The formula below computes the sample size needed to estimate
the population mean within a given margin of error and at a given
confidence level.
Move the sliders to change the values of the population standard
deviation σ , the margin of error E, and the confidence.
How does the sample size change as the standard deviation changes?
How does the sample size change as the margin of error changes?
How does the sample size change as the confidence changes?

The value z α/2 is the standard score corresponding to
an area of α/2 in the right tail of the normal distribution.
If the confidence is converted to a decimal value C, then
α = 1 - C. For example, if the confidence level is 95%,
then C = 0.95 and α = 1 - 0.95 = 0.05.
This applet was updated October 2, 2013.