This free online percent error calculator measures how far an experimental (observed) value is from the theoretical (true) value, expressed as a percentage. It's commonly used in science labs and engineering to check the accuracy of measurements and experiments.
How to Use the Percent Error Calculator
Enter the value you measured or observed in the "Experimental (Observed) Value" field.
Enter the accepted or true value in the "Theoretical (True) Value" field.
Click "Calculate" to see the percent error.
Compare the result to your acceptable error tolerance to judge measurement accuracy.
How Percent Error Is Calculated
Percent error compares a measured result with a value that is accepted as correct, such as a textbook constant or a certified reference value. The calculator works in three steps:
Find the absolute error: subtract the theoretical value from the observed value and drop the sign.
Divide that difference by the absolute value of the theoretical value. This gives the relative error as a fraction.
Multiply by 100 to turn the fraction into a percentage. The result is rounded to two decimal places.
Because you divide by the theoretical value, the same absolute miss matters more for a small quantity than for a large one. Being off by 0.5 g is a 5% error on a 10 g sample but only a 0.5% error on a 100 g sample.
Worked Example: Measuring g with a Pendulum
A Class 11 physics student times a simple pendulum and works out the acceleration due to gravity as 9.62 m/s². The accepted value is 9.81 m/s². The absolute error is |9.62 − 9.81| = 0.19 m/s². Dividing by 9.81 gives 0.01937, and multiplying by 100 gives a percent error of 1.94%. Entering 9.62 as the observed value and 9.81 as the theoretical value gives the same answer.
More examples from common school and college experiments:
Experiment
Observed
Accepted value
Percent error
Density of aluminium (g/cm³)
2.65
2.70
1.85%
Speed of sound in air at 20 °C (m/s)
330
343
3.79%
Boiling point of water at sea level (°C)
98.6
100
1.40%
Mass of a 50 g standard weight (g)
52
50
4.00%
Interpreting Your Result
A low percent error means your result was close to the accepted value. It does not prove that your method was good, because two errors can cancel each other out.
What counts as acceptable depends on the experiment and the equipment. Many school lab manuals treat a few percent as reasonable for simple apparatus, while analytical chemistry or calibration work may demand far less than 1%. Check what your teacher or procedure specifies.
The calculator always reports a positive number. If you need to know whether you measured too high or too low, compare the two values yourself: observed above theoretical means an overestimate.
For temperatures, the answer depends on the scale. 98.6 °C against 100 °C is a 1.40% error, but the same readings in kelvin (371.75 K against 373.15 K) give only 0.38%. Use the scale your course or report expects, and say which one you used.
Percent Error vs Percent Difference
Percent error needs a value you trust as correct. When you are comparing two measurements and neither is the reference, for example two students timing the same event, use percent difference instead: divide the gap by the average of the two values. Readings of 52 and 48 give a percent difference of 4 ÷ 50 × 100 = 8%. Using percent error here would give 7.69% or 8.33% depending on which reading you wrongly treat as the true value.
Frequently Asked Questions
It uses Percent Error = |Observed − Theoretical| / |Theoretical| × 100. For example, if the observed value is 9.8 and the theoretical value is 10, the percent error is |9.8 − 10| / |10| × 100 = 2.00%.
Taking the absolute value of the difference and of the theoretical value keeps the percent error non-negative, so it's always reported as a plain percentage regardless of whether the observed value is higher or lower than expected.
Since the theoretical value is the denominator, a value of zero would make the calculation undefined, so the calculator shows "Theoretical value cannot be zero" instead of a result.
Absolute error is the raw gap between the measured and true values, in the same units as the measurement (for example 0.19 m/s²). Relative error divides that gap by the true value, giving a unitless fraction such as 0.0194. Percent error is the relative error multiplied by 100, so 0.0194 becomes 1.94%.
Yes. If the observed value is more than double the theoretical value, or has the opposite sign, the difference is larger than the true value itself and the percent error goes above 100%. For example, an observed value of 25 against a true value of 10 gives a 150% error. A result like this usually points to a unit mix-up or a calculation slip rather than ordinary measurement error.