Percent Error Calculator
Percent error measures the accuracy of an experimental or measured value compared to an accepted or theoretical value. It expresses the discrepancy as a percentage, making it easy to compare errors across different scales and units.
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Tip: Percent error uses the theoretical (accepted) value in the denominator, not the experimental value. Using the wrong denominator is a common mistake that gives a different — and incorrect — result.
- 1Percent error = |Experimental − Theoretical| / |Theoretical| × 100%
- 2The absolute value removes the sign — percent error is always positive
- 3Signed percent error indicates direction: positive = measured too high, negative = too low
- 4Used in chemistry, physics, engineering, and manufacturing quality control
Measured density: 9.7 g/cm³, True density: 10.0 g/cm³=3.0% error|9.7−10| / 10 × 100 = 3%
Predicted 50, actual 47=6.0% error|50−47| / 47 × 100 = 6.38%
| Field | Typical acceptable error | Notes |
|---|---|---|
| Pharmaceutical manufacturing | <1% | Active ingredient content |
| Engineering / machining | <0.1–2% | Depends on tolerance |
| Chemical lab experiments | <5% | Educational context |
| Survey / opinion polls | ±3–5% | Sampling error |
| Medical diagnostics | <5% | Varies by test type |
| Weather forecasting (24hr) | <10% | Temperature predictions |
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Fun Fact
NASA's Mars Climate Orbiter was lost in 1999 due to a unit conversion error — one team used metric units while another used imperial. The spacecraft was $327 million. The percent error in trajectory was small, but catastrophic at interplanetary scale.
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