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Percent Error

Also known as experimental error · accuracy check

PE=∣xmeas−xacc∣xaccPE = \frac{|x_{\text{meas}} - x_{\text{acc}}|}{x_{\text{acc}}}

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Learning zone

Percent error grades a measurement against a known truth: take the size of the miss and divide it by the accepted value. Measuring the boiling point of water as 97.0 °C when the accepted value is 100.0 °C is a 3.0% error; determining a density as 9.7 g/cm³ against a reference 10.0 gives 0.3/10 = 0.03, or 3%. Pick the % display unit to read it directly as a percentage. It is the standard closing line of a school lab report and the standard acceptance criterion in instrument calibration.

The trap is the denominator. Percent error divides by the accepted value, not by your measurement and not by the average of the two — divide by the wrong one and a 3% error becomes 3.09%, which is the sort of thing that costs marks. If there is no accepted value, because you are comparing two equally trustworthy measurements, you want percent difference instead. And note what this number is not: a small percent error means your result is accurate, but it says nothing about precision. A thermometer reading 97.0 every single time is beautifully precise and still 3% wrong.

Percent Error
PE=∣xmeas−xacc∣xaccPE = \frac{|x_{\text{meas}} - x_{\text{acc}}|}{x_{\text{acc}}}
Where
  • PEPE= Percent error
  • xmeasx_{\text{meas}}= Measured value
  • xaccx_{\text{acc}}= Accepted value
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