Percent Error Calculator
Compare a measured value against a known or expected value and see the percent error — with the full working shown.
What is percent error?
Percent error tells you how far a measured (observed) value strays from a known or accepted true value, expressed as a percentage of the true value. Scientists, students and engineers use it to judge how good a measurement is: a small percent error means the experiment or instrument is close to the target, and a large one hints at a mistake in the method or a limitation of the tool.
Two flavours exist. The absolute percent error is always positive and answers "how far off, in %?". The signed percent error keeps the sign, so a positive number means the observation was too high and a negative number means it was too low. Toggle the switch in the calculator to choose which one you want.
Percent error calculator, piece by piece
Each card explains one thing the tool actually does with your observed value and reference — how the three arithmetic steps are chained, why the sign toggle changes the meaning of the answer, and what the "how close?" verdict is based on.
Three chained steps — how the % number is built
The result is not a single formula: it is three operations run in sequence on the two numbers you enter. Subtract to get the raw miss, divide by the reference to make it scale-free, then multiply by 100 so the answer reads as a percentage. Each of the three intermediate values is shown in the solution steps below the result.
Absolute vs signed — what the toggle changes
The absolute setting wraps the numerator in bars, so the answer is always positive and tells you only the magnitude of the miss. Turning the signed toggle on drops those bars: a positive number means the observation overshot the reference and a negative number means it undershot. The absolute value shown by the calculator is the same in both modes; only the sign changes.
"How close is that?" — the verdict badge under the result
Underneath the numeric result the calculator prints a plain-English verdict. The magnitude of the percent error is compared against fixed bands used in most lab-report rubrics: under 1% is excellent, 1–5% is acceptable, 5–10% is worth a second look, and anything above 10% is a cue to check the method or the tool. The colour of the badge tracks the same bands.
Features of this calculator
- Computes both the signed and absolute percent error
- Accepts any experimental and theoretical (accepted) values
- Explains what a negative percent error means for your measurement
- Guards against a zero theoretical value and flags it clearly
- Shows the |experimental − theoretical| / |theoretical| working step by step
Frequently asked questions
+Can percent error be over 100%?
Yes. It just means the observation is more than double the true value in the wrong direction — usually a sign of a unit mix-up or a mistake in the method rather than measurement noise.
+Is a smaller percent error always better?
For accuracy, yes — smaller means closer to the accepted value. But precision (repeatability) is a separate quality; a run of readings can be tightly clustered (precise) yet all off from the target (poor accuracy / high percent error).
+What if the true value is zero?
Percent error is undefined when the true value is zero because you would divide by zero. Report the absolute error on its own, or switch to a different metric (e.g. absolute deviation).
+Absolute or signed — which should I quote?
Use signed when the direction matters (calibration, bias, quality control). Use absolute when you just need a single "how close?" number for a summary or report.