Sample Size Calculator

How many survey responses do you actually need? This calculator finds the minimum sample size required to achieve your desired confidence level and margin of error — so your results are statistically valid.

How to Use This Calculator

1. Enter the population size (total number of people in your target group — enter a large number if unknown/very large).
2. Select the confidence level: 90%, 95%, or 99% (95% is the research standard).
3. Enter the margin of error (also called confidence interval; ±5% is common).
4. Enter the response distribution (use 50% if unknown — gives the most conservative/largest sample size).
5. Click Calculate to see required sample size.

Sample Size Formula

n = Z² × p(1−p) / E² (for large or unknown population)

Adjusted n = n / (1 + (n−1)/N) (finite population correction)

• Z = Z-score for confidence level (1.96 for 95%, 2.576 for 99%)
• p = response distribution (0.5 for maximum conservatism)
• E = margin of error as decimal (0.05 for ±5%)
• N = population size

Example Calculation

Population: 10,000 | Confidence: 95% | Margin of error: ±5% | Distribution: 50%

• n = (1.96² × 0.5 × 0.5) / 0.05² = 384.16 ≈ 385 (large pop.)
• Adjusted: 385 / (1 + 384/10,000) = 370 responses needed

Confidence Level and Margin of Error

• 95% confidence, ±5% error: Standard for most surveys. If you ran 100 identical surveys, 95 would give results within 5% of the true value.
• More confidence or smaller error: Requires larger sample size. 99% confidence with ±3% error roughly quadruples the required sample.

Common Mistakes to Avoid

• Confusing sample size with response rate — If you need 385 valid responses and expect a 20% response rate, you need to invite 1,925 people.
• Using a known distribution instead of 50% — Unless you have strong prior data, use 50% for p to ensure your sample is large enough for any outcome.
• Assuming larger samples are always better — Doubling your sample size reduces margin of error by only √2 ≈ 1.41×. Diminishing returns set in quickly above a few hundred responses.

Frequently Asked Questions

Is 100 respondents enough for a survey?

For a large population at 95% confidence, 100 responses gives a ±9.8% margin of error — meaningful but imprecise. 384 responses gets you to ±5%. The right sample size depends on how much precision you need.

Does population size matter much?

Surprisingly little once the population is large. The sample size needed for a 10,000-person vs. 10,000,000-person population differs only slightly (370 vs. 384 in the example above). Very small populations (under 1,000) require proportionally larger samples.

What is a confidence interval?

A range of values that is likely to contain the true population parameter. A 95% CI of 45%±5% means you're 95% confident the true value is between 40% and 50%. See our Confidence Interval Calculator.

Conclusion

Getting your sample size right is the difference between actionable insights and meaningless data. Use this calculator before any survey, study, or experiment to ensure your results will be statistically valid.

Related: Confidence Interval Calculator | Z-Score Calculator | Statistics Calculator | Probability Calculator