Percent Error Calculator
Enter a measured (experimental) value and an actual (true) value to see the percent error — the standard metric used in physics, chemistry, and engineering labs to express how close a measurement is to the accepted value.
Percent error
5%
- Absolute error
- 0.5
- Signed error (measured − actual)
- -0.5
- Signed percent error
- -5%
Underestimate — the measured value is lower than the actual value.
How to use this calculator
Type the measured value (what you actually observed or recorded) into the first box and the actual value (the true, accepted, or theoretical value you are comparing against) into the second box. The primary result is the percent error — always reported as a non-negative magnitude. Below it, the calculator also shows the absolute error (the raw difference, |measured − actual|), the signed error (measured − actual; positive when your measurement was too high, negative when it was too low), and the signed percent error so you can tell at a glance whether the measurement overshot or undershot. Numbers can include commas, underscores, or spaces as thousands separators (1,234 and 1_234 are both accepted) and the calculator works for negative values, decimals, and very small or very large magnitudes.
How the calculation works
Percent error is defined as the absolute difference between the measured value and the actual value, divided by the magnitude of the actual value, expressed as a percentage: %error = |measured − actual| / |actual| × 100. The denominator uses the absolute value of the actual figure so that a negative reference (for example, a temperature below zero or a debit balance) still produces a non-negative percent error. This is the convention used in NIST Technical Note 1297 (the standard reference for expressing uncertainty in physical measurements) and in introductory physics texts such as Taylor's "An Introduction to Error Analysis" §1.6. Percent error is undefined when the actual value is exactly zero, because dividing by zero is not meaningful; in that case only the absolute error has a sensible value, and the calculator displays it explicitly. Percent error measures accuracy — how close a single measurement is to a known truth — and should not be confused with percent difference, which compares two measurements neither of which is taken as the reference, or with percent change, which describes growth or decay over time.
Worked example
Suppose you measure the boiling point of water and read 99.2 °C, but the accepted value at standard atmospheric pressure is 100 °C. The absolute error is |99.2 − 100| = 0.8 °C. Divide by the absolute value of the actual: 0.8 / 100 = 0.008. Multiply by 100 to convert to a percentage: 0.8%. Because the signed error is 99.2 − 100 = −0.8, the signed percent error is −0.8%, telling you the measurement was an underestimate. A second example: you weigh a sample and record 5.05 g for what should be exactly 5.00 g. The absolute error is 0.05 g, percent error = 0.05 / 5.00 × 100 = 1%, and the signed percent error is +1% — an overestimate by 1 percent of the accepted mass.
Frequently asked questions
What is the formula for percent error?
Percent error = |measured − actual| / |actual| × 100, where measured is the value you observed and actual is the true or accepted reference value. The absolute value bars in the numerator turn the difference into a positive magnitude, and the absolute value in the denominator means the formula works correctly even when the actual value is negative. The result is reported as a percentage between 0% (a perfect measurement) and arbitrarily large (a terrible measurement). Some textbooks omit the absolute value in the numerator to preserve sign; this calculator reports both forms — the unsigned percent error as the primary result and the signed percent error in the breakdown.
What is the difference between percent error and percent difference?
Percent error compares a measurement to a known true or accepted value — one number is the reference, the other is being judged against it. Percent difference compares two values neither of which is taken as the truth, for example two independent measurements of the same quantity. Percent difference uses the average of the two values in the denominator: |a − b| / ((a + b) / 2) × 100. Use percent error when you have a textbook value, a calibrated standard, or a theoretical prediction; use percent difference when you are comparing two empirical readings on equal footing.
What is the difference between percent error and percent change?
Percent change describes how a single quantity moves from an initial value to a final value over time: (final − initial) / initial × 100. The denominator is the starting value, not a "true" reference. Percent change has a natural sign — positive for growth, negative for decay — and is what you use for share prices, populations, or temperature over a season. Percent error has no time dimension; it is a snapshot measure of how close one number is to another that is treated as correct.
Can percent error be greater than 100%?
Yes. If the measured value differs from the actual value by more than the magnitude of the actual value, the percent error exceeds 100%. For example, if the actual value is 5 and you measure 12, the percent error is |12 − 5| / 5 × 100 = 140%. Large percent errors usually indicate a systematic problem — a miscalibrated instrument, a unit-conversion mistake, or a calculation error — rather than ordinary measurement noise.
Why is percent error undefined when the actual value is zero?
The formula divides by the absolute value of the actual figure, and division by zero is mathematically undefined. If the true value is exactly zero, percent error cannot be computed, and the only meaningful comparison is the absolute error |measured − 0| = |measured|. When both the measured and actual values are zero the percent error is conventionally taken to be 0%. This calculator detects the actual = 0 case and displays the absolute error instead of an arbitrary or infinite percentage.
Should I take percent error as a sign of a good or bad measurement?
It depends on context. In a high-school chemistry lab a percent error under 5% is usually considered acceptable; in a precision physics experiment 0.1% might be poor. The right benchmark is the published uncertainty of the instrument and the historical reproducibility of the measurement, not a fixed threshold. Percent error tells you accuracy (closeness to truth) but not precision (closeness of repeated measurements to each other) — for a complete picture you also need a standard deviation or other dispersion statistic across multiple trials.