What is Cochran's formula?

n₀ = (Z² · p · (1−p)) / E² — where Z is the z-critical value for your confidence level, p is the expected proportion, and E is the desired margin of error. The finite-population correction is n = n₀ / (1 + (n₀−1)/N).

Why use 50% as the default proportion?

When p = 0.5, the product p·(1−p) is at its maximum (0.25), giving the largest sample size. Without prior data, this is the most conservative choice — it ensures your sample is large enough regardless of the true proportion.

What's a good margin of error?

±5% is standard for most surveys. ±3% is used for high-precision polling (e.g. election polls). ±10% is acceptable for rough directional feedback. Halving the margin quadruples the required sample size.

When should I use finite population correction?

When your population is small (typically fewer than 100,000) and you're sampling a meaningful fraction of it. For example, surveying 500 employees out of 2,000 total — without correction, the formula overestimates the needed sample.

What confidence level should I use?

95% is the default for most surveys. Use 99% for high-stakes research where you need extra certainty, or 90% for quick directional reads.

Sample Size Calculator

Find out how many respondents you need using Cochran's formula.

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How to use Sample Size Calculator

Follow these steps — everything happens instantly in your browser.

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Step 1. Pick a confidence level (90%, 95%, or 99%).
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Step 2. Set your desired margin of error (e.g. 5% means ±5 percentage points).
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Step 3. Set the expected proportion (use 50% for the most conservative sample size).
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Step 4. Optionally enter a finite population size for the corrected sample.