Math & Engineering
Percent Error Calculator
Calculate the percentage error between experimental and theoretical values to determine measurement accuracy.
Enter values to calculate percent error
Related to Percent Error Calculator
The percent error calculator determines the accuracy of a measurement by comparing the experimental (measured) value to the theoretical (accepted) value. It calculates both the absolute error and the percentage error using standardized formulas in scientific measurements.
Percent Error Formula
Percent Error = |Experimental Value - Theoretical Value| / |Theoretical Value| × 100%
Absolute Error Formula
Absolute Error = |Experimental Value - Theoretical Value|
The vertical bars in the formulas represent the absolute value, ensuring that the result is always positive. This is important because percent error is always expressed as a positive number, regardless of whether the experimental value is higher or lower than the theoretical value.
Understanding your percent error results is crucial for evaluating the accuracy of measurements and experimental procedures. The calculator provides two key metrics:
Percent Error
Expressed as a percentage, this value indicates how far your experimental measurement deviates from the accepted theoretical value. A smaller percentage indicates a more accurate measurement. For example, a 5% error means your measurement was 95% accurate.
Absolute Error
This represents the actual difference between your experimental and theoretical values in the original units of measurement. It provides a concrete value of how far off your measurement was from the accepted value.
Generally, in scientific measurements: - Less than 1% error is considered excellent - 1-5% error is good - 5-10% error is acceptable - Greater than 10% error might indicate problems with the measurement procedure
1. Why is my percent error negative?
The percent error calculator always returns a positive value because percent error is an absolute measure of accuracy. The sign (positive or negative) is not relevant when expressing how far a measurement deviates from the accepted value.
2. What is a good percent error?
What constitutes a "good" percent error depends on the context and precision requirements of your measurement. In general, less than 5% is considered good for most applications, but some scientific experiments may require even lower error rates.
3. Can percent error be greater than 100%?
Yes, percent error can exceed 100% if your experimental value is more than double the theoretical value or is in the opposite direction. However, such large errors usually indicate significant problems with the measurement procedure.
4. Why can't the theoretical value be zero?
The theoretical value cannot be zero because it appears in the denominator of the percent error formula. Dividing by zero is mathematically undefined and would not provide a meaningful result for the error calculation.
5. What is the scientific source for this calculator?
This calculator implements the standard percent error formula widely accepted in scientific and engineering fields. The formula and methodology are based on fundamental principles of measurement theory and error analysis as described in NIST (National Institute of Standards and Technology) guidelines and standard physics textbooks such as "An Introduction to Error Analysis" by John R. Taylor. The calculations follow the internationally recognized standards for experimental uncertainty evaluation (ISO/IEC Guide 98-3:2008).