What Is Percent Error?
Percent error is a fundamental concept in science, engineering, and statistics that measures the accuracy of a measurement or calculation. It quantifies the difference between an experimental or observed value and a known or accepted "true" value, expressing this difference as a percentage of the true value. A low percent error indicates that the observed value is very close to the true value, suggesting a high degree of accuracy. Conversely, a high percent error signifies a large discrepancy. This percent error calculator is an essential tool for students and professionals alike who need to quickly evaluate the precision of their work.
The Percent Error Formula
The formula for calculating percent error is simple and focuses on the absolute difference between the two values to ensure the result is always positive:
- Observed Value: This is the value you measured or calculated in your experiment.
- True Value: This is the universally accepted or theoretical value for a quantity.
For example, if you measure the acceleration due to gravity in an experiment and get 9.6 m/s², while the accepted value is 9.8 m/s², the percent error would be `|(9.6 - 9.8) / 9.8| × 100% ≈ 2.04%`. For more general percentage calculations, you can use our Percentage Calculator.
Why is Percent Error Important?
Percent error provides a standardized way to assess the quality of data and the reliability of experimental methods. Its applications are widespread:
- Scientific Research: In chemistry and physics, it's used to validate experimental results against theoretical predictions. A low percent error strengthens the validity of an experiment.
- Engineering and Manufacturing: It's crucial for quality control. If a machine part is supposed to be 10 cm long but is consistently manufactured at 10.1 cm, the percent error helps quantify the manufacturing tolerance and identify potential issues.
- Financial Modeling: Analysts use percent error to evaluate how well their financial models predict actual stock prices or company earnings.
It's important not to confuse percent error with other statistical measures like standard deviation, which measures the dispersion of data points around an average. You can explore this concept with our Standard Deviation Calculator. For a deeper academic understanding of experimental errors and data analysis, resources from universities like Wisc-Online provide clear tutorials and examples.