In a school lab you measure the density of aluminum and get 2.61 grams per cubic centimeter. The textbook says the accepted value is 2.70. Your number is close, but how close? "Close" is not a measurement. Percent error turns that comparison into a single, honest percentage that tells you how far your experiment landed from the known truth. This tool computes it from your measured value and the accepted value.
The formula
Percent error compares the size of your mistake to the size of the thing you were measuring, then expresses it as a percentage.
Formula: percent error = |experimental - accepted| / |accepted| x 100
The absolute-value bars mean the direction of the error does not matter, only its size: being 5 percent high or 5 percent low both read as 5 percent error. Dividing by the accepted value is what makes the result a relative measure, so a 0.1 gram error on a 1 gram sample and on a 100 gram sample score very differently, as they should.
How to use it
- Enter your experimental or measured value.
- Enter the accepted or true value.
- Read the percent error. Smaller means your measurement was closer to the mark.
When your data involves counting outcomes rather than measuring quantities, the permutation and combination calculator helps with the probability side, while the factor calculator can tidy up the fractions that appear in lab math.
Worked example
A student measures the boiling point of a liquid as 78.1 degrees while the accepted value is 81.5 degrees. Step one, find the difference: |78.1 - 81.5| = |-3.4| = 3.4. Step two, divide by the accepted value: 3.4 / 81.5 = 0.0417. Step three, convert to a percentage: 0.0417 x 100 = 4.17 percent, about 4.2 percent. So the measurement was roughly 4.2 percent off. For a classroom thermometer that is a respectable result; for a calibrated lab instrument it would suggest something needs attention.
Reading the result like a scientist
Low percent error means high accuracy, but accuracy is not the whole story. Repeated measurements can cluster tightly together (precise) while all sitting far from the true value (inaccurate), which points to a systematic problem like a miscalibrated scale. Random scatter around the true value points instead to technique or reading noise. Percent error flags the accuracy question; spotting which kind of error you have tells you how to fix it.
Mistakes that distort the answer
- Dividing by the experimental value. The denominator must be the accepted value. Using your own measurement there shrinks real errors and hides problems.
- Skipping the absolute value. Signed errors can cancel across trials and fake a good average. Percent error is deliberately direction-free.
- Confusing error with uncertainty. Percent error compares you to a known truth. Measurement uncertainty describes the spread of your own readings. Different ideas, different formulas.
What it cannot tell you
The formula needs a trustworthy accepted value to compare against. In cutting-edge work where the true value is what you are trying to discover, percent error has nothing to anchor to, and uncertainty analysis takes over. It also says nothing about whether an error is acceptable; a 4 percent error in cooking is invisible, while in pharmaceuticals it can be a failed batch. The combination calculator is the companion for the sampling-probability side of experimental design.