Measuring how far off you are
When you compare a measurement or an estimate with a known value, the percent error tells you how large the difference is relative to that value. A 1 cm error matters a lot when measuring a 5 cm part, and very little when measuring a 100 m field. Percent error puts both on the same scale, which is why it is standard in lab reports and quality checks.
The formulas
- Absolute error = |measured − true|
- Percent error = |measured − true| ÷ |true| × 100
- Signed error = (measured − true) ÷ |true| × 100
The usual percent error is always positive. The signed version keeps the direction: positive when you overestimated, negative when you underestimated.
Worked example
In a physics lab, you measure the acceleration of gravity with a pendulum and find 9.6 m/s². The accepted value is 9.81 m/s².
- Absolute error = |9.6 − 9.81| = 0.21 m/s².
- Percent error = 0.21 ÷ 9.81 × 100 = 2.14%.
- Signed error = −2.14%: the measurement was too low.
Interpreting the result
| Percent error | Typical reading |
|---|---|
| under 1% | excellent agreement |
| 1 to 5% | good for most school labs |
| 5 to 10% | acceptable for rough estimates |
| over 10% | look for a systematic error |
The acceptable level depends entirely on the field. A carpenter may accept a few percent; a pharmacist dosing a medicine or an engineer machining an engine part may need well under 1%.
Percent error versus percent difference
Percent error compares a value with a reference that is assumed to be correct. When two measurements are compared and neither is the reference, use the percent difference instead: the difference divided by the average of the two values. The percentage change calculator covers that case, as well as increases and decreases over time.
Sources of error
- Random errors vary from one measurement to the next, such as reaction time with a stopwatch. Repeating the measurement and averaging reduces them.
- Systematic errors push every result in the same direction, such as a miscalibrated scale or a pendulum string measured too short. Averaging does not help; you must find and correct the cause.
A consistent sign in the signed error across several trials is a clue that a systematic error is present.
A note on zero
Percent error cannot be computed when the true value is zero, because the formula divides by it. In that case, report the absolute error instead.