Percent Error Calculator
A percent error calculator is a scientific utility used to determine the accuracy of an experimental measurement by comparing it to an accepted or theoretical value. It calculates percent error by taking the absolute difference between the experimental value and the theoretical value, dividing that difference by the theoretical value, and multiplying the result by one hundred. The resulting percentage indicates the magnitude of deviation from the true value, with lower percentages representing higher precision. Chemists, physicists, engineers, and students use this calculator to assess experimental precision and analyze source errors in laboratory testing.
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.
Quick Answer
Calculate the percentage difference between your experimental measurement and the true, theoretical value. Enter both numbers to see the absolute percent error instantly.
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.
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