Percent Error Calculator

Why is my percent error negative?

This calculator keeps the sign. A negative result means your measurement came in below the accepted value, a positive one means above. For 98.6 measured against 100 it shows −1.4% and “Low (under-estimated)”. Many textbooks and lab manuals quote percent error as a positive number; the |Percent Error| row gives exactly that.

Which number goes in the denominator?

The theoretical, accepted value, taken as an absolute value. Swapping the two inputs therefore changes the percentage: 24.1 measured against 22.4 gives 7.5893%, while treating 22.4 as the measurement of 24.1 would give a different figure. If neither number is a trusted reference, you want percent difference or percent change instead.

What if the theoretical value is zero?

The calculator returns an error, because dividing by zero has no meaning. A relative error is not defined when the true value is zero. Report the absolute error instead, which is the size of the difference in the original units.

How does it handle negative accepted values?

The denominator uses the absolute value of the accepted value, so the sign of the percent error always reflects whether the experimental number is above or below the accepted one. With −3 measured against −4, the signed error is +1 and the percent error is 25%. Note that “High” here means numerically larger, so −3 is classed as high relative to −4 even though its magnitude is smaller.

What counts as an acceptable percent error?

There is no universal threshold. It depends on the instrument, the method and the course or industry standard, and the calculator does not judge pass or fail. Use the tolerance given in your lab instructions or specification.

Is percent error the same as uncertainty?

No. Percent error compares one result with a known reference, so it requires an accepted value. Uncertainty describes the spread you expect from the measurement process itself and can be stated without any reference value. A small percent error from one trial does not prove the method is precise.

How many decimals are shown?

Percentages and errors are rounded to four decimal places, with trailing zeros dropped. A very small error, such as 0.00004%, displays as 0%, so the Direction row is the one that confirms the values are not exactly equal.