Percent Error Calculator
Compare a measured value with an accepted or reference value. The calculator reports absolute error, signed error, relative error, percent error, and a short interpretation note.
Formula
|measured - accepted| / accepted
Outputs
Absolute + signed
Use
Lab reports
Live calculator
Measured vs accepted value
Percent error
0.102041%
Absolute error
0.01 m
Signed error
0.01 m
Relative error
0.00102
| Signed percent error | 0.102041% |
|---|---|
| Absolute percent error | 0.102041% |
| Interpretation | The measured value is within 1% of the accepted value for this calculation. |
Scope note
Percent error compares one measured value with a reference value. It does not prove precision, repeatability, calibration status, or whether the experiment meets a formal tolerance.
Formula
|measured - accepted| / accepted
Outputs
Absolute + signed
Use
Lab reports
Compare measured and accepted values clearly
Percent error
Calculate the absolute percent difference from the accepted reference value.
Signed difference
See whether the measured value is above or below the accepted value.
Relative error
Review the decimal error ratio before it is converted into a percent.
Percent error formulas used on this page
Percent error expresses the size of a measurement difference relative to the accepted value. It is an accuracy check, not a full uncertainty analysis.
Working formulas
Absolute error
absolute error = |measured - accepted|
The unit stays the same as the original measurement.
Relative error
relative error = absolute error / |accepted|
The denominator is the magnitude of the accepted value.
Percent error
percent error = relative error x 100
The calculator also shows signed percent error for direction.
Symbols
- measured - measured value
- The experimental or calculated value being compared.
- accepted - accepted value
- The reference value used as the comparison basis.
- | | - absolute value
- Removes the sign when reporting the size of the error.
- % - percent form
- The relative error multiplied by 100.
Interpret this calculation before using it
Percent error compares the absolute difference between an experimental value and a nonzero accepted or reference value with that reference value. The absolute value makes the reported percentage nonnegative, while signed error should be retained separately when direction matters. Percent error is not the same as percent difference between two peer measurements.
Worked example
If an experimental result is 98 and the accepted value is 100 in the same units, percent error = |98 - 100| / |100| x 100 = 2%. The signed error is -2 units, which shows the measurement is low even though percent error is reported as positive. Entering inconsistent units would make both quantities meaningless despite valid arithmetic.
Assumptions to keep
- Experimental and accepted values describe the same measurand and use compatible units and conditions.
- The accepted value is nonzero; a zero denominator makes this relative calculation undefined.
- Input precision and significant figures come from the measurements, not from the number of digits the calculator can display.
Limits of this result
A small percent error does not establish method validity, and a large one does not identify the cause. Calibration, bias, repeatability, uncertainty, sampling, and transcription need separate analysis. Use this page for a classroom comparison and report units, signed difference, and measurement uncertainty where the work requires them.
Useful next step: Significant Figures Calculator — Round the reported comparison according to the measurement precision rather than copying every display digit.
Percent error with direction and unit labels included
Error rows for report writing
- Absolute error keeps the original unit label for lab-report sentences.
- Signed error shows whether the measurement is high or low compared with the accepted value.
- Relative error and percent error are displayed separately to make the formula auditable.
- The calculator flags accepted values of zero because percent error cannot use a zero denominator.
Accuracy scope
- The page explains that percent error is an accuracy comparison, not a precision or repeatability test.
- FAQ answers distinguish signed error, absolute error, and relative error.
- Related links connect percent error to significant figures and density measurements.
- The guide uses OpenStax and NIST terminology references for measurement context.
Percent error support for lab reports
Students
Check lab-report arithmetic while keeping unit labels, accepted values, and rounding choices visible.
Lab classes
Create source-backed examples for density, percent error, and measurement precision discussions.
Report reviewers
Audit whether a result includes the formula, substitution, units, precision, and scope notes.
How it works in three quick steps.
Enter measured value
Type the value observed or calculated from your experiment.
Enter accepted value
Type the reference value from the lab handout, data table, or source used for comparison.
Read error rows
Review signed error, absolute error, relative error, and percent error before writing the report sentence.
Save or print a percent error result
Copy the calculation
Copy the result with units and assumptions so it can be pasted into notes or a draft report.
Print the result
Print inputs, outputs, formula notes, FAQ answers, and related lab-calculation links.
Attach to a report
Use the formulas and table rows below the calculator to document the arithmetic clearly.
Frequently Asked Questions
What is percent error used for?
Why does the calculator show signed error?
Can the accepted value be zero?
Is percent error the same as percent difference?
Does low percent error mean the experiment was precise?
Related lab error and measurement tools
Why percent error needs both absolute and signed views
Percent error is often introduced as one short formula, but lab reports usually need more context. The absolute value tells how far the measured value is from the accepted value. The sign tells whether the measurement was high or low. Toolarithm's Percent Error Calculator keeps both views visible so the final percent does not hide useful interpretation.
The calculator is intended for educational measurement reports. It does not define an acceptable tolerance by itself, because tolerances depend on the experiment, instrument, rubric, and source value. The result should be paired with significant-figure rules, units, repeated-trial precision, and the lab's expected error discussion.
Who maintains this page
Ownership and review
Written and maintained by the Toolarithm editorial team. No review date is shown without a maintained editorial record. No independent professional review is claimed.
Methodology
The method identifies the governing relationship, units, significant assumptions, and educational scope. SI terminology is checked against the BIPM reference.
Read the editorial methodologyDates and sources
Review dates change only after a substantive method or content check.
Keep building