Accuracy Has a Number — Here It Is
You measured the boiling point of water at 101.5°C. The accepted value is 100°C. Were you close? “Close” is a feeling — percent error is the number: 1.5%, small enough for most school labs.
This percent error calculator compares your experimental value against the accepted (true) value and returns percent error, absolute error and relative error — with an optional signed mode that keeps the +/− direction, and a percent difference mode for comparing two measurements with no “known” answer.
Percent error · percent difference · absolute & relative error
? Percent error vs. percent difference \u2014 which do I need?
Percent error compares your measurement against a known true value: |experimental − accepted| / |accepted| × 100. Use it in labs, when a correct answer exists.
Percent difference compares two measurements with no “correct” one: |A − B| / average(A, B) × 100. Use it to compare two trials, two methods, or two estimates.
The signed option keeps the direction: positive means your value was above the reference, negative means below. Unsigned (absolute) just gives the size of the gap.
Please enter valid numbers. For percent error, the accepted value cannot be zero.
Percent error measures accuracy (closeness to the true value), not precision (repeatability). A reading can be precise yet inaccurate — use standard deviation alongside percent error for the full picture.
How to Use the Percent Error Calculator
- Choose a mode: Percent Error (you have a true value) or Percent Difference (comparing two measurements).
- Enter your two values — experimental and accepted, or A and B.
- Tick “signed” if you want the direction (+/−), not just the size of the gap.
- Click Calculate and read the full breakdown with steps.
The Formulas
Percent difference = |Δ| / average(|A|, |B|) × 100
Absolute error = |Δ| | Relative error = |Δ| / |accepted|
Worked example: experimental 101.5°C, accepted 100°C. Δ = 1.5; absolute error = 1.5; relative error = 1.5/100 = 0.015; percent error = 1.5%. Signed: +1.5% (above the true value).
What Counts as “Good” Percent Error
| Context | Typical acceptable error |
|---|---|
| School / introductory labs | Under 5–10% |
| General engineering | Under 2–5% |
| Precision engineering | Under 1% |
| Analytical / pharma chemistry | Often under 0.5% |
“Good” is always relative to the field — a 2% error is superb in biology and sloppy in metrology.
Accuracy vs. Precision — Don’t Confuse Them
Percent error measures accuracy: how close you are to the true value. It says nothing about precision: how repeatable your measurements are. Darts clustered tightly far from the bullseye are precise but inaccurate; darts scattered around the bullseye are accurate on average but imprecise.
Use percent error for accuracy, standard deviation for precision — and fix your technique when error is high (calibration, procedure, environment) rather than just repeating the measurement.
How to Calculate Percent Error, Step by Step
- Subtract the accepted (true) value from your measured value.
- Take the absolute value of that difference — this is the size of the miss, ignoring direction.
- Divide by the accepted value (use its absolute value too, if it is negative).
- Multiply by 100 to express the result as a percentage.
Keeping the sign instead of taking the absolute value gives the signed percent error: positive means you overshot, negative means you came in under — a distinction that matters in the two examples below.
Two Worked Examples: Overestimate and Underestimate
Example 1 — overestimate. A kitchen scale reads 512 g for a calibration mass whose true weight is 500 g. Percent error = |512 − 500| ÷ |500| × 100 = 12 ÷ 500 × 100 = 2.4%. The signed error is +2.4%: the scale reads high.
Example 2 — underestimate. A class measures gravity as g = 9.53 m/s² against the accepted 9.81 m/s². Percent error = |9.53 − 9.81| ÷ |9.81| × 100 = 0.28 ÷ 9.81 × 100 ≈ 2.85%. The signed error is −2.85%: the measurement came in low.
Same method, opposite directions. The absolute value tells you how far off you were; the sign tells you which way — and a consistent sign across many trials is the fingerprint of a systematic error rather than random noise.
Edge Cases: A Zero True Value, and Errors Over 100%
True value of zero. The formula divides by the accepted value, so a true value of zero makes percent error undefined — division by zero has no answer. In that situation report the absolute error (the size of the miss, in the original units), or use percent difference when comparing two measurements, neither of which is “true.”
Errors over 100%. They are entirely possible: whenever the miss is bigger than the true value itself, the error exceeds 100%. A reading of 260 against a true value of 100 gives |260 − 100| ÷ 100 × 100 = 160%. Errors that large usually signal a blunder — a wrong unit, a misread scale, a swapped sample — rather than ordinary inaccuracy, so treat them as a prompt to re-measure.
Where Percent Error Shows Up Outside the Lab
Weather forecasting scores predicted rainfall and temperatures against what actually arrived. Manufacturing checks that parts and fill weights stay within tolerance of their targets. Finance compares forecast earnings and budgets against actuals. Polling measures predicted vote shares against election results. In each case the question is the same one the lab asks: how big was the miss, relative to the real value?
Frequently Asked Questions
How do you calculate percent error?
Subtract the accepted value from your experimental value, take the absolute value, divide by the accepted value, and multiply by 100: |Δ| / |accepted| × 100.
What is the difference between percent error and percent difference?
Percent error compares a measurement to a known true value. Percent difference compares two measurements with no “correct” one, dividing by their average instead.
Can percent error be negative?
Yes, in signed mode: positive means your value was above the reference, negative means below. Unsigned (absolute) percent error is always ≥ 0.
What is a good percent error?
It depends on the field: under 5–10% is usually fine for school labs, under 2–5% for engineering, under 1% for precision work, and under 0.5% for analytical chemistry.
What is the difference between accuracy and precision?
Accuracy is closeness to the true value (measured by percent error). Precision is repeatability — how tightly clustered repeated measurements are (measured by standard deviation).
Why is my percent error so high?
Common causes: uncalibrated instruments, procedural mistakes, environmental interference (temperature, humidity), parallax reading errors, or using the wrong technique. A very high error usually signals a method problem, not bad luck.
What happens if the true (accepted) value is zero?
Percent error is undefined, because the formula divides by the accepted value and division by zero has no answer. Report the absolute error instead — the size of the miss in the original units — or use percent difference when comparing two measurements and neither one is the known true value.
Can percent error be more than 100%?
Yes. Percent error passes 100% whenever the miss is bigger than the true value itself: measuring 260 g against a true 100 g gives |260 − 100| ÷ 100 × 100 = 160%. Errors that large usually point to a blunder, a wrong unit or a misread instrument rather than ordinary inaccuracy.
What is the difference between percent error and relative error?
Relative error is the same comparison written as a plain fraction or decimal: |measured − true| ÷ |true|. Percent error is simply that relative error multiplied by 100 and reported with a % sign. A relative error of 0.024 and a percent error of 2.4% describe exactly the same miss.
Final Thoughts
Every measurement is a claim about reality — percent error is how you grade that claim. Keep it in your lab toolkit next to your calculator, and let the number (not your optimism) judge the result.
Error Checked? Sharpen More Math
Next up: our percentage calculator and standard deviation calculator.