Percent Error Calculator
Percent error = |measured - accepted| / |accepted| x 100.
Enter the measured and accepted values
Put your experimental result in the measured field and the reference value in the accepted field. The order matters, because the accepted value is the base of the whole calculation.
The accepted value usually comes from a textbook, a constants table or the instructor. If neither of your values is a recognized reference, you want percentage difference instead, which treats both numbers equally.
Reading an error percentage
The result says how large your miss is compared with the true value. A 2 percent error on a gravity measurement means the number landed within 2 percent of 9.81.
Small is not automatically good and large is not automatically failure. A 10 percent error with a ruler and a stopwatch can be honest work, while 1 percent might be suspicious from a setup that cannot measure that finely.
The formula and the absolute value
Percent error is the difference between measured and accepted, divided by the accepted value, times 100, with the sign dropped. The absolute value is the convention because the question is usually how far off, not in which direction.
Some courses keep the sign to show whether the measurement ran high or low. The signed difference is shown separately in the result, so both conventions are covered.
A gravity lab example
A pendulum experiment gives g as 9.6 meters per second squared. The accepted value is 9.81. The difference is 0.21, and 0.21 divided by 9.81 is about 0.0214, so the percent error is 2.14 percent.
Dividing by the measured 9.6 instead gives 2.19 percent. Close enough to look right, wrong enough to lose the point on a graded lab.
Errors over 100 percent and other red flags
A percent error above 100 means the measurement missed by more than the accepted value itself. Before blaming the experiment, check the units. Mixing grams with kilograms, or centimeters with meters, produces exactly this kind of result.
A zero accepted value breaks the formula entirely, since dividing by zero is undefined. Comparisons against zero need a different measure, usually plain absolute error.
Percent Error Calculator FAQ
What is the formula for percent error?
Take the measured value minus the accepted value, drop the sign, divide by the accepted value and multiply by 100.
In symbols: |measured - accepted| / |accepted| x 100.
Can percent error be negative?
Under the standard convention, no. The absolute value removes the sign. Some chemistry and physics courses keep it so the direction of the miss stays visible.
Check your course rule. The calculator shows the signed difference too, so you can report either way.
What counts as a good percent error?
There is no universal cutoff. School labs often treat anything under 5 percent as solid, but the honest answer depends on the equipment and the quantity being measured.
Judge the error against what your instruments can resolve, not against a fixed number.
Percent error or percentage difference, which one do I need?
Use percent error when one value is a recognized reference, like a published constant. Use percentage difference when comparing two measurements with no clear truth between them.
Why did I get an error over 100 percent?
The measurement is further from the accepted value than the accepted value is from zero. Unit mistakes are the usual cause, because a missing power of ten makes the percentage jump.
Does percent error account for measurement uncertainty?
No. It compares two point values and says nothing about instrument precision. Uncertainty analysis is a separate calculation that often appears alongside it in lab reports.