Percent Error Calculator

How to Calculate Percent Error

Percent error is a measure of how inaccurate a measurement is, expressed as a percentage of the correct value. It's commonly used in scientific experiments to quantify the difference between an experimental (measured) value and the theoretical (true or accepted) value.

Percent Error Formula

The formula to calculate percent error is:

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

Where:

• Experimental Value is the measured value in an experiment
• Theoretical Value is the expected or true value
• The vertical bars || represent the absolute value

Calculation Steps

1. Identify the experimental (measured) value and the theoretical (true) value.
2. Subtract the theoretical value from the experimental value.
3. Divide this difference by the theoretical value.
4. Take the absolute value of the result.
5. Multiply by 100 to convert to a percentage.

Example Calculation

Let's calculate the percent error when the theoretical value is 100 and the experimental value is 90.

Step 1: Identify the values

Theoretical Value = 100

Experimental Value = 90

Step 2: Apply the formula

\[ Percent Error = \left|\frac{90 - 100}{100}\right| \times 100\% \]

Step 3: Calculate

\[ Percent Error = \left|\frac{-10}{100}\right| \times 100\% = 0.1 \times 100\% = 10\% \]

Step 4: Interpret the result

The percent error is 10%. This means the experimental value differs from the theoretical value by 10% of the theoretical value.

Visual Representation

This diagram illustrates the 10% error between the theoretical value (100) and the experimental value (90), showing their relative sizes and the difference between them.