Relative Standard Error (RSE) Calculator
Enter sample observations to compute mean, standard error, and relative standard error expressed as a percentage.
Mean
19.5000
Standard error
2.2913
Relative standard error
11.75%
How to Use This Calculator
- Enter sample measurements separated by spaces or commas.
- Review the sample mean, standard error, and RSE percentages.
- Use RSE to report estimation precision relative to the estimate.
- Smaller RSE indicates more reliable estimates.
Formula
Mean μ̂ = Σxi / n
Standard error (SE) = s / √n, where s is sample standard deviation
Relative standard error = (SE / μ̂) × 100%
RSE communicates standard error as a percentage of the estimate, improving interpretability across different scales.
Full Description
Relative standard error (also called coefficient of variation of the estimate) gauges the precision of a sample estimate. Government statistics and survey research often report RSE to highlight estimation quality.
RSE values below 10% usually indicate reliable estimates, while values above 30% suggest caution—though thresholds vary by discipline.
Frequently Asked Questions
Is RSE the same as RSD?
No. RSE uses the standard error (s / √n) whereas RSD uses the standard deviation in the numerator.
Can RSE exceed 100%?
Yes. Large standard errors relative to the mean yield high RSE values, indicating high uncertainty.
Why is standard error zero?
If all sample values are equal, standard deviation is zero and so is the standard error.
How many observations are required?
At least two values are needed to estimate sample standard deviation and standard error.