Sample Size For Estimating A Mean

Estimate the number of independent measurements needed to bound a continuous mean by a target margin of error.

Concept

Results

Enter inputs and select Calculate to display reviewed results.

Inputs

Confidence level *

Known or prior standard deviation *

Target margin of error *

Standard deviation is an estimate

Shows a planning caution when sigma comes from prior data.

Response unit labelOptional label for notes; math treats values as matching response units.

Formula & Variables

n ≥z_1-α/2σE²

n: Sample size; [1]
σ: Standard deviation; [response]
E: Margin of error; [response]

Assumptions

Observations are independent continuous measurements.
The standard deviation is known or defensibly estimated before planning.
Margin of error uses the same response units as the standard deviation.

⚠ Limitations

Planning without a prior standard deviation or planning for power to detect a mean shift requires a different method.
Does not handle proportions, counts, rates, or nonnormal small-sample edge cases.