Percent Error Calculator
Calculate the percent error between a measured and an accepted value.
Try an example
2%
About this calculator
What Is Percent Error?
Percent error (or percentage error) measures how far a measured or estimated value is from the true, accepted or expected value, expressed as a percentage of the true value. Scientists, engineers and students use it to judge how accurate a measurement was — for example, how close an experiment's result for the density of a metal comes to the textbook figure. Enter the observed value and the true value in this calculator and it returns the error as a percentage.
The Percent Error Formula
Percent error = |Measured value − True value| ÷ |True value| × 100%
The absolute-value bars make the answer positive, showing the size of the error but not its direction. Some courses keep the sign — a negative result means the measurement came in below the true value — so check which version your teacher or textbook expects. If an experiment measures 9.6 m/s² for gravity and the accepted value is 9.81 m/s², the error is |9.6 − 9.81| ÷ 9.81 × 100 ≈ 2.1%.
Worked Example
A measured value of 98 against a theoretical value of 100 gives a percent error of 2% — the measurement differs from the accepted value by 2% of that value.
Why Measurements Differ From the True Value
- Human error: misreading a scale or timing a reaction late.
- Instrument limits: every device has finite precision and may need calibration.
- Environmental conditions: temperature, air resistance and vibration can all interfere.
- Estimation and rounding: approximations along the way accumulate.
Percent Error vs. Percent Difference vs. Percent Change
- Percent error compares a measurement with a known true value.
- Percent difference compares two measured values when neither is the "true" one, using their average as the base.
- Percent change describes growth or decline from an old value to a new one.
How Small Is Small Enough?
What counts as acceptable depends on the field. A few percent is common in school labs; precision manufacturing may demand a fraction of a percent. If you repeat a measurement several times, use the average — see the Mean, Median, Mode Calculator — and the Standard Deviation Calculator to understand the spread. For general percentage problems, use the Percentage Calculator.
Worked example
A measured value of 98 against a theoretical value of 100 gives a percent error of 2% — the measured value differs from the accepted value by 2%.
Frequently asked questions
Why does percent error use absolute value?
Percent error is typically reported as a magnitude — how far off the measurement is, regardless of whether it's too high or too low. The signed difference (shown separately) tells you the direction.
What counts as a 'good' percent error?
It depends entirely on context — a physics lab experiment might target under 5%, while some fields require much tighter tolerances. There's no universal threshold.
What if the theoretical value is zero?
Percent error is undefined when the theoretical value is zero, since it requires dividing by that value — a different error metric is needed in that case.
