How Many People Do You Actually Need to Survey? Less Than You'd Guess, and It Barely Depends on Population Size

National polls report a margin of error of about three points from roughly 1,000 respondents, drawn from a population of over 250 million adults. That's 0.0004% of the population.

Most people assume this is a compromise — that a bigger sample would obviously be better and pollsters simply can't afford one. Partly true, but it misses the more interesting fact: sampling 10,000 people instead of 1,000 would only take the margin of error from about 3.1 points to about 1.0. And sampling from a population of 250 million rather than 25,000 makes almost no difference at all.

Sample size is governed by the precision you want, not by the size of the group you're describing. Once you see why, survey planning becomes a straightforward calculation.

The Formula and What Each Piece Does

For estimating a proportion, the required sample for an infinite population is:

n = (z² × p × (1−p)) ÷ e²

Four inputs, each doing a specific job.

z — your confidence level. How often the method produces an interval containing the true value. 95% confidence gives z = 1.96; 99% gives z = 2.576; 90% gives z = 1.645. Note this is not the probability that your particular interval is correct — it's a property of the procedure over repeated sampling.

p — the expected proportion. The variance of a proportion is p(1−p), which is maximised at p = 0.5. Using 0.5 when you don't know gives the most conservative (largest) sample requirement — which is why 0.5 is the default. If you have good reason to expect a proportion near 0.1 or 0.9, the required sample drops substantially: p(1−p) is 0.25 at p = 0.5 but only 0.09 at p = 0.1.

e — your margin of error. How precise you need the answer, in the same units as the proportion. ±3 points is e = 0.03.

And the term that isn't in the formula: population size. For an infinite population it doesn't appear at all. That's the counter-intuitive part, and it's real.

Worked example. 95% confidence, p = 0.5, e = 0.03: n = (1.96² × 0.5 × 0.5) ÷ 0.03² = (3.8416 × 0.25) ÷ 0.0009 = 1,067. That's where the familiar polling number comes from. The sample size calculator will run this for any combination of inputs.

Why Population Size Barely Matters

The intuition that a bigger population needs a bigger sample is strong and wrong, and the reason is worth understanding rather than just accepting.

A sample estimates a proportion, not a count. What varies from sample to sample is the proportion you observe. The sampling variability of that proportion depends on how many observations you have — not on how many you didn't take. A well-mixed pot of soup needs the same size spoonful to taste whether the pot holds two litres or two hundred.

The finite population correction. For finite populations there is an adjustment: multiply by √((N−n)/(N−1)), where N is the population. It only bites when your sample is a large fraction of the population — conventionally above about 5%.

What it means in practice. For a ±3 point margin at 95% confidence: a population of 1,000 needs 517; 10,000 needs 965; 100,000 needs 1,056; 1,000,000 needs 1,067; 250,000,000 needs 1,067. Between one hundred thousand and a quarter of a billion, the requirement is essentially identical.

Where the correction genuinely helps. Surveying a 200-person company at ±5% needs only 132 responses rather than the 385 an infinite population would require. Small-population surveys benefit substantially — which is the reverse of most people's intuition.

The Square-Root Problem

Precision improves with the square root of sample size, and this single fact governs the economics of every survey.

Halving the margin of error quadruples the sample. ±5% needs 385. ±2.5% needs 1,537. ±1% needs 9,604. The cost curve is brutal at the precise end.

Which is why most surveys settle at ±3 to ±5. It's not laziness — it's the point where each additional respondent buys very little precision.

And why very large samples are usually a warning sign. A survey of 50,000 respondents has a margin of error around ±0.4%, which is far more precision than almost any decision requires. If someone has spent that, the binding constraint is usually something other than sampling error — and the money would have been better spent on the problem in the next section.

The Error That Dwarfs All of This

Margin of error only describes random sampling variability. It assumes a genuine random sample from the population you care about. That assumption is violated far more often than it holds, and the resulting bias is not reduced by increasing n at all.

Non-response bias. If 8% of those contacted respond, your sample is people willing to answer surveys — a group that differs systematically from those who aren't. No sample size fixes this. A large biased sample is simply a precisely wrong answer.

Coverage bias. Your sampling frame excludes people. A landline survey misses mobile-only households; a web panel misses those without internet access; an in-store survey misses everyone who stopped shopping with you, which is usually the group you most needed to hear from.

Question wording. Small changes in phrasing move results by more than the margin of error routinely. "Do you support X?" and "Do you oppose X?" do not produce complementary answers.

Timing effects. A customer satisfaction survey sent immediately after purchase measures something different from one sent after ninety days of ownership.

The famous illustration remains the 1936 Literary Digest poll: 2.4 million responses, and a confidently wrong prediction, because the sampling frame skewed toward wealthier households. Sample size was never the problem.

Planning a Survey Properly

Decide the margin of error from the decision, not the other way round. If you'll act the same way whether the answer is 40% or 46%, ±3 points is wasted money. Ask what difference would change what you do, then size for that.

Set the confidence level to the stakes. 95% is conventional. Use 99% where being wrong is expensive; 90% is defensible for exploratory work and cuts the sample by about 30%.

Apply the finite population correction if you're sampling more than 5% of the group. For internal surveys, customer bases and small memberships, this often halves the requirement.

Budget for response rate, not sample size. Needing 385 responses at an 8% response rate means contacting about 4,800 people. This is the step that derails survey plans.

Spend the marginal dollar on non-response, not on n. Following up with non-respondents, or weighting to known population characteristics, addresses the error that sample size can't touch.

Then check your result with the confidence interval calculator to see the actual interval your realised sample produced, and the statistics calculator for the underlying summary figures.

A thousand people can describe a nation, provided they were chosen properly. Ten thousand chosen badly describe nothing at all, very precisely.