how to find percent error

Natasha willow

3 min read

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19-03-2025

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Percent error, also known as percentage error, is a measure of the discrepancy between a measured or experimental value and a true or accepted value. Understanding how to calculate percent error is crucial in various fields, from science experiments to financial analysis. This comprehensive guide will walk you through the process step-by-step, providing clear explanations and examples. Knowing how to calculate percent error helps you understand the accuracy of your measurements or predictions.

Understanding Percent Error

Before diving into the calculation, it's essential to understand what percent error represents. It quantifies the relative difference between an observed value and a known true value. A smaller percent error indicates higher accuracy, while a larger percent error indicates lower accuracy.

Calculating Percent Error: A Step-by-Step Guide

The formula for calculating percent error is straightforward:

Percent Error = |(Experimental Value - Theoretical Value) / Theoretical Value| × 100%

Let's break down each component:

• Experimental Value: This is the value you obtained through measurement or experimentation.
• Theoretical Value: This is the accepted or true value. This could be a known constant, a value from a reliable source, or a theoretical prediction.
• | | (Absolute Value): This ensures the percent error is always positive, regardless of whether the experimental value is higher or lower than the theoretical value.

Step 1: Find the difference between the experimental and theoretical values. Subtract the theoretical value from the experimental value.

Step 2: Find the absolute value of the difference. This step simply removes any negative sign.

Step 3: Divide the absolute difference by the theoretical value. This gives you the relative difference between the two values.

Step 4: Multiply the result by 100% to express the difference as a percentage. This final step converts the relative difference into a percentage, which is easier to interpret.

Examples of Percent Error Calculation

Let's illustrate the calculation with a couple of examples:

Example 1: Measuring the length of a table

• Experimental Value: You measured the table's length as 1.95 meters.
• Theoretical Value: The actual length of the table is 2.00 meters.

1. Difference: 1.95 m - 2.00 m = -0.05 m
2. Absolute Difference: |-0.05 m| = 0.05 m
3. Relative Difference: 0.05 m / 2.00 m = 0.025
4. Percent Error: 0.025 × 100% = 2.5%

Therefore, your measurement had a 2.5% error.

Example 2: Calculating the density of a substance

• Experimental Value: You calculated the density as 8.90 g/cm³.
• Theoretical Value: The accepted density of the substance is 8.96 g/cm³.

1. Difference: 8.90 g/cm³ - 8.96 g/cm³ = -0.06 g/cm³
2. Absolute Difference: |-0.06 g/cm³| = 0.06 g/cm³
3. Relative Difference: 0.06 g/cm³ / 8.96 g/cm³ ≈ 0.0067
4. Percent Error: 0.0067 × 100% ≈ 0.67%

Your density calculation had an approximate 0.67% error.

Interpreting Percent Error

The magnitude of the percent error is crucial in interpreting the results. A small percent error indicates high accuracy, while a large percent error suggests low accuracy. The acceptable level of percent error varies depending on the context. In scientific experiments, a small percent error is often desired, while in other fields, a larger margin of error might be acceptable.

Frequently Asked Questions (FAQs)

Q: What does a negative percent error mean?

A: The formula uses absolute value, so the percent error is always positive. A negative difference simply indicates that the experimental value was lower than the theoretical value.

Q: How can I reduce percent error in my experiments?

A: Several factors contribute to error. Improving measurement techniques, using more precise instruments, and carefully controlling experimental conditions can significantly reduce error.

Q: What is the difference between percent error and percent difference?

A: Percent difference compares two experimental values, whereas percent error compares an experimental value to a known true value.

By understanding the concepts and following the steps outlined above, you can confidently calculate and interpret percent error in various applications. Remember that accurate calculations are crucial for meaningful analysis and informed decision-making.