How to use the percent error calculator
- Enter your experimental value: the number you measured or calculated in the lab.
- Enter the theoretical value: the accepted, true or textbook value you are comparing against.
- Read the percent error. The calculator also shows the signed error, which tells you whether you came in high or low, and each step of the working.
The percent error formula
The experimental value is what you got. The theoretical value is the reference you trust. The vertical bars mean absolute value, so the usual percent error is never negative: it only measures how big the miss was. The signed version drops the bars on the top, so a positive answer means your value was too high and a negative one means it was too low.
Worked example
The calculator starts with a classic physics lab: timing a falling object gave a gravitational acceleration of 9.6 m/s², and the accepted value is 9.81 m/s².
- Difference: 9.6 − 9.81 = −0.21.
- Absolute value: |−0.21| = 0.21.
- Divide by the accepted value: 0.21 ÷ 9.81 = 0.0214067.
- Multiply by 100: 0.0214067 × 100 = 2.14%.
The signed percent error is −2.14%, so the measurement was an underestimate. If the same experiment had given 10.2 m/s², the error would be 0.39 ÷ 9.81 × 100 = 3.98%, this time an overestimate.
Absolute, relative and percent error
The three terms describe the same miss in different units:
| Measure | Formula | Gravity example |
|---|---|---|
| Absolute error | |E − T| | 0.21 m/s² |
| Relative error | |E − T| ÷ |T| | 0.0214 |
| Percent error | relative error × 100 | 2.14% |
Absolute error keeps the units of the measurement, so it only makes sense next to the value itself. Relative and percent error have no units, which lets you compare the accuracy of very different measurements. Being 2 cm off on a 2 m table is a 1% error, while being 2 cm off on a 10 cm pencil is 20%.
What counts as a good percent error?
It depends on the equipment and the experiment. In a school lab with a stopwatch and a meter stick, results within about 5% are often considered good, and 10% may be acceptable. In analytical chemistry or precision engineering, tolerances can be far below 1%. Your teacher or the method you are following usually sets the limit.
Percent error measures accuracy (closeness to the true value), not precision (how close repeated measurements are to each other). A set of readings can agree closely with each other and still all be wrong by the same amount if the instrument is miscalibrated.
Frequently asked questions
Can percent error be negative?
The standard percent error uses absolute values, so it is always zero or positive. Some textbooks and lab manuals use the signed version instead, where a negative result means your measurement was below the accepted value. The calculator shows both so you can report whichever your class uses.
Why can't the theoretical value be zero?
The formula divides by the theoretical value, and dividing by zero has no answer. If the accepted value is 0, report the absolute error instead, for example "the reading was 0.03 V away from zero".
Is percent error the same as percent difference?
No. Percent error compares a measurement with a known correct value and divides by that value. Percent difference compares two measurements where neither is the reference, and it divides by their average. You can work out percent difference with the percentage calculator.
How many decimal places should I report?
Match the precision of your data. If your measurement has two or three significant figures, a percent error to two or three significant figures, such as 2.14%, is plenty. The rounding calculator can round to significant figures for you.
Related calculators
- Percentage Calculator — Percent of a number, what percent one number is of another, percentage change and difference.
- Rounding Calculator — Round to decimal places, significant figures, the nearest 10, 100 or 1,000, or the nearest fraction, with six rounding rules.
- Scientific Notation Calculator — Convert numbers to scientific, E and engineering notation and back, and add, subtract, multiply or divide in a × 10ⁿ form.
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