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Percent Error Calculator

Percent Error Calculator

What is Percent Error Calculator?

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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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How to Percent Error Calculator

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  1. 1Percent error = |Experimental − Theoretical| / |Theoretical| × 100%
  2. 2The absolute value removes the sign — percent error is always positive
  3. 3Signed percent error indicates direction: positive = measured too high, negative = too low
  4. 4Used in chemistry, physics, engineering, and manufacturing quality control

Worked Examples

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Example 1
Given:Measured density: 9.7 g/cm³, True density: 10.0 g/cm³
Result:3.0% error

|9.7−10| / 10 × 100 = 3%

Example 2
Given:Predicted 50, actual 47
Result:6.0% error

|50−47| / 47 × 100 = 6.38%

Acceptable Percent Error by Application

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FieldTypical acceptable errorNotes
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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Pro 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.

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Did you know?

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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Reviewed October 2026
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