Percent Error Calculator
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Results
Percent error 2.14067%: measured 9.6 vs true 9.81
How to use the percent error calculator
- Enter your measured (experimental) value, or switch to Several trials and paste all your readings.
- Enter the true value: the accepted figure from your textbook, data sheet or a standard reference.
- Choose an absolute result (always positive) or a signed one, which shows whether your measurement was too high (+) or too low (−).
- Use the absolute error to state the size of the error in your own units, and the percent error to compare accuracy between experiments.
Percent error formula
Signed percent error = (measured − true) ÷ |true| × 100
Absolute error = |measured − true| · Relative error = absolute error ÷ |true|
The measured value is what you found; the true value is the accepted reference. The difference between them, divided by the size of the true value, tells you how far off you were relative to the quantity itself, so an error of 0.2 counts for far more in a value of 1 than in a value of 1,000. Dividing by the absolute value of the true value keeps the sign meaningful even when the true value is negative. When the true value is 0 the formula would divide by zero, so percent error is undefined; quote the absolute error instead.
Worked example: measuring g with a pendulum
A class times a pendulum and calculates the acceleration due to gravity as 9.6 m/s². The accepted value is 9.81 m/s². The absolute error is |9.6 − 9.81| = 0.21 m/s². Dividing by 9.81 and multiplying by 100 gives a percent error of 2.141%. The signed version is −2.14%: the minus sign shows the measurement came out low, which often points to a systematic cause such as timing the swings late.
With three trials of 9.6, 9.75 and 9.9 m/s², the mean is 9.75 m/s² and its percent error is only 0.61%. Averaging reduces random error, but it cannot remove a systematic one, so check both the mean and the spread of your trials.
Percent error in common school experiments
| Quantity | Measured | Accepted | Absolute error | Percent error |
|---|---|---|---|---|
| Acceleration due to gravity (m/s²) | 9.6 | 9.81 | 0.21 | −2.14% |
| Boiling point of water at sea level (°C) | 101.5 | 100 | 1.5 | +1.5% |
| Density of aluminum (g/cm³) | 2.65 | 2.7 | 0.05 | −1.85% |
| Speed of sound in air at 20 °C (m/s) | 335 | 343 | 8 | −2.33% |
| Freezing point of water (°C) | −0.4 | 0 | 0.4 | Undefined (true value is 0) |
The measured values are illustrations, not real results. The last row shows why a zero reference value has no percent error.
Percent error, percent difference and percent change
- Percent error compares a measurement with a known correct value. The true value goes in the denominator.
- Percent difference compares two measurements when neither is known to be correct, dividing by their average. Use the percentage calculator for it.
- Percent change compares a new value with an old one, so the starting value goes in the denominator.
Tips for lab reports
- Keep units out of the percentage. Absolute error has the units of the measurement; percent error has none.
- Round sensibly. Two or three significant figures are usually enough for a percent error; the rounding calculator can help.
- A small percent error is not proof of a good method. Errors in opposite directions can cancel. Discuss likely sources of error whatever the number.
- There is no universal pass mark. What counts as acceptable depends on the equipment and the method, so compare your result with the uncertainty of your measurements or your teacher's guidance.
Frequently asked questions
What is the formula for percent error?
Percent error = |measured − true| ÷ |true| × 100. For a measured g of 9.6 m/s² against the accepted 9.81 m/s², that is 0.21 ÷ 9.81 × 100 ≈ 2.14%.
Can percent error be negative?
The usual definition takes the absolute value, so it is never negative. Some courses use a signed percent error, (measured − true) ÷ |true| × 100, where a negative result means the measurement was too low: 9.6 against 9.81 gives about −2.14%.
What if the true value is zero?
Percent error is undefined, because you would divide by zero. Report the absolute error (the difference in your measurement units) instead, for example 0.4 °C for a freezing point measured at −0.4 °C.
What is the difference between percent error and percent difference?
Percent error compares a measurement with an accepted true value and divides by the true value. Percent difference compares two measurements, neither known to be correct, and divides by their average.
How do I find the percent error of several trials?
Average the trials and compare the mean with the true value. Trials of 9.6, 9.75 and 9.9 m/s² have a mean of 9.75 m/s², which is about 0.61% below the accepted 9.81 m/s².