Percent Error Calculator
Compare a measured value to the true value.
Results update as you type.
How it works
Percent error measures how far an experimental or measured value strays from the true, accepted, or theoretical value, expressed as a percentage of that reference. It is the standard way scientists, students, and engineers report the accuracy of a measurement, because a raw gap of one gram means something very different when you expected a kilogram than when you expected two grams. This percent error calculator takes your experimental result and the theoretical value, then returns both the absolute error and the percent error so you can judge a reading at a glance. The absolute error is simply the size of the gap between the two numbers, ignoring sign, while the percent error scales that gap against the magnitude of the accepted value. A small percent error signals a precise, trustworthy measurement, whereas a large one points to flawed technique, faulty equipment, or a wrong assumption. In a physics lab measuring gravity, comparing a reading of 9.8 against the accepted 9.81 gives a percent error near 0.1 percent, which is excellent. Chemists checking reaction yields, engineers validating instruments, and teachers grading experiments all rely on this percent error calculator to quantify accuracy consistently rather than eyeballing whether a result is close enough.
percent error = |experimental − theoretical| ÷ |theoretical| × 100
Percent error divides the absolute error by the magnitude of the accepted value, then multiplies by one hundred to express it on a familiar percentage scale. Taking the absolute value of the difference ensures the result stays positive whether the measurement overshoots or undershoots. Dividing by the theoretical value rather than the measured one keeps the reference fixed, so identical gaps against different true values report different, correctly weighted percentages.
Source:Standard mathematics
We review all our tools from time to time to ensure accuracy.
Worked example
How to use this calculator
- 1
Enter your values
Enter experimental value and theoretical value.
- 2
Adjust the options
Fine-tune any options to match your situation.
- 3
Read your result
Percent error updates instantly as you type — no button to press.
Frequently asked questions
What is a good percent error?
There is no single threshold, because acceptability depends on the field and the equipment involved. In a school physics lab, anything under about five percent is usually considered good, and under one percent is excellent. Precision engineering and analytical chemistry often demand errors well below a tenth of a percent. Always compare your result against the tolerance expected for that specific experiment rather than a universal number.
Why divide by the theoretical value?
The theoretical or accepted value is treated as the correct reference, so measuring your error against it tells you how wrong the experiment was relative to the truth. Dividing by the experimental value instead would scale the gap against a number you already suspect is inaccurate. Using the accepted value keeps the comparison consistent, so two labs testing the same quantity report percentages that can be fairly compared side by side.
Can percent error be negative?
By the standard definition it cannot, because the formula takes the absolute value of the difference before dividing. That keeps the result positive whether your measurement came out higher or lower than the accepted value. Some instructors do ask for a signed version to show the direction of the deviation, in which case you drop the absolute value bars, but the conventional percent error reported here is always zero or positive.
What is the difference between percent error and percent difference?
Percent error compares a measurement against a known correct value, so one number is trusted as the reference. Percent difference compares two experimental values when neither is considered the true answer, dividing by their average instead. Use percent error when checking a result against a textbook or accepted constant, and percent difference when comparing two independent measurements of the same quantity to each other.
What causes a large percent error?
A high percent error usually points to systematic or random problems in the experiment. Common culprits include miscalibrated instruments, misread scales, environmental factors like temperature or air resistance, and simple arithmetic mistakes. It can also reveal a flawed method or an incorrect assumption in the underlying theory. Identifying whether the error is consistent or scattered helps you decide whether to recalibrate equipment or repeat the measurement more carefully.