A sample size calculator helps determine the minimum number of participants needed for a survey or study to achieve statistically reliable results.

This calculator uses Yamane’s (1967) formula:

Where:

n = required sample size

N = population size

e = margin of error (expressed as a decimal, e.g., 0.05 for 5%)

The margin of error (e) represents the level of precision for your survey results. A lower margin of error (e.g., 3%) requires a larger sample size, while a higher margin of error (e.g., 10%) requires a smaller sample.

The population size (N) refers to the total number of individuals in the group you are studying. For example, if you are surveying a company’s employees and there are 5,000 employees, then N = 5,000.

It depends on the level of precision needed:

• 1-3% = Very high precision (large sample size required)
• 4-5% = Standard level of precision for most surveys
• 6-10% = Lower precision but suitable for quick estimates

If the population size is unknown or infinite, use a standard sample size formula for large populations (e.g., Cochran’s formula). As a general rule, for large populations, a sample size of 400-1,000 is often sufficient.

For large populations, the sample size calculation reaches a plateau. For example, whether your population is 100,000 or 10 million, the required sample size won’t change drastically because the margin of error and confidence level primarily drive the calculation.

Yes, it is useful for:

• Business surveys (customer feedback, employee engagement, market research)
• Academic research (thesis studies, social science research)
• Public policy research (large-scale opinion polls)

In Yamane’s formula, the margin of error (e) determines the confidence level indirectly. A 5% margin of error (e = 0.05) corresponds to a 95% confidence level, while a 10% margin of error (e = 0.10) would correspond to a lower confidence level (~90%).