Percent Error Calculator

Calculate the percent error between experimental and theoretical values with step-by-step solution.

Enter Values

Result

Percent Error
4.08163%
Experimental Value 10.2
Theoretical Value 9.8
Absolute Error 0.4
Percent Error 4.08163%
Error Direction Above theoretical

Step-by-Step Solution

% Error = |10.2 - 9.8| / |9.8| x 100 = 4.08163%

Understanding Percent Error

Percent error is a measurement of the discrepancy between an observed (experimental) value and a true (theoretical or accepted) value. It is widely used in science, engineering, and statistics to assess the accuracy of measurements and experiments.

Percent Error Formula

The standard formula for percent error uses the absolute value of the difference to ensure the result is always positive:

Standard Formula

The absolute difference divided by the theoretical value, expressed as a percentage.

% Error = |Exp - Theo| / |Theo| x 100

Absolute Error

The magnitude of the difference between measured and accepted values.

Absolute Error = |Exp - Theo|

Relative Error

The absolute error expressed as a fraction of the theoretical value.

Relative Error = |Exp - Theo| / |Theo|

When to Use Percent Error

Laboratory Experiments

In chemistry and physics labs, percent error helps students understand how close their experimental results are to the known values. A low percent error indicates high accuracy.

Quality Control

Manufacturing processes use percent error to verify that products meet specifications. If a component should weigh 100g but weighs 98.5g, the percent error is 1.5%.

Important Considerations

  • Percent error is always calculated relative to the theoretical (accepted) value.
  • A percent error of 0% means perfect accuracy.
  • The formula uses absolute values, so percent error is always non-negative.
  • If the theoretical value is 0, percent error is undefined (division by zero).
  • Small percent errors (under 5%) are generally considered acceptable in most experiments.
  • Systematic errors produce consistent bias, while random errors vary unpredictably.

Interpreting Results

A high percent error can indicate issues with equipment calibration, experimental procedure, or environmental conditions. Always consider the context: a 1% error in a chemistry experiment might be excellent, while a 1% error in precision engineering could be unacceptable.