how to find percent error

2 min read 20-03-2025

Percent error, also known as percentage error, is a measure of how much a measured or experimental value differs from a true or accepted value. It's a crucial concept in science, engineering, and various other fields where accuracy is paramount. This guide will walk you through how to calculate percent error, provide examples, and highlight its significance.

Understanding Percent Error

Percent error quantifies the relative difference between an experimental value and a true or accepted value. A small percent error indicates high accuracy, while a large percent error suggests significant inaccuracy. This is different from absolute error, which simply measures the difference without considering the relative scale.

The Formula for Calculating Percent Error

The formula for calculating percent error is straightforward:

Percent Error = [(|Experimental Value - True Value|) / True Value] x 100%

Let's break this down:

Experimental Value: This is the value you obtained through measurement or experimentation.
True Value: This is the accepted or theoretical value. This might come from a reliable source, a textbook, or a standard.
| | (Absolute Value): This ensures the result is always positive, regardless of whether the experimental value is higher or lower than the true value.

Step-by-Step Calculation of Percent Error

Here's a step-by-step guide to calculating percent error:

Identify the Experimental and True Values: Clearly define both values. Ensure they are in the same units.
Find the Absolute Difference: Subtract the true value from the experimental value. Take the absolute value of the result (make it positive).
Divide by the True Value: Divide the absolute difference by the true value.
Multiply by 100%: Multiply the result by 100 to express the error as a percentage.

Examples of Percent Error Calculation

Let's illustrate with examples:

Example 1: Measuring the Length of a Table

True Value: The actual length of the table is 2.00 meters.
Experimental Value: You measure the table's length as 1.95 meters.

Percent Error = [|(1.95 m - 2.00 m)| / 2.00 m] x 100% = [(0.05 m) / 2.00 m] x 100% = 2.5%

Example 2: Determining the Density of a Substance

True Value: The accepted density of water is 1.00 g/cm³.
Experimental Value: You experimentally determine the density to be 0.98 g/cm³.

Percent Error = [|(0.98 g/cm³ - 1.00 g/cm³)| / 1.00 g/cm³] x 100% = [(0.02 g/cm³) / 1.00 g/cm³] x 100% = 2%

Interpreting Percent Error Results

Low Percent Error (e.g., < 5%): Indicates high accuracy and precision in your measurements or experiment.
High Percent Error (e.g., > 10%): Suggests significant inaccuracy. It implies potential errors in the measurement process, experimental design, or the equipment used. This necessitates reviewing the methodology and identifying potential sources of error.

Common Sources of Error

Understanding the sources of error is crucial in reducing percent error. These include:

Instrumental Errors: Limitations or inaccuracies inherent in the measuring instruments used.
Random Errors: Unpredictable variations due to fluctuations in conditions or human error.
Systematic Errors: Consistent biases introduced by flawed procedures or equipment calibration.

Conclusion: Mastering Percent Error Calculations

Calculating percent error is a fundamental skill. Understanding how to compute and interpret it allows you to evaluate the accuracy of your measurements and experiments, enhancing your scientific rigor and analytical capabilities. By carefully considering potential sources of error, you can strive for greater precision in your work. Remember always to use the correct units and clearly identify your experimental and true values. This simple yet powerful tool provides a quantitative measure of accuracy that is invaluable across numerous fields.