Percent Error Calculator
Your measured value against the accepted value: the percent error, signed and absolute, with the working.
The calculator never sends or saves what you type.
Comparing a lab product with its theoretical yield? Percent yield calculator. Two measurements, neither one accepted? Percentage difference calculator.
The percent error formula
Percent error = |Measured − Accepted| ÷ |Accepted| × 100
The measured value is what your experiment gave you — also called the experimental or observed value. The accepted value is the reference you compare it with: a textbook constant, a manufacturer's figure, the theoretical yield. The divisor is always the accepted value, because the question is how far you are from the truth, measured in units of the truth.
Before the ×100 the same ratio is the relative error, a decimal: 0.0214 is a relative error of 0.0214, or a percent error of 2.14%.
Signed or absolute percent error
The standard formula takes the absolute value, so percent error is a size and is never negative. Many lab courses also want the signed version, which keeps the direction: (measured − accepted) ÷ |accepted| × 100 is negative when your result came out low and positive when it came out high. A consistent sign across repeated trials is the tell-tale of a systematic error — a miscalibrated scale, heat lost to the room — rather than random scatter.
Conventions vary: a few textbooks subtract the other way round, (accepted − measured), so check which your course uses before you write the sign down. The calculator shows the unsigned percent error as the answer, the signed figure under it, and the absolute error — |measured − accepted|, in the measurement's own units — beside both.
A worked example
Chemistry: you measure the density of an aluminium block as 2.55 g/cm³. The accepted value is 2.70 g/cm³.
- Absolute error: |2.55 − 2.70| = 0.15 g/cm³
- Relative error: 0.15 ÷ 2.70 = 0.0556
- Percent error: 0.0556 × 100 = 5.56%
- Signed: the measurement is low, so −5.56%
Physics works the same way. Timing a pendulum gives g = 9.6 m/s² against the accepted 9.81 m/s²: |9.6 − 9.81| = 0.21, and 0.21 ÷ 9.81 × 100 = 2.14% — a result 2.14% low. Units cancel in the division, so a percent error never carries any; the absolute error always does.
Percent error, percent difference, percentage change
Three close relatives that divide by different things, and picking the wrong one is the commonest mistake in a lab write-up:
| Measure | Divides by | Use it when |
|---|---|---|
| Percent error | the accepted value | one value is known to be correct |
| Percent difference | the average of the two | neither value is the reference |
| Percentage change | the starting value | something moved from one value to another |
Percent error is percentage change with the sign dropped, measured from the accepted value to yours. Percent difference is the odd one out: with no reference it uses the average, so swapping the two numbers gives the same answer. The percentage difference calculator works it through, with the gap and the average.
When percent error is over 100%
There is no ceiling. A measurement of 25 against an accepted 10 is off by 15, and 15 is 150% of 10. Exactly 100% means you measured 0, or twice the accepted value. Past 100% the cause is rarely experimental scatter: look for a unit slip (grams for kilograms, cm for m), a misplaced decimal point, or the two values entered the wrong way round.
Temperatures are the other trap. Celsius and Fahrenheit have arbitrary zeros, so the same 2-degree miss on boiling water is 2% of 100 °C but only 0.54% of 373.15 K. Convert to kelvin before dividing; close to 0 °C a Celsius percent error is meaningless, and at exactly 0 °C it cannot be computed.
Percent error in Excel or Google Sheets
With the measured value in A1 and the accepted value in B1, enter =ABS(A1-B1)/ABS(B1) and format the cell as a percentage. For the signed version, drop the first ABS: =(A1-B1)/ABS(B1). Fill the formula down a column to get the percent error of every trial at once.
Frequently asked questions
What is the formula for percent error?
Percent error = |measured − accepted| ÷ |accepted| × 100. Subtract the accepted (true) value from your measured value, drop the sign, divide by the accepted value and multiply by 100. Measuring g as 9.6 m/s² against 9.81: |9.6 − 9.81| = 0.21, 0.21 ÷ 9.81 = 0.0214, so the percent error is 2.14%.
Can percent error be negative?
The usual definition takes the absolute value, so percent error is never negative. Some courses keep the sign — (measured − accepted) ÷ accepted × 100 — so that a negative result means your measurement came out low and a positive one high. The calculator shows both: the unsigned percent error as the answer, and the signed figure underneath.
What is a good percent error?
It depends on the experiment and the equipment, so the course or the method sets the bar. As a rule of thumb, introductory school and college labs often treat anything under about 5% as good and under 10% as acceptable, while careful work with precise instruments expects well under 1%. A large percent error is a prompt to look for a systematic mistake, not just a bad grade.
What is the difference between percent error and percent difference?
Percent error compares a measurement with a known correct value, so it divides by the accepted value. Percent difference compares two values when neither is known to be correct — two students’ measurements, say — and divides by their average: |a − b| ÷ ((a + b) ÷ 2) × 100. Use percent error when you have a reference value, percent difference when you do not.
Why is my percent error different in Celsius and Kelvin?
Because the Celsius zero is arbitrary, and percent error divides by the accepted value. Water boiling at 98 °C against 100 °C is a 2% error in Celsius but 2 ÷ 373.15 = 0.54% in kelvin. Near 0 °C the Celsius figure explodes and at exactly 0 °C it cannot be computed at all. Use kelvin — an absolute scale — for temperature percent errors.
Can percent error be more than 100%?
Yes. Percent error has no ceiling: a measurement of 25 against an accepted value of 10 is off by 15, which is 150% of the accepted value. Exactly 100% means the measurement was 0, or double the accepted value. An error over 100% usually points to a unit mix-up or a misread instrument rather than ordinary experimental scatter.
Why can’t the accepted value be zero?
Percent error divides by the accepted value, and nothing can be divided by zero. If the true value is 0, report the absolute error — |measured − 0| — in the measurement’s own units instead. The calculator says so rather than printing an infinite or meaningless percentage.