RSE Calculator — Relative Standard Error
Enter a sample mean, standard deviation, and sample size to compute the Relative Standard Error (RSE) — a key survey-quality indicator — and the 95% confidence interval.
SE as a percentage of the mean — lower RSE means a more reliable estimate
- 1
Standard error of the mean
18 ÷ √50 = 2,5456SD divided by the square root of sample size — how precisely the mean estimates the true population mean. - 2
SE as fraction of mean
2,5456 ÷ |120| = 0,021213 - 3
RSE (%)
0,021213 × 100 = 2,12
Hoe werkt deze rekenmachine?
RSE = (SD / (|mean| × √n)) × 100. It expresses the standard error as a percentage of the mean to show how reliable a survey estimate is. RSE < 10% is considered reliable; above 25% is high uncertainty. The 95% CI = mean ± 1.96 × SE gives the plausible range for the true population mean.
Formule
How this is calculated
The Relative Standard Error (RSE) measures how precise a sample estimate is relative to its own size. It is computed in two steps: first, the standard error of the mean SE = SD / √n (the standard deviation divided by the square root of the sample size); then RSE = (SE / |mean|) × 100 expressed as a percentage. Unlike the raw SE, which is in the same units as the data, RSE is dimensionless so you can compare the reliability of estimates with different scales or units.
RSE is widely used in official statistics and survey methodology. Statistical agencies (including the ABS, ONS, and Eurostat) typically flag estimates with RSE above 25–30% as having high relative uncertainty and below 10% as reliable. The 95% confidence interval — mean ± 1.96 × SE — gives the range within which the true population mean is expected to fall 95% of the time under repeated sampling, assuming a normal approximation (reasonable when n ≥ 30).
Note that RSE and the coefficient of variation (CV) look similar but measure different things: CV = SD / mean describes the spread within the data, whereas RSE = SE / mean = CV / √n describes the precision of the mean estimate itself. Increasing sample size n reduces RSE by a factor of √n without changing CV.
Veelgestelde vragen
Statistical agencies commonly use RSE < 10% as "highly reliable", 10–25% as "usable with care", and RSE ≥ 25% as "too unreliable to publish" without caveats. These are guidelines — the acceptable level depends on the use case.
CV = SD / mean describes the relative spread within the data. RSE = SE / mean = CV / √n describes the precision of the mean estimate. RSE shrinks as sample size grows; CV does not change with n.
RSE ∝ 1 / √n, so increasing the sample size is the most direct lever. Quadrupling n halves the RSE. You can also reduce SD through better measurement methods, stratification, or more homogeneous sampling units.
TG we-Calculate Editorial Team. (2026). RSE Calculator — Relative Standard Error [Online calculator]. TG we-Calculate. https://we-calculate.com/nl/calculator/rse-calculator
TG we-Calculate Editorial Team. "RSE Calculator — Relative Standard Error." TG we-Calculate. 2026. https://we-calculate.com/nl/calculator/rse-calculator.
TG we-Calculate Editorial Team, "RSE Calculator — Relative Standard Error," TG we-Calculate, 2026. [Online]. Available: https://we-calculate.com/nl/calculator/rse-calculator
@misc{wecalculate_rse_calculator, title = {RSE Calculator — Relative Standard Error}, author = {{TG we-Calculate Editorial Team}}, howpublished = {\url{https://we-calculate.com/nl/calculator/rse-calculator}}, year = {2026}, note = {TG we-Calculate} }
Heeft deze rekenmachine je geholpen?