Sample Size Calculator

Determine the minimum sample size required for your research or calculate the margin of error for an existing survey.

Calculate Required Sample Size

Enter your target confidence level, desired margin of error, and population parameters.

Confidence Level (%):

Margin of Error (%):

Population Size (optional):

Population Proportion (%):

Calculate Margin of Error

Determine the margin of error based on your actual survey sample size.

Confidence Level (%):

Sample Size (n):

Population Size (optional):

Population Proportion (%):

Sample Size Formula & Explanation

For an infinite or unknown population, the required sample size ($n$) is calculated as:

$$n = \frac{Z^2 \cdot p \cdot (1 - p)}{E^2}$$

If the population size ($N$) is known, Cochran's finite population correction factor is applied:

$$n_{adjusted} = \frac{n}{1 + \frac{n - 1}{N}}$$

$Z$: Z-score corresponding to the chosen confidence level.
$p$: Estimated proportion of the population ($0.5$ yields maximum sample size).
$E$: Margin of error expressed as a decimal.

Frequently Asked Questions (FAQs)

Sample size is the number of individual observations or data points collected from a larger population to conduct a survey or research study.

Margin of error represents the range of error or uncertainty around a survey result. A 5% margin of error means your result is within 5 percentage points of the true population value.

A higher confidence level (e.g., 99% vs 95%) requires a larger sample size to ensure greater certainty in the results.

A proportion of 50% (0.5) represents the most conservative estimate (maximum variance), guaranteeing that the calculated sample size is sufficiently large regardless of the actual population distribution.

If the population size is very large or unknown, leave the Population field blank or enter a very high number. The formula automatically uses the infinite population approximation.