Sample Size Calculator for Surveys & Studies

Study Parameters

Leave population at 0 for a very large or unknown population.

What are you measuring?

Confidence level

Margin of errorPercentage points for proportions, units for means

Expected proportionUse 50 when unknown — it needs the largest sample

Population standard deviationMean mode only

Population size0 = unknown or very large

Expected response rateHow many invitations you must send

RESPONSES NEEDED

—

Invitations to send—

Without population correction—

Critical value (z)—

Sampling fraction—

Achieved margin of error—

Population used—

What other margins would cost you

For ±10 points—

For ±5 points—

For ±3 points—

For ±1 point—

—

Population size hardly matters — and here is why

To get ±3 points at 95% confidence you need about 1,067 responses whether the population is 50,000 or 50 million. The formula for an unknown population does not contain the population at all. It only appears through the finite population correction, and that correction is negligible until your sample exceeds roughly 5% of the whole group.

This is the most counter-intuitive result in survey design. A national poll of 1,000 people is not "only 0.003% of the country" in any way that hurts — what matters is how the thousand were chosen, not what fraction they represent.

Why 50% is the safe assumption

The variance of a proportion, p(1 − p), peaks exactly at p = 0.5. If you have no prior estimate, assuming 50% gives the largest and therefore safest sample size. If you genuinely expect a lopsided result — say 10% — the required sample drops by about two thirds, but you had better be right, because underestimating here inflates your real margin of error after the fact.

Sampling error is the smallest of your problems

Everything on this page concerns random sampling error only. It assumes every member of the population had a known chance of being selected and everyone selected responded. Neither is ever true. Non-response bias, a skewed sampling frame, and leading question wording routinely produce errors several times larger than the ±3 points printed under the chart — and no sample size fixes them.

Response rate and how many to invite

If you need 400 completed responses and expect 20% to reply, you must invite 2,000 people. The calculator does this division for you. Be pessimistic: email survey response rates in the general population are routinely under 10%, and the people who do respond are systematically different from those who do not.

Frequently Asked Questions

How many people do I need for a survey?

For ±5 points at 95% confidence, about 385 responses regardless of population size. For ±3 points, about 1,067. For ±1 point, about 9,604. The jump is quadratic, which is why very tight margins are rarely worth the cost.

Does a bigger population need a bigger sample?

Barely. Above roughly 20,000 the required sample is effectively constant. The finite population correction only produces a meaningful reduction when your sample is a large fraction of a small population.

What expected proportion should I enter if I have no idea?

Use 50%. It maximises the required sample size, so your actual margin of error can only come out better than planned, never worse.

Does this account for statistical power?

No — this sizes an estimate to a target margin of error, which is the right framing for surveys and polls. Sizing a hypothesis test to detect a specific effect at a given power is a different calculation requiring the effect size and the power level.

Where these numbers come from

Sources

Official publications only. Links open the original document in a new tab.

National Institute of Standards and Technology Special Publication 811 — Guide for the use of the SI Significant figures and rounding conventions
National Institute of Standards and Technology CODATA fundamental physical constants Values of the fundamental physical constants

Sample Size Calculator