Percent Error and Percent Difference Calculator

How it works

Percent error says how far a measurement is from the value it should have been, as a share of that accepted value. It is the standard way to report the accuracy of a lab result against a textbook or reference figure: take the gap between measured and accepted, divide by the accepted value, and multiply by 100. The result is always reported as a positive percentage; the explanation line tells you whether you were above or below.

Percent difference is for the case where neither value is the reference, such as two students measuring the same thing or two instruments reading the same sample. Dividing by one of them would favour that one, so the gap is divided by the average of the two instead. Swapping the values gives the same answer.

Pick the calculation first. Only the two fields that calculation needs are read; the other two are ignored.

Formula

percent error      = |measured − accepted| ÷ |accepted| × 100
percent difference = |a − b| ÷ |(a + b) ÷ 2| × 100

Example

A block of aluminum is measured at 2.68 g/cm³ and the accepted density is 2.70 g/cm³. The gap is 0.02, and 0.02 ÷ 2.70 × 100 = 0.74%, so the measurement is 0.74% below the accepted value.

Two readings of 10 and 12 differ by 2. Their average is 11, and 2 ÷ 11 × 100 = 18.18%, the percent difference. Entering them as 12 and 10 gives the same 18.18%.

Assumptions and limitations

• Percent error uses the absolute value of the gap, so it is never negative. Read the explanation for the direction.
• The denominator of percent error is the accepted value, not the measured one; if the accepted value is zero the percentage is undefined.
• Percent difference divides by the absolute value of the average, so for two positive values it lies between 0% and 200%. It is undefined when the two values cancel to an average of zero.
• Results are rounded to four decimal places for display only.

Frequently asked questions