How do you calculate percent error?

Subtract the true (accepted) value from your measured value, take the absolute value, divide by the absolute value of the true value, and multiply by 100. For a measurement of 90 against a true value of 100, that is |90 - 100| / 100 x 100 = 10%.

Can percent error be negative?

As usually defined, no: the absolute value bars make it positive whichever side you missed on. Some courses do keep the sign, writing (measured - true) / true x 100, so a low measurement shows as negative. Follow your course convention, and either way say in words whether you ran high or low: the direction is real information about your setup.

What is the difference between percent error and percent difference?

Percent error assumes one of the two values is the accepted truth and divides by it. Percent difference assumes neither value outranks the other and divides by their average, which makes it symmetric. Comparing 90 and 100 gives a 10% error against a true value of 100, but a 10.53% difference.

What if the true value is zero?

Then percent error is undefined, because the formula divides by the true value, and division by zero has no answer. The honest move is to report the absolute error instead. This comes up with quantities measured around zero, like a temperature in Celsius, where the zero point is a chosen reference rather than a real absence.

Is a high percent error bad?

It is a finding, not a failure. A large error with a clear explanation (a warm ruler, a slow stopwatch, a draft on the balance) makes a better lab report than a suspiciously perfect number with no discussion. The question that matters is whether the error is about what your instrument can deliver, and what you learned from the gap.

Why do you divide by the true value and not the measured value?

Because the true value is the yardstick: percent error grades your measurement against the accepted answer, so the accepted answer sets the scale. Dividing by your measured value gives a different number (11.11% instead of 10% for a measurement of 90 against a true value of 100) and it changes with every measurement you make, which is exactly what a yardstick must not do.

Percent Error Calculator: Measured vs True Value

Enter your measured (experimental) value and the true (accepted) value. You get the absolute error, the percent error with every substitution of the formula shown, and whether your measurement ran high or low.

How percent error works

Percent error answers one question: how far did my measurement land from the accepted value, as a share of that accepted value? You time a pendulum and get gravity at 9.8 m/s², the textbook says 9.81, the gap is 0.01, and 0.01 is about 0.102% of 9.81. The division is the whole point: an error of 2 means nothing until you know whether you were measuring a 4 cm bolt or a 4,000 km coastline. Dividing by the true value puts every measurement, in any unit, on the same scale.

And one thing worth saying plainly, because lab courses rarely do: a big percent error is a result, not a verdict on you. It is information about your instrument, your technique, or occasionally the fine print behind the accepted value, and the interesting part of a lab report is explaining where the gap came from. Some of the best writeups have the largest errors and the sharpest explanations.

The formula

percent error = |measured - true| ÷ |true| × 100

measured is your experimental value, true is the accepted or theoretical value, and the vertical bars mean absolute value. The true value goes in the denominator because it is the yardstick you are grading against; the absolute value on top is why percent error is normally reported as a positive number, whichever side you missed on. The direction still belongs in your report in words, and this calculator states it for you.

Worked example

You time a pendulum and calculate g = 9.8 m/s². The accepted value is 9.81 m/s².

Absolute error = |9.8 - 9.81| = 0.01. Divide by the true value: 0.01 ÷ 9.81 = 0.001019. Multiply by 100: percent error = 0.102%. And since 9.8 sits below 9.81, your measurement came in 0.102% low, which is the sentence a lab report actually wants.

Percent error, percent difference, percent change: same numbers, three answers

Three formulas wear this costume, and the only thing that changes is the denominator. Run one pair of numbers, 90 and 100, through all three:

Percent error treats one value as the truth and divides by it: |90 - 100| ÷ 100 × 100 = 10%. Use it when 100 is the accepted value and 90 is your measurement.
Percent difference treats neither value as the truth and divides by their average: |90 - 100| ÷ 95 × 100 = about 10.53%. That is the right tool for two peer measurements with no referee, and our percentage difference calculator owns it.
Percent change is directional and divides by the starting value: 100 to 90 is -10%, while 90 to 100 is +11.11%. That is percentage calculator territory: the same thing measured at two times, before and after.

One pair of numbers and defensible answers of 10%, 10.53%, -10% and +11.11%. None of them is wrong; they answer different questions, which is why a lab report names its formula and why this page divides by the true value and says so. It also means the classic mistake, dividing by your measured value, is not random noise: it quietly computes the percent change from your measurement back to the truth, an answer to a question nobody asked.

What counts as a good percent error

Honestly: it depends on the instrument and the field, and any single number offered for all of science is a guess. A meter stick and a stopwatch in an intro physics lab often land within 5 to 10% of the accepted value, and that is a solid result for that equipment. A buret in a titration should get you inside about 1%. A calibrated analytical balance lives below 0.1%, and a mass spectrometry lab argues about parts per million. A ruler and a mass spectrometer live on different planets, so the question a report should answer is not "is 4% good" but "is 4% about what this equipment can deliver, and if not, what happened?"

To shrink the error, the honest levers are the boring ones: a better or freshly calibrated instrument, technique fixes like reading the meniscus at eye level, and more trials averaged together, since random wobbles partially cancel. Averaging cannot fix a systematic error, though: a scale that reads 2 grams heavy does it on every trial, and the average is 2 grams heavy too. That is exactly the story the signed direction of your error helps you tell, and our significant figures calculator will keep you honest about how many digits of that answer you have actually earned.

Percent Error Calculator