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Calculate the required sample size for surveys, research, and statistical studies. Determine how many participants you need for accurate results with customizable confidence levels and margins of error.
How confident you want to be that the true value falls within your margin of error. Common values are 90%, 95%, or 99%.
The amount of error you're willing to accept. A smaller margin requires a larger sample size.
The expected percentage of your population that has the characteristic of interest. If unknown, use 50% for maximum sample size (worst case).
Enable this if your population is finite and relatively small. For large populations (>100,000), leave this off as it won't significantly affect the sample size.
You need to survey 385 participants to be 95% confident that your results are within ±5% of the true population value.
This calculator provides sample size estimates for educational and planning purposes. Always consult with a statistician for critical research decisions.
Calculations assume simple random sampling. Stratified or cluster sampling may require different approaches. The finite population correction is applied when the population size is specified and when the sample is more than 5% of the population.
Sample size is the number of participants or observations needed in a study to draw valid conclusions about a population. An adequate sample size ensures your research results are statistically significant and can be generalized to the broader population. Too small a sample may miss important effects, while too large a sample wastes resources. Calculating the correct sample size is crucial for survey design, clinical trials, market research, and academic studies.
For infinite or large populations, the sample size formula is:
n = (z² × p × (1-p)) / e²Where n is the sample size, z is the z-score for your confidence level (1.96 for 95%), p is the expected proportion (0.5 for maximum sample size), and e is the margin of error as a decimal (0.05 for 5%).
When sampling from a small population, we apply a finite population correction: n_adjusted = n / (1 + (n-1)/N), where N is the population size. This correction reduces the required sample size when the sample represents a significant portion of the total population.
A good sample size depends on your confidence level and margin of error. For a 95% confidence level and ±5% margin of error, you typically need about 385 participants for a large population. For ±3% margin of error at the same confidence level, you need about 1,067 participants.
95% is the most common confidence level in research and surveys. It means you can be 95% confident that your results reflect the true population within your margin of error. Use 90% for less critical decisions or 99% for high-stakes research where greater certainty is needed.
Margin of error is the range of values above and below your sample result within which the true population value is expected to fall. A ±5% margin of error means if 60% of your sample says yes, you can be confident that 55-65% of the total population would say yes (at your chosen confidence level).
Use the finite population correction when your total population is small (typically under 100,000) and known. It reduces the required sample size because sampling a larger fraction of the population provides more precision. If your sample would be more than 5% of the population, the correction makes a meaningful difference.
Expected proportion is your best estimate of what percentage of the population has the characteristic you're measuring. If you have no prior information, use 50% (0.5) because it produces the maximum sample size, ensuring adequate power regardless of the true proportion. If you know the approximate proportion from previous research, use that value to potentially reduce sample size.
For large populations (over 100,000), sample size is largely independent of population size—surveying 385 people gives similar precision whether the population is 100,000 or 100 million. For smaller populations, use the finite population correction to adjust the sample size downward.
Margin of error has an inverse square relationship with sample size. Cutting the margin of error in half requires four times the sample size. For example, a ±5% margin needs about 385 participants, while ±2.5% needs about 1,537 participants at 95% confidence.
This calculator works for basic proportion-based studies, but clinical trials often require more sophisticated power calculations that account for effect size, statistical test type, and other factors. Consult with a biostatistician for medical research sample size determination.