Percent Error Calculator
Calculate percent error between an experimental (observed) value and a theoretical (accepted) value, with the absolute error and clear percent error vs percent change guidance.
How It's Calculated
Formula
\text{percent error} = \frac{|\text{observed} - \text{accepted}|}{|\text{accepted}|} \times 100Percent error measures how far an experimental (observed) result is from a known or expected (accepted) value, expressed as a percentage of the accepted value's size. It is calculated by taking the absolute difference between the observed and accepted values, dividing by the absolute value of the accepted value, and multiplying by 100. Percent error is always reported as a non-negative magnitude — it tells you how big the mistake was, not which direction it went. This is different from percent change, which compares a starting value to an ending value ((new - old) / old x 100), keeps its sign to show increase or decrease, and can use either value as the "before" depending on context. Percent error always divides by the accepted (true) value specifically, never by the observed value, because the accepted value is the fixed reference point the observed value is being judged against. An accepted value of zero is not allowed, since dividing by zero would make the percent error undefined.
Worked Examples
Observed value above accepted: 11 vs. 10
- Absolute error: |11 - 10| = 1
- Percent error: 1 / |10| x 100 = 10%
Observed value below accepted: 48 vs. 50
- Absolute error: |48 - 50| = 2
- Percent error: 2 / |50| x 100 = 4%
Frequently Asked Questions
What's the difference between percent error and percent change?
Percent error compares a measured (observed) value to a known correct (accepted) value, always divides by the accepted value, and is always reported as a non-negative magnitude — it answers 'how far off was my measurement?' Percent change compares a starting value to an ending value, keeps its sign to show whether the value went up or down, and divides by whichever value is treated as the starting point. They use similar-looking formulas but answer different questions and are not interchangeable.
Why is percent error always positive?
The formula takes the absolute value of the difference between observed and accepted, so the result never comes out negative. Percent error is meant to show the size of a discrepancy, not its direction — whether your measurement was too high or too low, the percent error reports the same magnitude either way.
Why can't the accepted value be zero?
Percent error divides by the absolute value of the accepted value. If the accepted value is zero, that division is undefined, so this calculator rejects the input rather than returning an invalid result.
Does it matter which value I enter as 'observed' vs. 'accepted'?
Yes. The accepted value is the known, correct, or expected reference value, and it's always the denominator. The observed value is what you actually measured or calculated. Swapping them changes the result, since percent error is not symmetric — dividing by a different denominator gives a different percentage.