Relative Error Calculator
Enter a true value and an approximate or measured value to compute absolute and relative error (percentage).
Absolute error: -10.0000
Relative error: -4.0000%
How to Use This Calculator
- Enter the true or reference value.
- Enter the approximate or measured value.
- Review the absolute error (difference) and relative error (percentage of true value).
- Use relative error to gauge accuracy across different scales or units.
Formula
Absolute error = |approx − true|
Relative error = |approx − true| / |true|
Relative error (%) = (Relative error) × 100%
Full Description
Relative error measures the magnitude of an approximation error relative to the true value. It is especially useful when comparing errors across different magnitudes or units.
Always ensure the true value is non-zero; otherwise relative error is undefined. When the true value is small, relative errors can be large even for small absolute errors.
Frequently Asked Questions
Why can’t the true value be zero?
Relative error divides by the true value. When true = 0, the ratio is undefined.
What is acceptable relative error?
Depends on context. High-precision measurement might require <1%, while surveys may tolerate higher values.
How is relative error different from percent error?
They are the same concept—relative error expressed as a percentage.
Can relative error exceed 100%?
Yes. If the approximation differs greatly from the true value, the percentage can exceed 100%.