Loading calculator...
Loading calculator...
Calculate the required sample size for surveys based on confidence level, margin of error, and population proportion.
Sample Size Formula:
n = (Z² × p × (1 - p)) / E²
Finite population correction:
n_adj = (n × N) / (n + N - 1)
Z = z-score for confidence level, E = margin of error, p = proportion, N = population size
Sample size is the number of observations or survey responses needed to achieve a desired level of statistical confidence and precision. A larger sample reduces the margin of error but increases cost and effort.
The most common choice is 95%, meaning you are 95% confident the true population parameter falls within your margin of error. For more precision use 99%; for quicker/cheaper surveys, 90% may suffice.
When the true population proportion is unknown, using p = 50% gives the most conservative (largest) sample size estimate. This maximizes p × (1-p), which peaks at p = 0.5.
When your population is small relative to the sample, the finite population correction adjusts the required sample downward: n_adj = (n × N) / (n + N - 1). This is important when sampling more than 5-10% of the population.
The margin of error (E) is the maximum expected difference between the sample estimate and the true population value. A ±3% margin of error at 95% confidence means you are 95% certain the true value is within 3 percentage points of your result.