Percent Error Calculator
Enter a measured value and the accepted value to get the percent error, the absolute error and its direction.
What this tool does
Percent error measures how far a measurement is from the accepted value, as a percentage of that value: |measured − accepted| ÷ |accepted| × 100. If you measure 9.6 and the accepted value is 9.81, the percent error is 2.14%. Enter the two values and the calculator also shows the absolute error and the direction.
Calculates percent error, absolute error and signed error for a measured value against an accepted one.
Explains the formula used.
How to use it
- Enter the measured (experimental) value.
- Enter the accepted (theoretical) value.
- Read the percent error and the direction.
Why use this calculator
Calculates percent error from a measured and an accepted value, and shows the absolute and signed error as well. Percent error is the standard way to report how accurate an experiment was, and it appears in nearly every chemistry and physics lab report. Using the absolute value and the right denominator are the common slip-ups.
Why we built it
We built this to give the percent error from a measured and an accepted value, together with the absolute and signed error. Use the standard deviation calculator for spread across repeats and the percentage calculator for general percentage change.
For a neighbouring job there is also the Significant Figures Calculator, the One Rep Max Calculator and the Molar Mass Calculator.
Who this tool is for
- Science and engineering students writing lab reports
- Teachers marking practicals
- Technicians checking measurement accuracy
When to use it
- Lab reports in physics, chemistry and biology.
- Comparing a measurement with a reference value.
- Checking an instrument's accuracy.
- Homework and exams on measurement error.
How it works
Percent error = |experimental − theoretical| ÷ |theoretical| × 100. The absolute error is the difference without its percentage, and the signed error keeps the sign so you can see whether you measured high or low.
Example: g measured as 9.8 against 9.81 m/s² is an absolute error of 0.01 and a percent error of 0.10%.
Percent error compares to a known, accepted value. To compare two measured values with no reference, use percent difference, which divides by their average.
A worked example
These are the values the calculator opens with, so you can see exactly what it does with them. Change any value on the page and the result updates; the figures below come from the same calculation.
| Input | Value |
|---|---|
| Measured (experimental) value | 9.6 |
| Accepted (theoretical) value | 9.81 |
With those inputs, the calculator returns:
- Percent error: 2.1407%
- Absolute error: 0.21
- Signed error: -2.1407% (below the accepted value)
- Formula: |measured − accepted| ÷ |accepted| × 100
What you give it, and what you get back
| Item | Details |
|---|---|
| Measured value | Your experimental result. |
| Accepted value | The reference or theoretical value; it cannot be 0. |
| Result | Percent error, absolute error and signed percent error with direction. |
Issues you may run into
| What you see | Why it happens | What to do |
|---|---|---|
| "The accepted value cannot be 0" | Percent error divides by it. | Use the absolute error instead. |
| Negative percent error expected | The percent error is shown as positive. | The signed error shows the direction. |
| Percent difference needed | No accepted value exists. | Use percent difference (divide by the mean). |
| Large error | Systematic error or a unit slip. | Recheck units and the measurement. |
Assumptions and limitations
- Needs a non-zero accepted value.
- It does not combine uncertainties.
- It treats the accepted value as exact.
Frequently asked questions
What is the percent error formula?
|measured − accepted| ÷ |accepted| × 100.
What is a good percent error?
It depends on the experiment. Under 5% is often considered good in an introductory lab; precise work aims much lower.
Can percent error be negative?
The standard formula uses the absolute value, so it is positive. The signed error shows direction.
What is the difference between percent error and percent difference?
Percent error compares to an accepted value; percent difference compares two measurements to their average.
What do I do if the accepted value is 0?
Percent error is undefined; report the absolute error.
Is it free and private?
Yes. It runs in your browser.