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Sample Size Calculator

How many people you need to survey, and the margin of error.

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Margin of error at every sample size

Halving the margin costs four times the sample — the relationship is quadratic.

Sample sizeMargin of error

How population size affects it

PopulationSample needed

Responses needed

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Details

People to invite—
Z-score used—
Unadjusted size—
Finite correction—

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A 50% result would fall in this range

An expected proportion of 50 percent gives the largest — and therefore safest — required sample, which is why it is the default. Population size barely matters above about 20,000, which is why a national poll and a city poll use similar sample sizes.

Quick Tool Overview

The Sample Size Calculator works out how many survey responses you need for a given margin of error and confidence level, applies a finite population correction, and runs the same calculation backwards to show the margin a sample you already have actually delivers.

What it does
Calculates required sample size and margin of error
You give it
Confidence level, margin of error and population size
You get back
The responses needed, and invites at your response rate
Best for
Planning surveys, polls and market research
Calculators Free, unlimited use No sign-up Runs in your browser

About the Sample Size Calculator

Find how many responses a survey needs to reach a chosen margin of error at a chosen confidence level, and work the calculation backwards to see the margin of error a sample you already have actually delivers.

Two things surprise people the first time they run these numbers. The first is that population size barely matters once it is reasonably large: a sample of about 1,000 gives roughly a three percent margin whether the population is fifty thousand or fifty million, which is why national polls are the size they are. The second is how expensive precision becomes — halving the margin of error requires four times the sample, because the relationship is quadratic rather than linear.

Key features of the Sample Size Calculator

Works in both directions

Size from a target margin, or the margin a sample you already collected actually achieves.

Finite population correction

Applied automatically, which meaningfully reduces the requirement for smaller populations.

Response rate allowance

Shows how many people to invite, not just how many completed responses you need.

Explains the quadratic cost

Halving the margin of error needs four times the sample, which is the fact that reshapes most survey budgets.

Any confidence level

90, 95 and 99 percent presets, or a custom level you enter yourself.

How to use the Sample Size Calculator

  1. 1

    Choose a confidence level

    95 percent is the usual default; 99 percent needs a substantially larger sample.

  2. 2

    Set the margin of error

    How much error you can tolerate, typically 3 to 5 percent.

  3. 3

    Enter the population size

    Optional. Leave it out for a very large or unknown population.

  4. 4

    Read the sample size

    The number of completed responses you need, plus how many to invite for a given response rate.

Frequently asked questions

For a large population at 95 percent confidence, about 384 responses gives a 5 percent margin of error and about 1,067 gives 3 percent. Below a few thousand people, the population size starts to reduce the requirement.

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