Education
Percent Error Calculator
Enter an accepted value and an experimental value. We compute the percent error, the absolute error, and a step-by-step calculation that uses your numbers, with a clear note when the accepted value is zero.
The known, true, or theoretical value. Decimals and negatives are allowed; zero is not, because the formula divides by the accepted value. · e.g. 50
The measured or observed value from your experiment. · e.g. 48
Formula
percent error = |experimental − accepted| / |accepted| × 100
The numerator is the absolute error, so the result is reported as a positive percentage. Some advanced contexts use signed error when the direction of the error matters.
Percent error
4%
Absolute error: 2
- 1. Subtract the accepted value from the experimental value: 48 − 50 = -2
- 2. Take the absolute value of the difference: |-2| = 2
- 3. Divide by the absolute value of the accepted value: 2 / |50| = 0.04
- 4. Multiply by 100 to convert to a percent: 0.04 × 100 = 4%
In plain English: the experimental value of 48 differs from the accepted value of 50 by 2, which is 4% of the accepted value.
Examples
Accepted 50, experimental 48
4% percent error · absolute error 2
Accepted 100, experimental 110
10% percent error · absolute error 10
Accepted 80, experimental 72
10% percent error · absolute error 8
Accepted 9.81, experimental 9.74
≈ 0.71% percent error (gravity lab)
How it works
Percent error compares a measured or experimental value against an accepted or theoretical reference value, expressed as a percentage of the accepted value:
Percent error · |experimental − accepted| / |accepted| × 100
The numerator |experimental − accepted| is the absolute error: the size of the difference, with the sign dropped. Dividing by |accepted| turns that into a fraction of the accepted value, and multiplying by 100 converts the fraction into a percent.
The standard classroom formula uses absolute value so percent error is always reported as a positive percentage. When the accepted value is zero the formula is undefined, so the calculator flags that case rather than printing a misleading number.
What is percent error?
Percent error is a measure of how far an experimental or measured value is from a known accepted, true, or theoretical value, expressed as a percentage. It is the standard way to report measurement accuracy in math, chemistry, physics, and lab reports, because it scales the error against the size of the quantity being measured. A 1 cm error means very different things on a 10 cm ruler and on a 100 m field; percent error puts both on the same footing.
How to calculate percent error
- 1. Subtract the accepted value from the experimental value to get the signed difference.
- 2. Take the absolute value of the difference to get the absolute error.
- 3. Divide the absolute error by the absolute value of the accepted value.
- 4. Multiply by 100 to convert the fraction to a percent.
For example, if the accepted value is 50 and the experimental value is 48, the absolute error is 2 and the percent error is 2 / 50 × 100 = 4%.
When to use percent error
Use percent error whenever you have a known reference value to compare a measurement against. It is the right tool for accuracy: how close the measurement landed to the truth. If you only have repeated measurements without an accepted value, use standard deviation to describe how much the measurements vary among themselves. Standard deviation is about precision (closeness of repeated measurements to each other); percent error is about accuracy (closeness to truth). The two are not the same, and a precise measurement can still have a large percent error.
Percent error in chemistry and physics
Lab classes use percent error to compare a measured value against a published or theoretical reference. A density measurement that lands within a couple of percent of the textbook density is considered close; a percent error of 50% suggests the measurement, the technique, or the equipment is worth investigating. The same logic applies in physics labs for measurements like the acceleration of gravity, the speed of sound, or the specific heat of a metal. Percent error does not, by itself, tell you why a measurement is off; it tells you how far off it is, which is the first step in figuring out the why.
Common mistakes
- Forgetting the absolute value, which can produce a misleading negative percent error in the standard formula.
- Dividing by the experimental value instead of the accepted value. The accepted value is the reference, so it goes in the denominator.
- Trying to compute percent error when the accepted value is zero. The formula is undefined in that case; report the absolute error instead.
- Reporting too many decimal places. Two or three significant figures is usually enough for a lab report.
- Confusing percent error with percentage change. Percent change keeps the sign and is symmetric in the two values; percent error is reported as a positive number against a fixed reference.
Related calculators and guides
- Percent Error Formula the long-form guide with chemistry and physics examples.
- Standard Deviation Calculator for the spread of repeated measurements.
- Standard Deviation Formula with sample versus population formulas explained.
- Variance vs Standard Deviation for the relationship between the two spread measures.
- Quadratic Formula Calculator for solving ax² + bx + c = 0.
- Distance Formula Calculator for the distance between two points.
- Slope Calculator for the slope of a line through two points.
Frequently asked questions
Percent error measures how far a measured or experimental value is from an accepted, true, or theoretical value, expressed as a percentage of the accepted value. It is the standard way to report measurement accuracy in math, chemistry, and physics labs.
Percent error = |experimental − accepted| / |accepted| × 100. Subtract the accepted value from the experimental value, take the absolute value of that difference, divide by the absolute value of the accepted value, then multiply by 100. The vertical bars mean absolute value.
Subtract the accepted value from the experimental value to get the signed difference. Take the absolute value to get the absolute error. Divide the absolute error by the absolute value of the accepted value, then multiply by 100. The result is the percent error.
The standard classroom formula uses absolute value so the result is always reported as a positive percentage, which makes errors easier to compare across experiments. Whether the experimental value came in higher or lower than the accepted value is usually not the point. The point is the size of the discrepancy. Some advanced contexts do use signed error when the direction matters.
In the standard formula, no. The absolute value forces the result to be zero or positive. If you see a negative percent error, the version being used has dropped the absolute value and is reporting signed error, which preserves the direction of the difference. Both forms are valid, but the absolute-value version is the one taught in most science classes.
In a chemistry lab, percent error compares a measured value (such as the density of a metal, the molar mass of a gas, or the concentration from a titration) against the published or theoretical value. A small percent error means the measurement is close to the accepted value; a large one usually points to a measurement, technique, or equipment problem worth investigating.
Percent error is undefined when the accepted value is zero, because the formula divides by the accepted value. The calculator flags this case rather than printing a misleading or infinite number. When that happens, report the absolute error on its own, or pick a non-zero reference value.
Related calculators
Education
Final Grade Calculator
Calculate your final course grade from your current grade and your final exam score.
Education
Weighted Grade Calculator
Combine assignments, quizzes, and exams by weight to get a precise weighted course average.
Education
Final Exam Calculator
Find out exactly what you need to score on your final exam to hit your target course grade.