Sample Size Calculators

The calculator determines the sample size needed to gain the required margin of error (MOE).
Confidence Interval = Estimated value ± MOE.

A larger sample size reduces the margin of error.

The calculator determines the sample size needed to gain the required test power, and draws the power analysis chart.
A larger sample size increases the statistical test power.

Researchers usually use a power of 0.8, meaning the probability of a Type II error (β) — failure to reject an incorrect H₀ — is 0.2. The commonly used significance level (α) is 0.05. β is usually four times bigger than α, since rejecting a correct null hypothesis is considered more severe than failing to reject an incorrect one.

The calculators create the following dynamic chart. When using the calculators, you may hover over any column to see the test power for each sample size.

The chart shows the power per each sample size.
The black bar shows the sample size that achieves the required power. In this example 102 achieves a power of 0.8.
When you hover over the power chart in the calculator, you may see the sample size and the power it achieves. In this example a sample size of 141 achieves a power of 0.93.