What Is Percent Error and How Is It Calculated?
Percent error is the absolute difference between a measured (experimental) value and the true (accepted) value, divided by the true value and multiplied by 100. It expresses how far a measurement is from the correct answer as a percentage, so a lower percent error means a more accurate result.
The percent error formula is: percent error = |measured − true| ÷ |true| × 100, where measured is the value you observed and true is the accepted reference value. The numerator, |measured − true|, is the absolute error; dividing it by the true value gives the relative error as a decimal.
Example: a pendulum experiment gives g = 9.6 m/s². The standard acceleration of gravity, fixed by the General Conference on Weights and Measures (CGPM) in 1901, is 9.80665 m/s² (usually rounded to 9.81). Percent error = |9.6 − 9.81| ÷ 9.81 × 100 = 2.14%.
How to Use This Percent Error Calculator
Pick a mode, enter two numbers, and the results update instantly with every step shown.
- Measured (experimental) value: the number you recorded in the lab, estimated, or forecast. Any units work, as long as both values use the same unit.
- True (accepted / theoretical) value: the reference number from a textbook, a published standard, or a theoretical calculation. It cannot be zero, because percent error divides by it.
- Percent Difference mode: use this when neither value is known to be correct, such as two trials of the same experiment. It divides by the average of the two values instead of a true value.
The calculator also shows the signed percent error. A positive sign means you overestimated the true value and a negative sign means you underestimated it. Many school chemistry courses in the US report the unsigned (absolute) version, while some physics courses and textbooks keep the sign to show the direction of the error, so check which your instructor expects. Because percent error is a ratio, the result is the same in metric or imperial units.
What Is a Good Percent Error?
There is no universal cut-off, but these ranges are widely used as rules of thumb in introductory science labs. Precision instruments and calibrated industrial measurements are held to much tighter tolerances.
| Percent Error | Rating | Typical Interpretation |
|---|---|---|
| Under 1% | Excellent | Careful technique with calibrated equipment |
| 1% – 5% | Good | Normal for high school and university labs |
| 5% – 10% | Acceptable | Some systematic or random error worth discussing |
| 10% – 25% | High | Check method, readings, and unit conversions |
| Over 25% | Very high | Likely a calculation, unit, or procedural mistake |
Percent Error vs Percent Difference vs Percent Change
| Measure | Formula | Use When |
|---|---|---|
| Percent error | |measured − true| ÷ |true| × 100 | Comparing a result with a known correct value |
| Percent difference | |V₁ − V₂| ÷ ((V₁ + V₂) ÷ 2) × 100 | Comparing two measurements, neither assumed correct |
| Percent change | (new − old) ÷ |old| × 100 | Tracking growth or decline over time |
Percent error measures accuracy (closeness to the true value), not precision (how close repeated measurements are to each other). The US National Institute of Standards and Technology (NIST) Technical Note 1297 (1994) and the international Guide to the Expression of Uncertainty in Measurement (JCGM 100:2008) treat these as separate concepts: a set of readings can be tightly grouped yet all wrong by the same systematic offset.
Frequently Asked Questions
What is a good percent error?
In most high school and introductory university labs, a percent error under 5% is considered good and under 1% is excellent. Results between 5% and 10% are usually acceptable with a discussion of error sources, while anything above 10% suggests a procedural or calculation mistake.
Can percent error be negative?
The standard percent error formula uses absolute values, so the result is always zero or positive. Some textbooks drop the absolute value to keep the sign: a negative percent error means the measured value was below the true value, and a positive one means it was above.
What is the difference between percent error and percent difference?
Percent error compares a measurement with a known true value and divides by that true value. Percent difference compares two measurements when neither is known to be correct, and divides by their average. Use percent error when you have an accepted reference value and percent difference when you are comparing two trials.
Can percent error be more than 100%?
Yes. If the measured value is more than double the true value, or has the opposite sign, the percent error exceeds 100%. For example, measuring 25 when the true value is 10 gives a percent error of 150%. Percent error is only undefined when the true value is exactly zero.
How do I reduce percent error in an experiment?
Calibrate instruments before use, take several readings and average them, read scales at eye level to avoid parallax, control temperature and other conditions, and carry extra significant figures until the final step. Recheck unit conversions, which cause many large errors.