Calculate percent error from a measured value and an accepted value.
Percent Error Formula
The calculator uses a different formula for each mode you select.
Absolute percent error (magnitude only):
PE = |measured - accepted| / |accepted| * 100
Signed percent error with the default magnitude denominator:
PE = (measured - accepted) / |accepted| * 100
Percent difference (two measured values, no accepted reference):
PD = |A - B| / ((|A| + |B|) / 2) * 100
Solve for a measured value from nonnegative percent-error magnitude p:
measured = accepted ± |accepted| * p / 100
- PE = percent error, expressed as a percentage
- PD = percent difference, expressed as a percentage
- measured = the experimental value you obtained
- accepted = the true, theoretical, or reference value
- A, B = the two values being compared in percent difference mode
Absolute percent error is nonnegative. Default signed error divides measured minus accepted by the magnitude of the accepted value, so its sign follows the numeric above/below direction. The advanced signed-denominator option divides by the accepted value itself; for a negative reference its sign reverses that direction, so read the explicit comparison. Conventions vary by method. Percent difference here uses the average-magnitude convention shown above, with neither measurement treated as correct. It is undefined when both are zero and equals 200% across opposite signs or when only one value is zero, so it cannot distinguish relative magnitudes across zero. Inverse mode takes a nonnegative magnitude and returns accepted plus or minus its absolute error; the higher and lower possibilities coincide at zero error.
How to Read Your Percent Error
There are no universal 2%, 5% or 10% pass/fail cutoffs. Compare the result with the applicable method, instrument specification, assignment or regulatory criteria. The percentage alone does not establish measurement quality.
| Result | Interpretation |
|---|---|
| 0% absolute error | Measured and accepted values agree numerically; this alone does not establish uncertainty. |
| Nonzero absolute error | Compare with the tolerance required by the applicable method. |
| Positive or negative signed error | Check the chosen denominator convention and explicit higher/lower comparison. |
| Small nonzero reference | A modest absolute difference can produce a large percentage. |
The next table shows which mode fits the situation you are in.
| Situation | Mode to use |
|---|---|
| You have a known true value | Absolute or signed percent error |
| You need to know if you overmeasured or undermeasured | Signed percent error |
| You compare two measurements; neither is correct | Percent difference |
| You know the target error and want the measured value | Solve for measured |
Example Problems
Example 1. You measure the density of a metal as 8.92 g/cm3. The accepted value is 8.96 g/cm3. Using absolute percent error: |8.92 - 8.96| / |8.96| * 100 = 0.04 / 8.96 * 100 = 0.45%. The absolute difference is 0.04 g/cm3; acceptability depends on the applicable criteria.
Example 2. Two students measure the same resistor and get 100 ohms and 104 ohms. Neither value is the accepted reference, so use percent difference: |100 - 104| / ((100 + 104) / 2) * 100 = 4 / 102 * 100 = 3.92%.
Frequently Asked Questions
Can percent error be negative? In absolute mode it cannot, because the absolute value forces the result to zero or higher. In signed mode it can: a negative value means your measured value was lower than the accepted value, and a positive value means it was higher.
What is the difference between percent error and percent difference? Percent error compares a measured value to an accepted or true value and divides by that reference. This calculator’s percent difference compares two values when neither is treated as correct and divides by the average of their magnitudes. Use percent error when you have a known correct value and percent difference when you do not.
Why is my percent error so large? A large percentage can arise from a small reference as well as from a substantial absolute difference; it does not by itself diagnose a faulty instrument or mistake. Check compatible units and the intended reference, inspect absolute error, and compare with the method’s requirements. Percent error is undefined at a zero reference. Display precision does not establish measurement accuracy.
