This percent error calculator compares an experimental value to an accepted value and reports how far off the measurement is as a percent. Enter both numbers to apply |experimental – accepted| ÷ |accepted| × 100. The default pair 9.8 and 10 returns 2 percent error.
Students use it for lab write ups. Technicians use it when a reference standard is known. For related math checks, try the slope calculator or the exponent calculator when your lab work needs those steps too.
How the formula works
Subtract accepted from experimental, take the absolute value, divide by the absolute accepted value, then multiply by 100. Absolute value keeps the result positive whether you overshot or undershot the reference.
Worked example
Experimental 9.8, accepted 10. Absolute difference 0.2. Divide by 10 to get 0.02. Multiply by 100 to get 2 percent.
| Input | Value |
|---|---|
| Experimental value | 9.8 |
| Accepted value | 10 |
| Percent error | 2% |
How to use the fields
- Experimental value is what you measured or calculated in the trial.
- Accepted value is the reference, theoretical, or true value for the comparison.
When percent error is the right metric
Use it when a trusted accepted value exists: a published constant, a calibrated standard, or a textbook answer key. If you only have two imperfect measurements and no reference, percent difference or uncertainty analysis fits better.
Common mistakes
- Dividing by the experimental value instead of the accepted value
- Dropping the absolute value and reporting a signed percent as if it were standard percent error
- Mixing units between the two inputs
- Entering zero as the accepted value
Lab report habits
State both raw values, show the formula once, then give the percent. Note instrument precision so readers know whether a 2 percent result is meaningful. If replicates exist, compute percent error for each trial or for the mean, and say which path you chose.
Significant figures
Do not invent more digits than your measurement supports. A calculator can return many decimals; your report should match lab rounding rules. The default example lands cleanly at 2 percent, which is easy to check by hand.
Comparing methods
Run the same accepted value against results from two methods. The method with the smaller percent error is closer to the reference under this metric. Still read method notes: a closer number from a biased procedure can mislead if you ignore how the data were collected.
Classroom practice
Ask learners to estimate before calculating. A measured 9.8 against 10 should be a small single digit percent, not 20 or 200. Estimation catches swapped inputs and forgotten multiplication by 100 faster than rechecking algebra alone.
Write the absolute difference on its own line. That habit makes it obvious when someone subtracted in the wrong order or forgot absolute value.
Beyond a single trial
One percent error number does not replace a full error analysis. Random scatter, systematic bias, and calibration drift need separate discussion. Treat this tool as the quick reference comparison step, then document uncertainty with the methods your course or workplace requires.
If the accepted value itself is an average of standards, cite the source so reviewers can repeat the check.
Reporting for different audiences
A lab notebook can show the full formula and intermediate absolute difference. A short executive note may only need the final percent with the two raw values. Match the depth to the reader while keeping the same arithmetic so nobody argues about a rounded shortcut.
When several trials exist, decide whether you report percent error on each trial, on the mean, or both. Say which choice you made in one clear sentence beside the table.
Accepted value sources
Accepted values can come from textbooks, calibrated instruments, or published constants. Cite the source so a reviewer can repeat your percent error with the same reference. If the accepted value is itself an average of standards, note that too.
Changing the accepted value changes the percent even when your experimental reading stays fixed. Keep the reference stable across a lab series unless the protocol updates it on purpose.
Relative scale intuition
A 2 percent error on a large accepted value is a different absolute miss than 2 percent on a tiny accepted value. The formula already divides by the accepted magnitude, which is why percent error is useful for comparing accuracy across scales.
Still narrate absolute difference when safety tolerances are written in raw units rather than percents.
Limitations
The calculator needs a non-zero accepted value and matching units. It does not model instrument error bars, confidence intervals, or outlier rejection. Use it for the classic percent error definition only.