Percent Error Calculator
What percent error measures
When a measurement misses the true value, percent error expresses that miss as a share of the truth. It puts a 2 gram gap on a 100 gram package and the same gap on a 10 gram one on a single comparable scale, which is the whole point of a relative measure. Lab courses, QA charts, and forecasting reviews all rely on it.
Use it wherever a trusted reference exists: calibration checks, chemistry yields, physics constants, and supplier tolerance audits. Interpretation is context-bound, with under 1 percent superb for lab work and 10 to 20 percent often workable for demand forecasts.
The formula and a worked case
Percent error = |observed - true| / |true| * 100, and the absolute value reports size without direction. Suppose a lab measures g as 9.78 m/s^2 against an accepted 9.81: the difference is 0.03, so percent error = 0.03 / 9.81 * 100 = 0.31 percent.
Scale changes everything. A 0.3 miss on a true value of 3 yields 10 percent, a far louder flag than 0.31 percent on the gravity measurement.
Using the calculator
Enter your Observed value, the number you measured or estimated. Then enter the True value, the accepted reference it should be compared against.
Press Calculate and the tool returns the percent error using the absolute-difference definition. Enter the raw numbers without worrying about the sign; if you need direction afterward, compare the two inputs directly to see whether you ran high or low, and remember that repeated errors in one direction usually mean instrument bias rather than random noise.
Frequently Asked Questions
What formula does the calculator apply?
It applies percent error = |observed - true| / |true| * 100. The absolute bars make the result a magnitude, so 9.78 versus 9.81 gives 0.31 percent no matter which side is high.
Why divide by the true value?
Dividing by the truth puts errors on a common scale, so a 2 gram miss matters more on a 10 gram part than a 100 gram one. Ratio, not raw gap, is what comparisons need.
Can percent error be negative?
Not with the standard formula, since the absolute value strips the sign. Some fields report signed error to track over versus under prediction, but this calculator returns the magnitude only.
What counts as an acceptable percent error?
It depends on context. Analytical chemistry often expects about 1 percent or less, engineering tolerances vary by part, and demand forecasting routinely accepts 10 to 20 percent as workable.
What if the true value equals zero?
The formula breaks down because you cannot divide by zero. Use absolute error, the plain difference between observed and true, when your reference point is zero.