Sample Size for Mean Calculator
Two-sided sample size for estimating a population mean: n = (z*sigma/E)^2 with z defaulting to 1.96.
Description
Estimate sample size for a population mean from standard deviation, margin of error, and z critical value.
This calculator gives the familiar normal-theory planning size for a two-sided confidence interval around a mean when the population standard deviation is treated as known.
When to use Sample Size for Mean Calculator
- Plan precision for an estimated mean
- Compare margins of error
- See how variability changes required sample size
How the calculation works
The critical z value times population standard deviation is divided by the desired absolute margin of error, then squared. The operational sample size is rounded up.
n = (zσ / E)² Interpreting the result
Halving the margin of error multiplies the requirement by four. The unrounded result supports auditability; always use the ceiling for planning.
Important limitations
- The formula assumes independent observations and a known or defensible population standard deviation.
- Finite-population correction, nonresponse, clustering, design effects, and t-based uncertainty are not included.