Percent Error Calculator
Compare a measured value against the accepted value. Shows the unsigned school formula and the signed version side by side.
Measured value against accepted value
Signed error
-5%
Absolute error
0.5
Your measurement reads low by 5%.
Percent error
5%
|9.5 − 10| ÷ 10 × 100
The percent error formula
Percent error = |Measured − Actual| ÷ |Actual| × 100
The bars mean absolute value: take the size of the gap and drop the sign. This is the form taught in school chemistry and physics, and it is always positive.
Worked example — you measured 9.5, the accepted value is 10
|9.5 − 10| = 0.5
0.5 ÷ 10 = 0.05
0.05 × 100 = 5
So the percent error is 5%.
Which value goes on the bottom
The accepted value always goes on the bottom, never your measurement. The accepted value is the fixed reference. If you divided by your own measurement, the same 0.5 gap would give a different error depending on how wrong you were, which defeats the purpose.
Keeping the sign
Dropping the sign throws away useful information. The signed form is:
Signed percent error = (Measured − Actual) ÷ |Actual| × 100
- A negative result means your measurement came in low.
- A positive result means it came in high.
A systematic bias in one direction points at a calibration problem. A scatter of errors in both directions points at random noise. The unsigned figure hides that difference, so this calculator shows both.
Percent error against percent difference
Use percent error when one value is known to be correct. Use percent difference when you have two measurements and neither is the reference — comparing two instruments, or two lab groups.
What counts as acceptable
There is no universal threshold, and any source that gives you one is oversimplifying. A school titration is usually treated as good below 5%. Measuring a physical constant might demand better than 0.1%. Ask what precision the method itself can reach before judging the number.
Common questions
- What is the percent error formula?
- Percent error = |measured − actual| ÷ |actual| × 100. Take the size of the gap between your measurement and the accepted value, divide by the accepted value, then multiply by 100.
- Should percent error be positive or negative?
- School chemistry and physics use the absolute form, which is always positive. Research often keeps the sign, because a negative error tells you the instrument reads low and a positive error tells you it reads high. This calculator shows both.
- Which number goes on the bottom of the fraction?
- The accepted or theoretical value, never your measurement. Dividing by your own measurement would make the error depend on how wrong you were.
- What counts as a good percent error?
- It depends on the experiment. A school titration is usually considered good under 5%. A precision physical constant might need to be under 0.1%. There is no universal threshold.
- What is the difference between percent error and percent difference?
- Percent error compares a measurement against a known correct value. Percent difference compares two measurements when neither is known to be correct.