TL;DR: Percent error = |experimental − accepted| / accepted × 100. The accepted value is the whole, not the experimental, not the average of the two, not 100 because you measured in a 100 mL cylinder. Absolute error is the numerator without the division. Lab rubrics want both, with units on absolute and % on the percent.
Accepted is not “the number I like”
Accepted might be a textbook density, a calibrated mass, or a class consensus the instructor named. Your first trial is not accepted just because you were careful. If there is no accepted value, you cannot have percent error. You can have a range, a standard deviation, a percent difference between two trials (a cousin formula with a different denominator convention). Do not relabel percent difference as percent error to look official.
Percent difference often uses the average of two experimentals as the whole. Percent error uses accepted. Swap those wholes and the lab report argues with the key.
Absolute value is a policy
Most intro labs want a positive percent error. The sign of (exp − accepted) is still worth a sentence: high or low. Some instructors want signed percent error without absolute value. Follow the rubric. Applying absolute value and also writing “too high” is coherent. Applying absolute value and claiming direction in the number is not.
If exp = accepted, percent error is 0%, a success, not a missing calculation. Write 0%, not “N/A because perfect.”
Sig figs and the theater of 0.000%
If accepted is 2.0 g/mL (two significant figures) and you compute 0.37% error, do not report 0.37281%. The division can manufacture digits the masses did not earn. Match the spirit of the measurements. A calculator will give many digits. You will throw most of them away on purpose.
If absolute error is smaller than the instrument’s resolution, a tiny percent error may be luck. Discuss resolution. A 0.01% error on a blunt ruler is a confession, not a trophy.
When accepted is small
Accepted 0.02, experimental 0.03, absolute error 0.01, percent error 50%. Large percents on small wholes are honest and scary. They do not mean you spilled a liter. They mean the whole was a mouse. Compare also the absolute error to what the lab can tolerate in original units. Both stories belong in the conclusion.
Accepted 0 is toxic: division by zero. You cannot percent-error against a true zero quantity (no contaminant). Use absolute error, or a detection limit as a stand-in if the instructor allows, labeled as stand-in.
Propagating nothing by accident
If you computed accepted with a percent of its own (a 5% impure reagent), that 5% is not your percent error. Your percent error compares your result to the value you were told to treat as accepted. Mixing reagent purity into the percent error formula without a proper uncertainty section is stew.
Multiple trials: some classes want percent error on the mean. Some want it on a representative trial. Some want it on each trial. Means shrink random scatter; they do not shrink a biased method. A tiny percent error on a mean can hide wild trials. Show the trials.
Worked lab line
Accepted density 1.00 g/mL, measured 0.96 g/mL. Absolute error 0.04 g/mL. Percent error 4%. Write units on 0.04, percent sign on 4. If 0.96 was 0.961, do not pretend 3.9% vs 4% is a new theory until the scale earns it. Then a sentence: low, possibly leftover water in the cylinder. The sentence is science. The 4% is the caption.
Percent error versus percent yield
Chem yield is actual/theoretical × 100, a part/whole, not |diff|/accepted. You can have 80% yield and 5% error on a density, in one lab, about different quantities. Copy-pasting the error formula into a yield blank produces nonsense like 20% error when they wanted 80% yield (if you did 1−yield by accident). Name the quantity. Density error is not yield.
If theoretical is 2.0 g and you got 1.6 g, yield is 80%, absolute shortfall 0.4 g. Percent error on mass if 2.0 was accepted is 20%. 80 and 20 sum to 100 here because yield + shortfall/theoretical = 1. That identity fails if yield uses a different theoretical than the accepted mass. Do not assume 100 − yield = percent error in every column of a notebook.
Class average as a fake accepted
Using the class mean as accepted turns percent error into a measure of how close you were to classmates, not to a true density. That can be an interesting extra, and it is not the lab’s accepted unless the instructor said the mean is the standard. A 2% “error” from the mean with an 8% error from the textbook is a method bias the mean hid. Report the textbook accepted first. Class mean comparisons go in a sentence, not in the official percent-error slot.
A density lab with a brass cube
The handbook density for the alloy is 8.40 g/cm cubed. Your cube mass and calipers give 8.07. Absolute error is 0.33 g/cm cubed. Percent error uses the handbook as the whole: 0.33 / 8.40 times 100, about 3.9%. Dividing 0.33 by your own 8.07 instead produces about 4.1% and quietly changes the assignment into a percent difference against yourself. The rubric asked for error against the accepted value. A partner who averages 8.40 and 8.07 and divides by that average has invented a third whole the lab sheet did not name.
If the scale was tared wrong and you report 80.7 because a decimal slipped, percent error explodes past 800% and the story is a data-entry fault, not a porous metal. Sanity-check the experimental number against the handbook before you decorate it with a percent. A tenfold miss is a transcription, and the percent will shout it if you let the accepted value stay in the denominator.
Tablet counts in a pharmacy tech drill
The stock bottle is labeled 100 tablets. The tray count is 96. Percent error is 4/100 times 100% = 4%, with the label as accepted. Reporting 4/96, about 4.2%, makes the miscount the whole and slightly flatters the procedure. If the “accepted” value was a classmate’s count of 97 because the instructor never opened the label, you do not have percent error. You have two experimentals. Say so. Inventing an accepted value to force the formula is how lab reports look complete and argue with the key.
