Use this percent error calculator to compare an experimental value with an accepted value and see both the standard answer and the direction of the difference.
How to use our Percent Error Calculator
- Enter the Accepted or true value, which is the reference or expected value you are comparing against.
- Enter the Experimental or observed value, which is the value you measured in your lab or problem.
- Choose Result style to show both results, only the standard percent error, or only the signed percent error.
- Click Calculate to see Percent error, Signed percent error, Absolute error, Relative error, and the plain-English Interpretation.
- Read Percent error as the size of the mistake compared with the accepted value. This result is never negative.
- Read Signed percent error only for direction: a negative value means your measurement is below the accepted value, and a positive value means it is above.
- Use Absolute error when you want the raw gap in the original units, and use Relative error when you want that gap as a decimal instead of a percent.
- Sanity-check the output: if your experimental value is a little lower than the accepted value, the percent should be small and the interpretation should say it is lower. If the accepted value is very close to 0, expect very large percent-based results.
Definitions
Accepted or true value: The reference value you compare against. It may be called the true, expected, known, or theoretical value.
Experimental or observed value: The value you measured or got from an experiment.
Percent error: The size of the difference between the two values, compared to the accepted value, written as a percent. It is usually the main classroom answer and is 0% for an exact match [2].
Signed percent error: A percent comparison that keeps direction. Negative means the experimental value is lower than the accepted value, and positive means it is higher.
Absolute error: The raw distance between the experimental and accepted values, ignoring sign.
Relative error: The same comparison as a decimal instead of a percent. For example, 0.08 means 8%.
Interpretation: A short sentence that tells you whether your measured value is above, below, or equal to the accepted value.
Common mistakes and quick fixes
Mistake: Putting your measured number in Accepted or true value and the reference number in Experimental or observed value .
Fix: Put the known or expected reference in Accepted or true value and your lab measurement in Experimental or observed value .
Mistake: Thinking Percent error should be negative when your measurement is too low.
Fix: Use Percent error for size only, and read Signed percent error for direction.
Mistake: Entering 0 for Accepted or true value and expecting a valid percent result.
Fix: Change Accepted or true value to a nonzero reference value. Percent-based error is undefined when the accepted value is 0.
Mistake: Reading Relative error as if it were already a percent.
Fix: Remember that Relative error is a decimal. For example, 0.08 matches 8% in Percent error .
Mistake: Ignoring the plain-language Interpretation and mixing up overestimate with underestimate.
Fix: Check Interpretation after every calculation to confirm whether the Experimental or observed value is above, below, or equal to the accepted value.
Mistake: Typing only one number and leaving Accepted or true value or Experimental or observed value blank.
Fix: Enter valid numbers in both fields before clicking Calculate. Blank inputs are errors, not zeros.
Limitations & Key Assumptions / Boundary Conditions
- Percent-based outputs require a nonzero Accepted or true value. If that value is 0, Percent error and Signed percent error are undefined.
- If the accepted value is extremely close to 0, the percent results can become very large and may be misleading even when the raw difference is small.
- This calculator compares only two values. It does not estimate uncertainty, precision, repeatability, or causes of measurement error.
- Negative inputs are allowed. For negative accepted values, the sign of Signed percent error follows the formula exactly, so interpret it carefully.
- Absolute error is shown in the same original units as your inputs, but the calculator does not know or display those units for you.
- Results depend entirely on the numbers you enter. If the reference value is not actually the correct accepted value for your lab, the outputs will not be meaningful.
Methodology
How the calculator works
The calculator compares your Experimental or observed value with the Accepted or true value. It reports both the standard classroom percent error and, if chosen, the signed version so you can see direction as well as size.
Formulas used
absolute error = |experimental value - accepted value|
relative error = |experimental value - accepted value| / |accepted value|
percent error = (|experimental value - accepted value| / |accepted value|) x 100
signed percent error = ((experimental value - accepted value) / accepted value) x 100
The standard percent error formula uses the absolute difference, so the result is never negative [2]. The signed version keeps the direction to show whether your measurement is above or below the accepted value.
Worked mini-example
Suppose the accepted value is 100 and the experimental value is 92.
absolute error = |92 - 100| = 8
relative error = 8 / 100 = 0.08
percent error = 0.08 x 100 = 8%
signed percent error = ((92 - 100) / 100) x 100 = -8%
Interpretation: the measured value is 8% lower than the accepted value.
What each result means
Percent error tells you how big the difference is. Signed percent error tells you the direction. Absolute error gives the gap in original units. Relative error gives the same comparison as a decimal.
Error handling and edge cases
If the accepted value is 0, the calculator stops and shows an error because division by zero makes percent error undefined. If the accepted value is very close to 0, the calculator can still compute a result, but the percent can become extremely large from a small raw difference.
Assumptions used
This tool assumes the accepted value is the correct reference for comparison, and it treats the two inputs as direct comparable values. It does not adjust for unit conversions, repeated trials, or laboratory uncertainty.