Percent Error Calculator
Calculate percent error between an experimental and a true value, or percent difference between two measurements, with the working shown step by step.
How to use this calculator
- 1Choose percent error if one value is a known accepted figure, or percent difference if you are comparing two equally valid measurements.
- 2Enter your measured value and the true or comparison value.
- 3For percent error, choose signed output if you need to know whether you over- or under-measured.
How it works
Percent error and percent difference
Percent error = |measured − true| ÷ |true| × 100 Signed error = (measured − true) ÷ |true| × 100 Percent difference = |a − b| ÷ ((|a + b|) ÷ 2) × 100 Relative error = |measured − true| ÷ |true|
Percent error divides the size of the mistake by the value that is assumed to be correct, which makes the error comparable across measurements of very different magnitudes. Percent difference divides by the average of the two values instead, because when neither measurement is authoritative there is no reason to prefer one denominator over the other.
Worked example
A pendulum experiment measures gravity as 9.65 m/s² against the accepted 9.81 m/s². The absolute error is 0.16, and 0.16 ÷ 9.81 × 100 gives a percent error of 1.6306% — a good result for a classroom experiment.
Percent Error Calculator: the complete guide
Percent error, percent difference, and percent change
These three are constantly mixed up, and they answer different questions. Percent error asks how far a measurement is from a known correct value, so it divides by the true value. Percent difference asks how far apart two equally credible measurements are, so it divides by their average. Percent change asks how much a quantity moved over time, so it divides by the starting value and keeps its sign.
Pick the denominator that matches the question. Using the measured value as the denominator for percent error is a common mistake that makes large errors look smaller than they are.
What counts as an acceptable error
There is no universal threshold — it depends entirely on the precision of the instrument and the tolerance of the application. In an introductory physics lab, under 5% is usually considered a good result and under 1% is excellent. Analytical chemistry often demands better than 0.5%. Manufacturing tolerances can be tighter still.
What matters more than the number is whether the error is random or systematic. Random error scatters around the true value and shrinks as you average repeated trials. Systematic error — a miscalibrated scale, a consistently late stopwatch trigger — pushes every trial the same direction and averaging will not fix it. A signed percent error that stays the same sign across many trials is the classic signature of a systematic problem.
Why the true value cannot be zero
Percent error divides by the true value, so a true value of zero makes the calculation undefined — any nonzero measurement would represent an infinite proportional error. This comes up with quantities that legitimately pass through zero, such as a temperature in Celsius or a net displacement.
In that situation, report the absolute error in its own units, or switch to percent difference where the denominator is the average of the two readings. This calculator flags the zero case rather than returning a misleading number.
Frequently asked questions
Should percent error be positive or negative?
Most lab reports use the absolute value, since the size of the error is what matters. A signed value is more informative when you are hunting for a systematic bias — if every trial comes back negative, your instrument is probably reading low. Both options are available above.
What is the difference between absolute and relative error?
Absolute error is the raw gap between the measured and true value, in the original units. Relative error is that gap divided by the true value, which makes it dimensionless and comparable across scales. Percent error is simply relative error expressed as a percentage.
Can percent error be more than 100%?
Yes. If the measurement is more than double the true value, the percent error exceeds 100%. That normally indicates a unit mix-up or a decimal-place mistake rather than a measurement problem.
How do I reduce percent error in an experiment?
Repeat the measurement and average the trials to cancel random error, calibrate instruments against a known standard to remove systematic bias, control the variables you are not measuring, and use an instrument with finer resolution than the precision you need to report.