The Percent Error Formula -

Formula

\text{Percent Error} = \frac{|\text{Measured Value} - \text{Accepted Value}|}{|\text{Accepted Value}|} \times 100\%

Used to calculate: The size of the error between a measured or experimental value and an accepted value, expressed as a percentage of the accepted value.

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What Is the Percent Error Formula?

The percent error formula measures how far a measured or experimental value is from an accepted or reference value. It compares the absolute difference between the two values with the magnitude of the accepted value and expresses the result as a percentage.

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Formula and Variables

\text{Percent Error} = \frac{|M - A|}{|A|} \times 100\%

Symbol	Meaning	Unit
M	Measured or experimental value	Depends on the problem
A	Accepted or reference value	Depends on the problem
Percent Error	Relative size of the error	Percent (%)

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How to Use the Formula

Identify the measured value and the accepted value. Subtract the accepted value from the measured value and take the absolute value of the difference. Divide the result by the absolute value of the accepted value, then multiply by 100 to express the error as a percentage.

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When Is This Formula Used?

The percent error formula is used when comparing an observed, measured, or experimental result with an accepted or reference value.

Common uses:

– Evaluating the accuracy of experimental measurements
– Comparing measured values with theoretical or accepted values
– Quantifying measurement error in science and engineering

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Important Notes

– The absolute value makes percent error nonnegative and measures the magnitude of the error rather than its direction.
– The accepted value cannot be zero because the formula would require division by zero.
– The measured and accepted values must represent the same quantity and use the same or equivalent units before calculation.
– A common point of confusion is percent error versus percent difference. Percent error uses an accepted value as the reference, while percent difference generally compares two values when neither is treated as the accepted reference.

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Alternate Forms

Alternate form:

\text{Absolute Error} = |\text{Measured Value} - \text{Accepted Value}|

Alternate form:

\text{Relative Error} = \frac{|\text{Measured Value} - \text{Accepted Value}|}{|\text{Accepted Value}|}

Alternate form:

\text{Percent Difference} = \frac{|A-B|}{\frac{|A|+|B|}{2}} \times 100\%

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