Sample size to test mean

Use this calculator to find the minimum sample size required to test mean $\mu$.

Sample Size to test mean
Confidence Level ($1-\alpha$)
Power ($1-\beta$)
Mean under H0 : ($\mu_0$)
Mean under H1 : ($\mu_1$)
Standard Deviation ($\sigma$)
Effect Size ($ES$)
Z value: $Z_{1-\alpha/2}$
Z value: $Z_{1-\beta}$
Required Sample Size : ($n$)

Sample size to test mean

The $ES$ is defined as $$ ES=\frac{|\mu_1-\mu_0|}{\sigma} $$

where $\mu_0$ is the mean under $H_0$ and $\mu_1$ is the mean under $H_1$, $\sigma$ is the standard deviation.

The formula for determining the sample size required to ensure that the test has a specified power is $$ n =\bigg(\frac{Z_{1-\alpha/2}+Z_{1-\beta}}{ES}\bigg)^2 $$


  • $\alpha$ is the selected level of significance,
  • $1-\beta$ is the selected power and
  • $ES$ is the effect size.

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