Percent Error Calculator

The Percent Error Calculator is a tool designed to determine the difference between a measured or experimental value and a known or accepted value, expressed as a percentage. This calculation is crucial in various scientific, engineering, and educational contexts to assess the accuracy of measurements or calculations.

This calculator is particularly useful in:

• Scientific Experiments: Evaluating the accuracy of experimental results compared to theoretical values.
• Engineering Projects: Assessing the precision of measurements and calculations in design and construction.
• Educational Settings: Helping students understand the concept of error and its impact on results.
• Quality Control: Determining the deviation of manufactured products from specified standards.
• General Measurement Analysis: Comparing any measured value to an accepted standard.

The percent error is calculated using the following formula:

$$\text{Percent Error}=\left(\frac{\mid \text{Experimental Value}-\text{Accepted Value}\mid }{\mid \text{Accepted Value}\mid }\right)\times 100$$

Where:

• Experimental Value = Measured or calculated value
• Accepted Value = Known or theoretical value
• | | = Absolute value (always positive)

For example, if the experimental value is 25.5 and the accepted value is 25:

Percent Error = |(25.5 - 25) / 25| × 100%

Percent Error = |0.5 / 25| × 100%

Percent Error = |0.02| × 100%

Percent Error = 2%

Another example, if the experimental value is 9.8 and the accepted value is 10:

Percent Error = |(9.8 - 10) / 10| × 100%

Percent Error = |-0.2 / 10| × 100%

Percent Error = |-0.02| × 100%

Percent Error = 2%

1. What is the difference between percent error and percent difference?

   Percent error compares an experimental value to an accepted value, indicating accuracy. Percent difference compares two experimental values to each other, indicating precision.

2. Can percent error be negative?

   No, percent error is always expressed as a positive value due to the absolute value in the formula. The absolute value ensures that the error is represented as a magnitude, not a direction.

3. What does a high percent error indicate?

   A high percent error indicates a significant difference between the experimental and accepted values, suggesting lower accuracy in the measurement or calculation.

4. What does a low percent error indicate?

   A low percent error indicates a close agreement between the experimental and accepted values, suggesting higher accuracy in the measurement or calculation.

5. What units should I use for experimental and accepted values?

   The experimental and accepted values must be in the same units. The percent error is a dimensionless quantity, so the units cancel out in the calculation.