How to use the percent error calculator
- Type your result in Measured (experimental) value.
- Type the accepted value in True (theoretical) value, for example from your textbook or data sheet.
- Read Percent error at the top. The other lines show the signed error, the absolute error and the relative error.
- Copy the Working line into your lab report if you need to show the calculation.
What it does and when to use it
Percent error tells you how far a measurement is from the value it should be, as a share of that value. Science students use it in almost every practical write-up: measuring g with a pendulum, finding the density of a metal, or timing a reaction. An error of 0.2 means a lot when the true value is 1 and very little when it is 1,000, so the percentage makes results comparable.
The tool reports four related numbers:
| Output | Meaning |
|---|---|
| Absolute error | |measured − true|, in the same units as your data |
| Relative error | absolute error ÷ |true|, as a decimal |
| Percent error | relative error × 100 |
| Signed error | percent error with + (too high) or − (too low) |
How it works
The formula is:
Percent error = |measured − true| ÷ |true| × 100
The values are converted to exact fractions before any arithmetic, so a result such as 0.21 ÷ 9.81 is not affected by computer rounding. Answers that end are shown in full. Answers that repeat are cut to 12 significant figures and end with “…”.
Step by step for a pendulum experiment (measured g = 9.6 m/s², true g = 9.81 m/s²):
- Find the difference: 9.6 − 9.81 = −0.21.
- Take the absolute value: |−0.21| = 0.21. This is the absolute error.
- Divide by the true value: 0.21 ÷ 9.81 = 0.021406727829… This is the relative error.
- Multiply by 100: 2.14067278287…%.
So your measurement was about 2.14% too low.
Worked examples
Gravity experiment. Measured 9.6, true 9.81: Percent error: 2.14067278287…%, signed error −2.14067278287…%.
Reading too high. Measured 105, true 100: Percent error: 5% and Signed error: +5%, absolute error 5.
Density of aluminium. Measured 2.65 g/cm³ against an accepted 2.7 g/cm³ gives Signed error: −1.85185185185…%, with absolute error 0.05.
Limits and tips
- Round the final answer to suit your data. If you measured to 3 significant figures, the significant figures calculator or the rounding calculator will tidy it up.
- Use the same units for both values. Convert first if one is in cm and the other in m.
- When you have several trials, average them first with the mean, median and mode calculator, then find the percent error of the mean.
- The calculation runs in your browser and nothing is uploaded.
Frequently asked questions
Is percent error always positive?
Which value goes on the bottom of the fraction?
What if the true value is zero?
What counts as a good percent error?
How is this different from percentage change?
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