Sample Size Calculator

Enter confidence level, margin of error, and population size to find the required sample.

Confidence level

Margin of error (%)

Population size (leave blank for infinite)

Expected proportion (%)

Required sample size —

Formula used —

n = (Z² × p × (1-p)) / E². With finite population correction: n_adj = n / (1 + (n-1)/N). Use 50% proportion for maximum (most conservative) sample size.

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Quick Reference

Confidence	Z-score	Common Use
90%	1.645	Exploratory research
95%	1.960	Standard for most research
99%	2.576	High-stakes decisions

How to Calculate Sample Size

Sample size determines how precisely your survey or experiment can estimate the true population value. Larger samples give more precision but cost more.

The three key inputs are: confidence level (how sure you want to be), margin of error (how precise), and expected proportion (use 50% if unsure, as this maximizes the required sample).

For finite populations, apply the finite population correction (FPC) to reduce the required sample. This matters most when your sample is more than 5% of the total population.

Example: planning a customer survey aiming for 95% confidence (z=1.96) and ±3% margin of error, expecting about 50% will answer "yes" (maximum variance). n = (1.96² × 0.5 × 0.5) / 0.03² = (3.8416 × 0.25) / 0.0009 = 1,067. You need 1,067 responses for this precision.

The 50% expected proportion assumption maximizes required sample size — use it when you genuinely don't know the proportion. If you expect 80% agreement based on prior data, n = (1.96² × 0.8 × 0.2) / 0.03² ≈ 683. Knowing the proportion in advance lets you survey fewer people.

Finite population correction (FPC): when sampling a fraction of a small population, the required sample is smaller. FPC formula: n_adj = n / (1 + (n−1)/N), where N is the total population. For N=2,000 and initial n=1,067: n_adj = 1,067 / (1 + 1066/2000) ≈ 675.

Response rate matters. If you expect a 40% response rate and need 1,067 complete responses, send 1,067 / 0.40 = 2,668 invitations. Sample size calculations assume completed responses, not invitations sent.