Percent Error Calculator
Calculate the absolute error, relative error, and percent error of experimental values relative to theoretical baselines.
Your measured, observed, or forecasted laboratory result.
The accepted, standard, or target benchmark constant.
Percent Error Deviation
3.0612%
Error Metrics Decomposition
Formula Substitution workings log
Understanding Percent Error
In chemistry, physics, and statistics, Percent Error measures how far off an experimental or observed value is from the true, accepted, or theoretical value. It is expressed as a positive percentage of the theoretical value.
The Algebraic Formulation
The mathematical derivation follows these three sequential equations:
- Absolute Error: The magnitude of difference without regard to sign: Absolute Error = |E - T|
- Relative Error: The proportion of difference relative to the target standard: Relative Error = |E - T| / |T|
- Percent Error: Scaled by 100 to represent a percentage rate: Percent Error = Relative Error × 100%
Overestimates vs. Underestimates
- If your experimental value E is larger than the accepted theoretical value T, your measurement has positive bias, representing an overestimate.
- If your experimental value E is smaller than T, it represents an underestimate.
Frequently Asked Questions About Percent Error
What is the formula for percent error?
The percent error formula is: Percent Error = (|Experimental Value - Theoretical Value| / |Theoretical Value|) * 100%. The absolute value signs ensure the result is positive.
Can percent error be negative?
No, standard percent error calculations use absolute values in the numerator, meaning the final error percentage is always represented as a positive number. However, you can check whether it is an underestimate or overestimate.
What happens if the theoretical value is zero?
If the theoretical value is zero, the calculation is mathematically undefined because division by zero is impossible. The calculator will flag this as undefined.
Does this calculate relative and absolute error?
Yes. Get percent error, absolute error, and relative error with step-by-step formulas.