Percent Error Calculator

Compare an experimental (measured) value to a theoretical (accepted) value and get the absolute error, percent error, and signed percent error.

Quick Facts

Percent error formula
%Error = |E − T| / |T| × 100%
E is the experimental (measured) value; T is the theoretical (accepted) value.
Signed percent error
(E − T) / T × 100%
Positive means the measurement overestimated T; negative means it underestimated T.
Undefined case
T = 0
Percent error is undefined when the theoretical value is zero (division by zero).

Your Results

Calculated
Percent Error
-
|E − T| / |T| × 100%
Absolute Error
-
|E − T|, same units as your values
Signed Percent Error
-
(E − T) / T × 100%, shows over/under
Result Quality
-
Rough guide only — compare to your field's tolerance

Ready

Enter your experimental and theoretical values, then press Calculate.

Formula and Method for Percent Error

Percent error measures how far a measured or calculated value (the experimental value) falls from a known, accepted, or predicted value (the theoretical value), expressed as a percentage of the theoretical value. It is one of the most common ways to judge the accuracy of a measurement, an experiment, or a calculation against a known standard.

How the calculation works

The standard formula is %Error = |E − T| / |T| × 100%, where E is the experimental value and T is the theoretical (accepted) value. First subtract the theoretical value from the experimental value to get the raw error, take the absolute value so the result is never negative, divide by the absolute value of the theoretical value to normalize it into a proportion, then multiply by 100 to express it as a percentage. This calculator also reports a signed percent error, (E − T) / T × 100%, without the absolute value — a positive sign means the experimental value overestimated the theoretical value, and a negative sign means it underestimated it. The theoretical value can never be zero, since dividing by zero makes percent error undefined.

Common sources of error

  • Swapping experimental and theoretical: always divide by the theoretical (accepted) value, not the experimental one — the denominator matters, since the two give different results whenever E ≠ T.
  • Dropping the absolute value: the standard percent error is always reported as zero or positive; use the signed version only when you specifically want to show direction.
  • Confusing percent error with percent difference: percent difference is used when comparing two measured values with no known "correct" answer, and divides by their average instead of a single accepted value.
  • Rounding too early: compute the full-precision absolute error and ratio first, and only round the final percentage.

Checking your result

A quick sanity check: if your experimental value is close to the theoretical value, percent error should be a small number close to 0%; if it is far off, percent error should be large. The sign of the signed percent error should match your intuition about whether the measurement came in high or low. If your theoretical value is very small, even a modest absolute error can produce a surprisingly large percent error — in that case, also look at the absolute error to judge practical significance.

Applications

  • Science lab experiments use percent error to judge how closely a measured result (like acceleration due to gravity) matches the accepted physical constant.
  • Manufacturing and quality control use percent error to check whether a produced part's dimension falls within tolerance of its specified target.
  • Sensor calibration and instrumentation compare a sensor's reading to a known reference value to quantify drift or bias.
  • Forecasting and estimation use percent error to score how close a prediction landed relative to the actual outcome once it is known.

Frequently Asked Questions

What is the formula for percent error?
Percent error equals the absolute value of (experimental value minus theoretical value), divided by the absolute value of the theoretical value, times 100: %Error = |E − T| / |T| × 100%. It expresses how far a measured or calculated value is from the accepted value, as a percentage of that accepted value.
What is the difference between percent error and percent difference?
Percent error compares a measured value to one known, accepted, or theoretical value and divides by that accepted value. Percent difference compares two experimental values where neither is known to be correct, and divides by the average of the two values instead.
Can percent error be negative?
The standard percent error formula uses an absolute value, so the reported result is always zero or positive. A signed version, (E − T) / T × 100%, is often shown alongside it to indicate direction: a positive signed value means the experimental value overestimated the theoretical value, and a negative value means it underestimated it.
What counts as a "good" percent error?
It depends on the field and the precision of the instruments involved. Introductory physics lab experiments often treat under 5% as acceptable, while precision manufacturing, chemistry titrations, or calibration work may require under 1%. Always compare your result to the tolerance standard used in your specific context.

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