Sample size calculator

Hardly at all, and this is the part nobody believes. At a margin of five points and 95 percent confidence you need 370 people for a population of ten thousand and 385 for a population of ten million. A thousand times more people asks for fifteen more interviews.

What drives the number is the margin of error, not the size of the place. That is why a national survey interviews two thousand people and not two million.

Because the margin enters the formula squared, in the denominator. Halving it multiplies the sample by about four: at 95 percent confidence the same study needs 97 people for ten points, 385 for five, 1537 for two and a half and 9604 for one.

That is the whole reason election polls stop at three or four points instead of going for one.

Fifty percent, unless you already have a good reason to expect something else. It is not laziness: the product p times one minus p peaks exactly at one half, so that value asks for the largest sample there is.

Any other guess needs fewer people, never more. At five points and 95 percent confidence, fifty percent asks for 385 and ten percent asks for 139.

It is the point of the standard normal curve that leaves your confidence level in the middle: 1.9600 for 95 percent, 1.6449 for 90 and 2.5758 for 99. It is shown on the screen because it is the only number in the formula that comes from outside it.

It is worked out here rather than looked up in a four line table, so a confidence level like 98 percent gets an answer instead of being rounded to the nearest familiar one.