Understanding Relative Error

Relative error quantifies the accuracy of a measurement by comparing the absolute error to the true value. It's crucial in scientific experiments, engineering, and statistics where measurement precision matters.

Calculation Steps

Compute absolute error: |Measured - True|
Compute relative error: Absolute Error / |True Value|
Convert to percentage: Relative Error × 100%

Example Calculation

True value = 100, Measured value = 102:

Absolute Error = |102 - 100| = 2
Relative Error = 2 / 100 = 0.02
Percentage Error = 0.02 × 100% = 2%

Common Reference Values

True Value	Measured	Relative Error
50	49	0.02
200	205	0.025
0.001	0.0012	0.2

Important Notes

Relative error is undefined when the true value is zero
Always use absolute value for denominators to maintain sign consistency
High relative errors indicate poor measurement accuracy

Frequently Asked Questions

What if the true value is zero?

Relative error becomes undefined when the true value is zero, as division by zero occurs. Consider using absolute error instead in these cases.

How is percentage error different?

Percentage error is simply the relative error multiplied by 100 to express it as a percentage.

Should I use dot or comma for decimals?

Both are accepted. The calculator automatically converts commas to dots for processing.

Relative Error Calculator

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Relative Error Calculator - Compare to True Value

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