Sample Size Calculator — How Many Responses Do You Need?

How Sample Size Is Calculated

Deciding how many people to survey isn't guesswork — it follows directly from three choices you make up front: how confident you want to be in the result, how much error you're willing to tolerate, and how varied you expect the answers to be. The base formula for an infinite (or very large) population is n₀ = (z² × p × (1−p)) / E², where z is the critical value tied to your confidence level, p is the expected proportion of respondents falling into the category you care about, and E is your acceptable margin of error, both expressed as decimals.

If you're sampling from a known, finite group — say, everyone enrolled in a specific course, or every employee at one company — you can shrink that number further with the finite population correction: n = n₀ / (1 + (n₀−1)/N), where N is the total population size. Smaller populations need proportionally fewer respondents to reach the same confidence level, because there's simply less unknown variation left to capture.

Why 50% Proportion Is the Safe Default

The product p × (1−p) is largest when p = 0.5, which is why leaving the proportion at 50% gives you the biggest, most conservative sample size estimate. If you already have a solid guess at the real proportion — from a pilot study or prior data — plugging that in instead will usually lower the required sample size, sometimes substantially.

Worked Example

Suppose you want 95% confidence (z = 1.96), a 5% margin of error (E = 0.05), and no strong prior belief about the outcome, so you leave p at 50% (0.5) with an unrestricted population.

1. Step 1: n₀ = (1.96² × 0.5 × 0.5) / 0.05² = (3.8416 × 0.25) / 0.0025 = 384.16
2. Step 2: Since there's no finite population to correct for, this is the final raw value
3. Step 3: Round up to a whole person — you need at least 385 respondents

Frequently Asked Questions