how to find percent error

3 min read 18-03-2025

Percent error, also known as percentage error, is a measure of how far off a measured value is from the true or accepted value. It's frequently used in science, engineering, and statistics to quantify the accuracy of measurements and calculations. Understanding how to calculate percent error is crucial for interpreting results and evaluating the reliability of data. This guide will walk you through the process step-by-step, offering examples and tips along the way.

Understanding the Components of Percent Error

Before diving into the calculation, let's define the key terms:

Experimental Value (or Measured Value): This is the value you obtain through experimentation or measurement. It might be slightly different from the true value due to limitations in equipment or experimental procedures.
Accepted Value (or True Value): This is the correct or established value. It could be a theoretical value, a value from a highly reliable source, or a standardized value.

The difference between these two values is crucial for calculating percent error.

The Formula for Percent Error

The formula for calculating percent error is straightforward:

Percent Error = [(|Experimental Value - Accepted Value|) / Accepted Value] * 100%

Let's break down this formula:

Find the difference: Subtract the accepted value from the experimental value. The absolute value (indicated by the vertical bars ||) is used because we're only interested in the magnitude of the error, not its direction (positive or negative).
Divide by the accepted value: This step normalizes the error, putting it in relation to the true value.
Multiply by 100%: This converts the result to a percentage, making it easier to interpret and compare.

Step-by-Step Calculation of Percent Error: Example 1

Let's say you're measuring the length of a table.

Accepted Value: The actual length of the table is 72 inches (measured with a highly precise instrument).
Experimental Value: Your measurement of the table is 70 inches.

Here's the calculation:

Difference: |70 inches - 72 inches| = 2 inches
Divide by accepted value: 2 inches / 72 inches = 0.0278
Multiply by 100%: 0.0278 * 100% = 2.78%

Therefore, the percent error in your measurement is 2.78%.

Step-by-Step Calculation of Percent Error: Example 2 (with a larger difference)

Imagine you're determining the density of a substance.

Accepted Value: The true density of the substance is 2.7 g/cm³.
Experimental Value: Your experiment gives a density of 3.1 g/cm³.

Here's the calculation:

Difference: |3.1 g/cm³ - 2.7 g/cm³| = 0.4 g/cm³
Divide by accepted value: 0.4 g/cm³ / 2.7 g/cm³ ≈ 0.148
Multiply by 100%: 0.148 * 100% ≈ 14.8%

In this case, the percent error is approximately 14.8%, indicating a larger discrepancy between the experimental and accepted values.

Interpreting Percent Error

A lower percent error indicates higher accuracy. An error of 0% means the experimental value is exactly the same as the accepted value. However, in practice, a small percent error is considered desirable, reflecting the precision limitations of the method. A high percent error suggests potential issues with the measurement techniques, instruments, or calculations.

Frequently Asked Questions (FAQs)

Q: What does a negative percent error mean?

A: While the formula uses absolute value, a negative difference before taking the absolute value would indicate that the experimental value was lower than the accepted value. The percent error itself remains positive, simply reflecting the magnitude of the difference.

Q: How can I reduce percent error?

A: Reducing percent error involves improving the precision of your measurements and experimental techniques. This could involve using more accurate instruments, refining experimental procedures, and increasing the number of trials to average out random errors.

Q: Is there a difference between percent error and percent difference?

A: While often used interchangeably, percent difference is typically calculated when neither value is considered definitively "true" or "accepted." It uses the average of the two values as the denominator in the calculation instead of the accepted value.

Conclusion

Calculating percent error is an essential skill for evaluating the accuracy of measurements and experimental results. By following the steps outlined in this guide, you can confidently determine the percent error in your data and understand its implications. Remember to always clearly state your experimental and accepted values, as well as the context of your calculation. Understanding percent error helps you improve experimental design and build a stronger understanding of the data you're working with.