Compare experimental and theoretical values to find percent error, absolute error, and relative error — with live updates, a difference chart, and step-by-step working.
Results update live as you type.
Percent error
Absolute error
0.5
|exp − theo|
Relative error
0.05
abs / |theo|
Signed error
−0.5
exp − theo
Accuracy
95%
100% − % error
| % Error | Quality | Typical context |
|---|---|---|
| < 1% | Excellent | Precision engineering / analytical chemistry |
| 1% – 5% | Good | Most school / lab experiments |
| 5% – 10% | Acceptable | Introductory physics or chemistry |
| 10% – 20% | Marginal | Crude measurement or systematic bias |
| > 20% | Poor | Investigate method or equipment |
The Method
Percent error tells you how far an experimental (measured) value lies from a theoretical (accepted) value, scaled by the size of the true value. Subtract the two values, take the absolute value, divide by the magnitude of the true value, and multiply by 100. The result is a unit-free percentage you can compare across experiments and quantities. It captures both the magnitude of an error and its significance relative to the thing being measured.
Working
About This Tool
A percent error calculator compares a value you measured (the experimental or observed value) against a value you expected (the theoretical or accepted value), and reports the difference as a percentage of the true value. It also reports the absolute error (the raw size of the discrepancy), the relative error (the unitless ratio), the signed error (which tells you whether the measurement was over- or under-estimated), and an accuracy figure for quick context.
Percent error is the workhorse metric in science labs, engineering tolerance checks, instrument calibration, numerical computation, and quality control. Whenever you have a "true" value to compare against — whether from a textbook, a calibrated standard, or a simulation reference — percent error is the natural way to summarise how close your result was. It standardises errors across different units and magnitudes, so a 0.5 mm error in a 10 mm part and a 50 mm error in a 1 m part both reduce to the same 5% figure.
This calculator uses the standard absolute formula: |experimental − theoretical| / |theoretical| × 100, with the magnitudes ensuring a non-negative result. Some textbooks omit the absolute value to preserve sign — this tool reports the direction separately so you get both pieces of information without ambiguity. When the theoretical value is zero, percent error is undefined; in that case fall back to absolute error or a percent-difference metric instead.
All calculations run entirely in your browser — no sign-up, no tracking, no data sent to any server. Use this free percent error calculator for school labs, university coursework, engineering tolerance reports, or any quick discrepancy check.
% Error
Standard formula: |exp − theo| / |theo| × 100.
Absolute Error
Raw magnitude of the deviation, in the same units as the measurement.
Relative Error
Unitless ratio — % error without the multiply-by-100.
Direction Flag
Spots whether you over- or under-estimated the true value.
100% Free & Private
No account, no tracking — every calculation runs locally in your browser.
Comparison Chart
See the experimental, theoretical and difference values side-by-side.
Two inputs give you a full error analysis in seconds.
Type your measured or observed value into the first field — whatever your experiment or instrument actually returned.
Provide the accepted or true value — from a textbook, calibration standard, or reference solution. This is the denominator of the percent-error formula.
The headline shows the percent error as a percentage. Compare it to the quality table to gauge whether your result is excellent, acceptable, or needs investigation.
The stat tiles report absolute, relative, and signed errors plus an accuracy figure — useful for full lab reports.
A simple bar chart shows the experimental, theoretical, and difference side-by-side — useful for slides or write-ups.
The formula card shows the full step-by-step working and direction flag (over- vs under-estimated) — perfect for pasting into a lab report.
Everything you need to know about percent error, related metrics, and how to interpret your result.
Percent error measures how far an experimental (measured) value deviates from a theoretical (accepted) value, expressed as a percentage of the theoretical value: % error = |experimental − theoretical| / |theoretical| × 100. It is the standard summary of accuracy in scientific experiments and engineering quality checks because it puts the size of the error in context of the size of what is being measured.
Absolute error is the raw magnitude of the difference, in the same units as the measurement (|exp − theo|). Relative error divides absolute error by the true value, producing a unitless ratio (or percentage when multiplied by 100). Relative error is usually more meaningful because a 1 mm error matters very differently for a 5 mm part than for a 5 m beam.
It depends on the field and the precision of your equipment. In an introductory chemistry or physics lab, under 5% is generally considered good, under 10% acceptable. In precision engineering or analytical chemistry, you often need under 1% — or even under 0.1%. Always compare to the smallest division of the instrument: you can't get a smaller error than the precision of your measurement allows.
The standard formula uses absolute value, so percent error is always non-negative. However, some textbooks omit the absolute value to preserve sign — then a positive value means the measurement was over-estimated and a negative value means under-estimated. This calculator gives you the non-negative percent error and reports the direction (over/under) as a separate field so you have both pieces of information.
Percent error is undefined when the theoretical value is zero, because the formula would divide by zero. In that case, the most you can do is report the absolute error, or use a different metric such as a percent-difference formula that divides by the mean of the two values rather than by one of them.
Use percent error when you have a known true or accepted value to compare against. Use percent difference when you're comparing two experimental values where neither is "the answer". Percent difference is computed by dividing the absolute difference by the average of the two values: |a − b| / ((a + b) / 2) × 100. It is symmetric in a and b, which is appropriate when neither is privileged.
High percent error typically comes from one or more of: systematic bias in equipment (miscalibrated scale, faulty timer), poor technique (parallax errors, contamination, premature readings), environmental factors (temperature, humidity, vibration), incorrect theoretical reference (wrong textbook value, mismatched conditions), or simply limited instrument precision. Look at the direction (over vs under) for clues about which factor dominates.
They are related but not the same. Accuracy is informally "how close your measurement is to the true value" — and 100% − % error is a quick summary of it. But "accuracy" in formal metrology also distinguishes from precision (how repeatable your measurements are) and resolution (the smallest distinguishable interval). A measurement can be accurate (low % error) but imprecise (large spread), or vice versa.
Generally, report percent error to no more significant figures than your least-precise measurement. So if your data is precise to two significant figures, write 4.7% — not 4.6837%. Quoting extra digits implies a precision you don't actually have. A common convention in school labs is two significant figures, or one decimal place when % error is below 10.
Yes — that's a major reason for using percent error rather than absolute error. Because % error is unitless, a 4% error in a density measurement and a 4% error in a time measurement are directly comparable. This makes it the standard summary statistic in cross-experiment comparisons, calibration reports, and grading rubrics.
Signed error is simply (experimental − theoretical) without the absolute value. A positive signed error means your measurement was higher than the true value (over-estimated); a negative signed error means it was lower (under-estimated). The signed direction is often more diagnostic than the magnitude: consistent positive errors suggest a systematic bias upward, for example.
No — inputs are taken at full IEEE-754 double precision (~15–17 significant figures). The outputs are displayed to four decimal places by default for readability, but the underlying values are computed to full precision. If you need more digits, copy the values directly out of the input fields or open your browser's developer tools.