Understanding Percentage Error

Percentage error quantifies the accuracy of a measurement by comparing experimental values to accepted theoretical values. It's calculated as the absolute difference between measured and actual values, divided by the actual value, expressed as a percentage.

Calculation Formula

Percentage Error = |(Measured Value - Actual Value)| / |Actual Value| × 100%

Example Calculation

If you measure a length as 12.5 cm but the actual value is 12.0 cm:

Difference = |12.5 - 12.0| = 0.5 cm
Percentage Error = (0.5 / 12.0) × 100% = 4.17%

Accuracy Guidelines

Error Range	Typical Interpretation
< 1%	Excellent accuracy
1-5%	Good accuracy
5-10%	Acceptable for some applications
> 10%	May need measurement review

Important Notes

Always use absolute value in numerator to ensure positive error values
Be consistent with units of measurement
Consider significant figures in your final calculation
For actual values of zero, percentage error is undefined

Frequently Asked Questions

Can percentage error be negative?

No, percentage error is always expressed as a positive value because it uses the absolute difference between measured and actual values.

What if my actual value is zero?

Percentage error is undefined when the actual value is zero, as division by zero is mathematically undefined. In such cases, consider using absolute error instead.

How many decimal places should I use?

This depends on your measurement precision. Typically, percentage error is reported with 1-2 significant figures when the error is large, or 2-3 decimal places when the error is small.

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Percentage Error Calculator - Measurement Accuracy

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