference would be negative, indicating an underestimation. Factors contributing to a higher relative percent error can include limitations of the measuring equipment, inconsistencies in the experimental procedure, or external environmental influences during the measurement process.