How do you calculate sample size for a survey?

n = z² × p × (1−p) / e². Where z is the critical z-value, p is the estimated proportion (0.5 for worst case), and e is the margin of error. For large populations, apply the finite population correction.

What is the typical sample size for a 95% CI with 5% margin of error?

For an infinite population with 95% confidence and 5% margin of error: n = (1.96² × 0.5 × 0.5) / 0.05² = 384 respondents.

Why use p = 0.5 when you don't know the proportion?

p = 0.5 maximizes p×(1−p) = 0.25, giving the largest (most conservative) required sample size. This ensures you don't underestimate the required n.

Does population size matter for sample size?

Yes, for smaller populations. Apply the finite population correction: n_adj = n / (1 + (n−1)/N). For large populations (N > 100,000), the correction barely matters.

How can I reduce the required sample size?

Increase the margin of error, lower the confidence level, or narrow the expected proportion range (if you have prior data). Each tradeoff reduces statistical precision.

🔬

Sample Size Calculator

Find the required sample size for your survey or study. Enter margin of error, confidence level, and population size.

Results

How to Determine Sample Size

Sample size calculation is a critical step in designing any survey, poll, experiment, or research study. The sample size calculator gives you the minimum number of respondents needed to achieve your desired accuracy with a specified level of confidence.

The Base Formula

For estimating a proportion: n = z² × p × (1−p) / e². Where z is the critical z-value (1.96 for 95%), p is the expected proportion (use 0.5 for maximum conservatism), and e is the margin of error as a decimal (0.05 for ±5%). For 95% CI with 5% ME: n = 1.96² × 0.25 / 0.0025 = 384.

Finite Population Correction

For a known population size N, apply the correction: n_adj = n / (1 + (n−1)/N). This can significantly reduce the required sample size when N is small. Example: For N=1,000, the adjusted n from 384 becomes about 278. For N=100,000+, the correction changes n by less than 1%.

Why 50% Proportion?

The expression p×(1−p) is maximized at p=0.5, giving 0.25. Using p=0.5 gives the worst-case (largest) required sample size, ensuring your study is adequately powered even if the actual proportion differs from your expectation. If you have a reliable estimate of p from prior research, using that value will require a smaller sample.

Practical Considerations

Response rate: if you expect a 60% response rate, divide the calculated n by 0.6 to determine the number of invitations needed. Budget: balance precision against cost — going from ±5% to ±3% ME at 95% confidence increases sample from 384 to 1,068. For clinical trials, power analysis (not this calculator) should determine sample size.

Frequently Asked Questions

n = z² × p × (1−p) / e². For 95% confidence and 5% ME: n = 1.96² × 0.5 × 0.5 / 0.05² = 384. If you know the population size N, apply the finite population correction.

384 respondents for a very large or unknown population. For smaller populations, the adjusted sample size will be less — e.g., about 278 for N=1,000.

p = 0.5 maximizes p×(1−p) = 0.25, giving the most conservative (largest) sample size estimate. This ensures you don't underestimate how many participants you need.

Yes. Going from 95% (z=1.96) to 99% (z=2.576) confidence increases the required sample by (2.576/1.96)² ≈ 1.73×. For 95% n=384, 99% needs about 664.

Divide the required sample size by your expected response rate. If you need 384 completed surveys and expect a 60% response rate, send invitations to 384/0.6 = 640 people.

Formula sources & accuracy standards: Calculator Methodology · Editorial Policy