Sample Size Calculator

The sample size needed for a survey at a given confidence and margin of error.

Result

Required sample size

385

How it works

n = z² · p(1−p) ÷ e²

Sample size answers how many people you must ask to reach a chosen precision: n = z² · p(1−p) ÷ e², where z encodes the confidence level, p the expected proportion and e the margin of error you will accept. The default p of 50% is deliberate. The product p(1−p) is largest exactly at one half, so assuming 50% gives the most demanding, safest sample size — any other true proportion needs fewer people. Use a different p only when you genuinely have prior data. The margin dominates the cost, because it is squared in the denominator. Halving the margin from 4% to 2% quadruples the sample. That is why national polls settle around 1,000 respondents: it buys roughly ±3% at 95% confidence, and each extra point of precision costs four times as much as the last.

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Frequently asked questions

Why use 50% proportion?

It gives the largest, safest sample size when you have no prior estimate of the result.

What margin of error is typical?

5% is common; a smaller margin needs a much larger sample.

Do I need a bigger sample for a bigger population?

Barely. Above a few thousand people, the required sample is almost independent of population size — the same 1,000 respondents serve a city or a whole country. It is the margin of error that drives the number, not the population.

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