NumberTally Sample Size Calculator
Use Cochran's formula to find the survey sample size for 90%, 95%, or 99% confidence. Set the margin of error, add an optional finite-population correction, and compare margins side by side. Results update instantly. Free, no sign-up.
0.5 = worst case (largest sample). Lower if you know p.
Leave blank for an infinite population.
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How Cochran's Formula Works
Cochran's formula n₀ = Z² × p(1−p) / E² balances three things: higher confidence (bigger Z) needs more people, a smaller margin of error needs many more people (halving E quadruples n), and p = 0.5 gives the safest, largest sample when you don't know the true proportion.
If your population is small, the finite-population correction shrinks the requirement: n = n₀ / (1 + (n₀−1)/N). Sampling 385 people from a town of 400 would be silly — the correction knows that.
Reading the Comparison Table
The table below shows how the required sample explodes as you demand tighter margins: going from ±5% to ±1% multiplies the sample by 25. That quadratic cost is why most public polls settle on ±3–4% — the sweet spot between precision and budget.
Frequently Asked Questions
What sample size do I need for 95% confidence and ±5%?
385 respondents (with p = 0.5). That's the textbook answer for most surveys.
What does margin of error mean?
If 60% of your sample agrees and the margin is ±5%, the true population figure is likely between 55% and 65% (at your chosen confidence level).
Why is p = 0.5 the default?
p(1−p) is largest at 0.5, so it gives the biggest — safest — sample size when you don't know the true proportion.
When do I need the finite-population correction?
When the sample would be more than ~5% of the population. For national polls it barely matters; for a 500-person company it matters a lot.
Does a bigger population need a bigger sample?
Barely. Past a few thousand people, the required sample flattens out — 385 works for a city of 100,000 and a country of 100 million alike.