Sample Size for a Mean Calculator
Plan a simple random sample for a population mean using an estimated standard deviation and a stated precision target.
How to use this calculator
- Enter the estimated standard deviation, desired absolute margin of error, confidence z-score and optional population size.
- Check that every input uses the stated units and covers the same period, population or project scope.
- Change one assumption at a time when comparing scenarios.
Formula used by sample size mean calculator
n₀ = (zσ/E)²; round up to a whole sample
- n₀ = (zσ/E)²; round up to a whole sample
- This planning approximation excludes clustering, non-response, measurement error and other survey-design effects.
- Inputs are validated against the tool-specific constraints; displayed results are rounded for readability.
Worked examples
Worked example
With a standard deviation of 12, margin of error 2 and z-score 1.96, the uncorrected estimate is about 139 observations.
The uncorrected sample size is rounded up; when a finite population is entered, a finite-population adjustment is also shown.
The uncorrected sample size is rounded up; when a finite population is entered, a finite-population adjustment is also shown.
Understanding the result
Plan a simple random sample for a population mean using an estimated standard deviation and a stated precision target.
This planning approximation excludes clustering, non-response, measurement error and other survey-design effects.
Important notes
This planning approximation excludes clustering, non-response, measurement error and other survey-design effects.
Treat the result as an estimate for the assumptions entered; verify important specifications against the relevant source or professional guidance.
Frequently asked questions
What does the margin of error mean?
It is the desired half-width of the confidence interval in the same units as the measured variable.
Why is sample size rounded up?
Rounding up avoids planning for fewer observations than the calculated requirement.
How should I use this result?
Enter the estimated standard deviation, desired absolute margin of error, confidence z-score and optional population size.
Related calculators
- Sample Size for a Proportion Calculator — Estimate sample size for a proportion at a chosen confidence z-score and margin of error.
- Sample Size Calculator — Estimate a simple random-sample size for a proportion using a chosen confidence z-score, assumed proportion and margin of error.
- Confidence Interval for Mean Calculator — Estimate a normal-approximation confidence interval around a sample mean from its spread and sample size.
- Margin of Error Calculator — Estimate a simple proportion margin of error from sample size, assumed proportion, and a critical z value.
- Root Mean Square Error Calculator — Compare observed and predicted numeric sequences using root mean square error, mean squared error and count of observations.
- Standard Error Calculator — Estimate the standard error of a sample mean from sample standard deviation and sample size.
Related explanations
Learn the method behind the number or compare the terminology before using the calculator.
- How to Calculate a Z-Score — Learn how a z-score shows how far a value is from the mean in standard-deviation units.
- How to Calculate Standard Deviation — Learn what standard deviation measures, the population and sample formulas, and how to interpret the result.
- Z-Score — Learn what a z-score measures and how it describes a value relative to a mean and standard deviation.
This page provides a calculation tool plus explanatory information so you can understand what the result means and when the underlying method may not fit your situation.