Percent Error Calculator
Calculate the percent error between an experimental (measured) value and a theoretical (accepted) value.
| Example | Experimental | Theoretical | % Error |
|---|---|---|---|
| Density measurement | 9.2 | 10.0 | 8.00% |
| Temperature reading | 98.5 | 100 | 1.50% |
| Concentration | 0.48 | 0.50 | 4.00% |
| Voltage | 4.85 | 5.00 | 3.00% |
Compare a measured (experimental) value against the accepted (theoretical) value to see exactly how far off your result was, expressed as a percentage.
How Percent Error Calculator Works
Absolute error is simply the size of the gap between your two values: |experimental − theoretical|. Percent error scales that gap relative to the theoretical value and multiplies by 100: percent error = (absolute error ÷ |theoretical|) × 100 — this version is always non-negative, since it measures "how far off" without regard to direction.
A separate "signed" percent error keeps the direction of the discrepancy: (experimental − theoretical) ÷ |theoretical| × 100. A positive signed result means your measurement overestimated the true value; a negative result means it underestimated it.
Relative error (absolute error ÷ theoretical, shown before the ×100 conversion) is the same calculation expressed as a plain decimal fraction rather than a percentage — useful in scientific contexts where relative error is reported directly rather than as a percent.
See It In Action
Who Uses Percent Error Calculator and Why
- Checking how far a chemistry lab measurement deviates from the accepted textbook value.
- Evaluating the accuracy of a physics experiment's result against a known theoretical constant.
- Determining whether a measurement overestimated or underestimated the true value using the signed error version.
- Reporting relative error as a decimal fraction for a scientific write-up that expects that format instead of a percentage.
Mistakes to Avoid
- Dividing by the experimental value instead of the theoretical (accepted) value — the formula specifically uses the theoretical value as the fixed reference point.
- Assuming percent error is always signed — the standard version is always zero or positive; only the separate 'signed' result shows over- versus under-estimation.
- Assuming there's a universal 'acceptable' percent error threshold — it depends entirely on the field and experiment, so check your course or lab's specific guidelines.
Tips for Best Results
- Use the signed percent error result specifically when you need to know the direction of the discrepancy, not just its size.
- Double-check which of your two numbers is the theoretical (accepted) value before entering them — swapping the two changes the result.
Fixing Common Problems
My percent error seems unexpectedly large. — Confirm the theoretical (accepted) value was entered in the correct field — percent error is calculated relative to it, so swapping it with the experimental value changes the result.
Terms Explained
Absolute error: The plain size of the gap between the experimental and theoretical value, before converting to a percentage: |experimental − theoretical|.
Relative error: The absolute error expressed as a plain decimal fraction of the theoretical value, before the ×100 conversion to a percentage.