Percent Error Calculator
Calculate the percent error between a measured (experimental) value and the accepted (theoretical) value, with the absolute error, relative error and the steps shown
Last updated: November 11, 2026
How to Use the Percent Error Calculator
How to use the percent error calculator
- Enter the experimental value. This is the number you measured, observed or calculated.
- Enter the theoretical value. This is the accepted or expected value, such as a textbook constant. It cannot be zero.
- Read the results. You get the percent error, whether your result is over or under, the signed percent error, the absolute and relative error, and the full working you can copy into a lab report.
Both values must use the same unit. If your measurement is in grams and the accepted value is in kilograms, convert one of them first.
As a rough guide, many school and college labs treat a percent error under 5% as good, and under 1% as excellent. Your teacher or field may use a different standard.
Formula & Methodology
The percent error formula
Percent error shows how far a measured value is from the true or accepted value, as a percentage of the accepted value:
Percent error = |Experimental − Theoretical| ÷ |Theoretical| × 100
- Experimental value: what you measured or calculated
- Theoretical value: the accepted, expected or true value
- The vertical bars mean absolute value, so the result is never negative
Worked example
In a physics lab you measure the acceleration due to gravity as 9.6 m/s². The accepted value is 9.81 m/s².
- Subtract: 9.6 − 9.81 = −0.21
- Take the absolute value: |−0.21| = 0.21
- Divide by the accepted value: 0.21 ÷ 9.81 = 0.0214
- Multiply by 100: 2.14%
Your measurement has a percent error of about 2.14%, and because it is lower than the accepted value it is an underestimate.
Absolute, relative and signed error
- Absolute error = |Experimental − Theoretical|. It is in the same units as your measurement (0.21 m/s² in the example).
- Relative error = Absolute error ÷ |Theoretical|. It is the percent error written as a decimal (0.0214).
- Signed percent error keeps the minus or plus sign to show whether you measured too low or too high. Some chemistry and physics courses ask for it.
Percent error vs percent difference
Use percent error when you compare a result with a known, accepted value. Use percent difference when you compare two measured values and neither one is the "correct" answer. The formula for percent difference divides by the average of the two values instead.
About Percent Error Calculator
Our percent error calculator is a free, easy-to-use tool designed to help youcalculate the percent error between a measured (experimental) value and the accepted (theoretical) value, with the absolute error, relative error and the steps shown. If you're a professional or just need quick calculations, our calculator provides accurate results instantly.
Frequently Asked Questions
How do you calculate percent error?
Subtract the theoretical value from the experimental value, take the absolute value, divide by the theoretical value and multiply by 100. For a measured 99.1 °C against an accepted 100 °C, the percent error is |99.1 − 100| ÷ 100 × 100 = 0.9%.
Can percent error be negative?
The standard formula uses absolute value, so percent error is always zero or positive. Some courses use a signed percent error, without the absolute value, so that a negative result shows the measurement was too low and a positive one shows it was too high. The calculator shows both.
What is a good percent error?
It depends on the experiment and the equipment. In most school labs, under 5% is considered good and under 1% is excellent. Precise professional measurements often need a much smaller error, while rough field estimates can accept more.
What is the difference between percent error and percent difference?
Percent error compares a measurement with a known accepted value and divides by that accepted value. Percent difference compares two measurements with no accepted value and divides by their average. Use percent error when there is a correct answer to compare against.
What is the difference between absolute and relative error?
Absolute error is the size of the gap between the measured and accepted values, in the original units. Relative error divides that gap by the accepted value, giving a unitless decimal. Multiply the relative error by 100 to get the percent error.
Why can't the theoretical value be zero?
The formula divides by the theoretical value, and dividing by zero is undefined. If the accepted value is zero, report the absolute error instead, or compare values with percent difference.
What causes percent error in an experiment?
Common causes include the limited precision of instruments, human reading error, rounding during calculations, changes in temperature or pressure, impure materials and flaws in the method. A large percent error is a signal to check each step.
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