Sample Size Calculator
Work out how many completed responses you need for results you can trust. Set your confidence level and the margin of error you're willing to accept, and — if you know it — your total population. Add an expected response rate to see how many people you'll need to invite.
Responses you need
370
completed responses
The formula
This calculator uses Cochran's formula, the standard method for estimating a sample size for a proportion. The base (infinite-population) sample size is n₀ = z² · p · (1 − p) / e², where z is the z-score for your confidence level, p is the expected response distribution, and e is your margin of error expressed as a decimal.
When you supply a population size N, a finite-population correction is applied: n = n₀ / (1 + (n₀ − 1) / N). This lowers the required sample because surveying a meaningful fraction of a small population gives you more information per response. The result is always rounded up and capped at the population size.
A worked example
Suppose you want to survey customers from a list of 10,000 people at a 95% confidence level with a ±5% margin of error. The z-score for 95% confidence is 1.96, and the most conservative distribution is 50% (p = 0.5).
The base sample is 1.96² · 0.5 · 0.5 / 0.05² ≈ 384.16, which rounds up to 385. Applying the finite-population correction for N = 10,000 brings it down to 370. If you expect a 20% response rate, you would need to invite about 1,850 people to net those 370 responses.
Choosing your inputs
Confidence level is how sure you want to be that the true value falls within your margin of error. 95% is the convention for most business and academic research; 90% is acceptable for quick directional reads, and 99% is used when the cost of being wrong is high.
Margin of error is the precision of your estimate — ±5% means a result of 60% could really be anywhere from 55% to 65%. Tightening the margin raises the sample size sharply, so balance precision against the cost of collecting responses.
Response distribution defaults to 50% because that's the value that requires the largest sample, making it the safe choice when you don't know how answers will split. If you have prior data suggesting a more lopsided split (say 80/20), entering it will reduce the required sample.
Frequently asked questions
- How many survey responses do I actually need?
- It depends on your population size, the confidence level you want, and the margin of error you can tolerate. As a rough benchmark, 385 responses give you ±5% at 95% confidence for a large population; tightening to ±3% pushes that past 1,000.
- What does margin of error mean?
- It's the range around your result that likely contains the true value. A ±5% margin on a 60% result means the real figure is probably between 55% and 65%. Smaller margins require larger samples.
- Why does a larger population barely change the sample size?
- Beyond a few thousand people, sample size grows very slowly with population. Surveying 384 people gives almost the same precision whether your population is 20,000 or 20 million — which is why national polls use samples of about 1,000.
- What should I use for response distribution?
- Use 50% unless you have a good prior estimate. Fifty percent maximizes the required sample, so it's the conservative default that guarantees your margin of error is met no matter how answers actually split.
Related reading
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