Understanding Percent Error

What is Percent Error?

Percent error is a measure of how inaccurate a measurement is, expressed as the relative difference between the experimental value and the accepted theoretical value. It is commonly used in scientific experiments to quantify the precision of measurements or the accuracy of predictions.

Formula

The formula for percent error is:

\[ \text{Percent Error} = \left|\frac{\text{Experimental Value} - \text{Theoretical Value}}{\text{Theoretical Value}}\right| \times 100\% \]

Where:

• Experimental Value is the measured or observed value
• Theoretical Value is the expected or accepted value
• The vertical bars \( | \) indicate absolute value

Calculation Steps

Let's calculate the percent error for an experiment where the theoretical value is 10 and the experimental value is 9.5:

1. Identify the values:
   • Experimental Value = 9.5
   • Theoretical Value = 10
2. Apply the percent error formula: \[ \text{Percent Error} = \left|\frac{9.5 - 10}{10}\right| \times 100\% \]
3. Calculate: \[ = \left|\frac{-0.5}{10}\right| \times 100\% = 0.05 \times 100\% = 5\% \]
4. The percent error is 5%

Example and Visual Representation

Let's visualize a percent error of 5%:

This diagram represents:

• The full circle represents 100% or no error
• The blue sector represents the 5% error
• The larger the blue sector, the greater the percent error