Percent Error Calculator
Calculate the percent error between an experimental value and a theoretical value.
Understanding Percent Error Calculator
Percent error measures how far an experimental or measured value differs from an accepted, theoretical, or reference value. It is commonly used in laboratory experiments, scientific measurements, engineering, and other situations where an observed result is compared with a known or expected value.
Unlike a simple numerical difference, percent error expresses the size of the discrepancy relative to the theoretical value. This makes it easier to compare errors when the measurements have different scales or magnitudes.
Using this calculator with your own numbers
Percent Error Calculator is intended to show the mathematical relationship behind the answer, not just return a number. Enter the quantities requested by the selected method—such as Experimental Value, Theoretical Value—and keep their units or mathematical meaning consistent. Where this calculator offers different shapes, methods, or forms, choose the one that matches the problem before entering the values.
When the result is an estimate
For a useful check, look at the units and the scale of the answer before accepting it. A formula can be evaluated correctly while an input is still inappropriate for the problem. Repeating the calculation with a simple test value or checking the result against the expected direction of change can help identify an input mistake.
Percent Error Calculator
Percent error measures how far an experimental or measured value differs from an accepted, theoretical, or reference value. It is commonly used in laboratory experiments, scientific measurements, engineering, and other situations where an observed result is compared with a known or expected value.
Unlike a simple numerical difference, percent error expresses the size of the discrepancy relative to the theoretical value. This makes it easier to compare errors when the measurements have different scales or magnitudes.
Percent Error Formula
The standard percent error formula uses the absolute value of the difference between the experimental and theoretical values. The theoretical value is used as the reference denominator.
The absolute value ensures that percent error represents the magnitude of the discrepancy. Therefore, percent error itself is normally reported as a nonnegative percentage.
Absolute Difference vs. Percent Error
The absolute difference tells you how many units separate the two values, while percent error expresses that difference relative to the magnitude of the theoretical value.
Percent Error = Absolute Difference ÷ |Theoretical| × 100
For example, if an experimental measurement is 95 and the theoretical value is 100, the absolute difference is 5 and the percent error is 5%.
Understanding the Direction of the Difference
Although the standard percent error is nonnegative, comparing the experimental value with the theoretical value can show whether the measurement is higher or lower than expected.
A positive signed difference means the experimental value is higher than the theoretical value. A negative signed difference means it is lower. A value of zero means the two values are exactly equal.
Interpreting Percent Error
A smaller percent error generally means that the experimental measurement is closer to the reference value. A larger percent error indicates a greater relative discrepancy.
Whether a particular percentage is considered acceptable depends on the field, measurement method, experimental conditions, and required level of accuracy. There is no universal percentage threshold that defines an acceptable error for every application.
Percent Error vs. Percent Difference
Percent error and percent difference are related but are not interchangeable. Percent error compares a measured value with an accepted or theoretical reference value. Percent difference is generally used when comparing two values without designating one of them as the accepted reference.
Therefore, when a known theoretical or accepted value is available, percent error is usually the appropriate calculation.
Why the Theoretical Value Cannot Be Zero
The theoretical value is the denominator of the percent error formula. If it equals zero, the calculation would require division by zero and the percentage would not be defined.
How to Use the Calculator
Enter the measured result in the Experimental Value field and the accepted or expected result in the Theoretical Value field. The calculator then determines the absolute difference, signed difference, percent error, and direction of the discrepancy.
The result also displays the formula with your actual values substituted into it, making it easier to verify the calculation and understand how the final percentage was obtained.
Experimental Value = 95
Theoretical Value = 100
Absolute Difference = 5
Percent Error = 5%
Disclaimer
This calculator is intended for informational purposes only. While we strive for accuracy, we cannot guarantee that every result is correct for every situation.