Percent Error Calculator
Type your measured (experimental) value and the accepted (theoretical) value to get the percent error, worked out the way lab reports expect.
Measured , accepted : what’s the error?
Percent error
1.94%
The measurement is about 1.94% below the accepted value.
How this works: Method, 3 sources, Checked against 1 worked example,
How this works
Method
Percent error says how far a measurement is from the accepted (true or theoretical) value, as a share of that value. Subtract the accepted value from your measurement, drop the sign, divide by the accepted value and multiply by 100. Full method
Sources
How it’s tested
One worked example for this page is checked by automated tests before every release: given the inputs, the tool must show the expected answer.
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Changes
- Added eight pages for common questions, from percent of a number to percent error and reverse percentages, each with its own method, examples and table.
- Added key facts with a worked example of each formula.
- Redesigned: type the numbers straight into a sentence, with bars on one scale that picture the answer.
- Results now update as you type, with no Calculate button.
- First published.
How to calculate percent error
Percent error says how far a measurement is from the accepted (true or theoretical) value, as a share of that value. Subtract the accepted value from your measurement, drop the sign, divide by the accepted value and multiply by 100.
A pendulum experiment that measured gravity as 9.62 m/s² against the accepted 9.81 m/s² is 0.19 off, and 0.19 ÷ 9.81 × 100 ≈ 1.94%. The calculator also tells you whether your value was above or below the accepted one, which the usual formula hides by taking the absolute value; some lab manuals keep the sign to show the direction of a systematic error.
Percent error needs a value you trust. When you are comparing two of your own measurements with no accepted value, use the percentage difference instead.
% error = |measured − accepted| ÷ |accepted| × 100
- The relative error of an approximation is the absolute error divided by the size of the exact value; multiplied by 100 it is the percent error. Source: Wikipedia, Approximation error.
- Standard gravity is defined as exactly 9.80665 m/s²; 9.81 m/s² is that value rounded, as used in many school labs. Source: NIST CODATA, standard acceleration of gravity.
- US grade 7 standards name percent error among the percent problems students solve with proportional reasoning. Source: Common Core State Standards, Grade 7 Ratios and Proportional Relationships (7.RP.A.3).
Percent error for measurements of g
Measured values of gravitational acceleration against the accepted 9.81 m/s².
| Measured (m/s²) | Error (m/s²) | Percent error | Direction |
|---|---|---|---|
| 9.40 | −0.41 | 4.18% | below |
| 9.50 | −0.31 | 3.16% | below |
| 9.60 | −0.21 | 2.14% | below |
| 9.65 | −0.16 | 1.63% | below |
| 9.70 | −0.11 | 1.12% | below |
| 9.75 | −0.06 | 0.61% | below |
| 9.78 | −0.03 | 0.31% | below |
| 9.80 | −0.01 | 0.1% | below |
| 9.81 | 0 | 0% | exact |
| 9.83 | 0.02 | 0.2% | above |
Show all 14 rowsShow fewer
| 9.85 | 0.04 | 0.41% | above |
| 9.90 | 0.09 | 0.92% | above |
| 10.00 | 0.19 | 1.94% | above |
| 10.20 | 0.39 | 3.98% | above |
Frequently Asked Questions
What is a good percent error?
It depends on the experiment and the equipment. Many school labs treat under about 5% as good agreement; precise work expects far less. Compare it with the uncertainty of your instruments rather than one fixed number.
Can percent error be negative?
With the usual formula, no: it takes the absolute value. If you keep the sign, a negative percent error means your measurement was below the accepted value.
What if the accepted value is zero?
Percent error is undefined then, because it divides by the accepted value. Report the absolute error (how many units off you were) instead.