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Sample Size Calculator | Find required sample size for confidence & margin

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Determine how large a survey sample you need for a chosen confidence level, margin of error and population size. Uses the standard sample-size formula with the 50% worst-case assumption explained — essential for planning polls, experiments and market research.

Last updated: June 2026 · Free · No sign-up required

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Results

Enter values above and click Calculate to see your result instantly.

Quick reference

Sample size for a large population (50% response):

Margin of error90% conf.95% conf.99% conf.
+/-5%271385664
+/-3%7521,0681,843
+/-2%1,6912,4014,147
+/-1%6,7649,60416,588

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Below the calculator we link a small set of plain-English explainer pages — "What is a percentage?", "Why does PEMDAS matter?", and so on. They cover the underlying concept in 4–6 short paragraphs. Read those before the calculator if the topic is new, or after if you want the extra context.

Interpretation guide

What changes the required size:

LeverEffect
Lower margin of errorNeeds a larger sample
Higher confidenceNeeds a larger sample
Response near 50%Needs the largest sample (most variance)
Small populationApply the finite population correction

lightbulb Worked example

Let's say you are using the Sample Size Calculator. Determines how many survey respondents you need for statistically reliable results. Enter your population size, desired confidence level — 90%, 95%, or 99% — and the margin of error you can accept, Enter the values that match your situation into the input fields and press calculate — using realistic numbers makes the result directly useful for you.

Result: The calculator instantly applies the formula n = z^2 x p(1-p) / e^2; then correct for finite population: n_adj = n / (1 + (n-1)/N) and returns the result with appropriate precision.

What this means: Read the result in the context of what you are measuring. The step-by-step breakdown lets you confirm the math and understand which input most affects the outcome.

Formula & methodology

Formula: n = z^2 x p(1-p) / e^2; then correct for finite population: n_adj = n / (1 + (n-1)/N)

The Sample Size Calculator is built on a well-established calculation method. It uses the formula n = z^2 x p(1-p) / e^2; then correct for finite population: n_adj = n / (1 + (n-1)/N) to turn your inputs into a reliable result. Determines how many survey respondents you need for statistically reliable results. Enter your population size, desired confidence level — 90%, 95%, or 99% — and the margin of error you can accept, and the tool returns The steps are shown on the page so you can follow the reasoning from input to output.

The calculator finds the minimum number of responses needed for results within your chosen margin of error at a given confidence level. It uses the standard formula with p = 0.5 (the most conservative, highest-variance assumption) unless you supply an expected proportion. For small or known populations it applies the finite population correction so you don't over-sample. Tighter margins and higher confidence both demand larger samples.

Authoritative source: Wolfram MathWorld

Frequently asked questions

How big should my survey sample be?
The Sample Size Calculator is free, private, and accurate: it runs entirely in your browser (no uploads, no accounts), applies the standard calculation, and explains each step so you can verify the result. Determines how many survey respondents you need for statistically reliable results. Enter your population size, desired confidence level — 90%, 95%, or 99% — and the margin of error you can accept, and the tool returns the minimum sample size required, plus There is no limit on usage, and it works on any device.
What is margin of error?
The margin of error is the maximum expected difference between your sample statistic and the true population value, at a chosen confidence level — usually ±5% at 95% confidence. It comes from the standard error of the estimate, scaled by the critical z-value. A 5% margin means the true value is expected to lie within 5 points of your result 95 times out of 100.
Why assume a 50% response rate?
The 50% assumption is the worst case: p = 0.5 maximizes the variance p(1−p) in the sample-size formula, producing the largest required sample. It is used when the true proportion is unknown, because any actual value below 50% needs a smaller sample. This conservative choice guarantees your sample is large enough regardless of the real response distribution.
Does population size matter?
Surprisingly little for large populations: the sample size needed to achieve a given margin of error barely changes whether the population is 10,000 or 10 million, because the standard error depends mainly on the sample itself. Population size only starts to matter for small populations (under a few thousand), where the finite population correction reduces the required sample.
How does confidence level affect sample size?
Enter the required values into the input fields and press the calculate button. The tool applies the formula n = z^2 x p(1-p) / e^2; then correct for finite population: n_adj = n / (1 + (n-1)/N) and returns the result with a short explanation of each step, so you can check the working yourself.
Why does the formula assume 50% for the proportion?
Because p = 0.5 maximizes p(1−p), giving the largest — safest — sample size. A true proportion of 10% or 90% would need fewer respondents, but that's rarely known in advance. The 50% assumption guarantees the margin of error holds no matter the outcome.
What does the finite population correction do?
It shrinks the required sample when the population is small — surveying 400 of 500 employees is nearly a census, so the raw formula's demand would be overkill. The correction n_adj = n / (1 + (n−1)/N) accounts for sampling a large fraction of the whole. Skip it only when the population is effectively infinite.
How do confidence level and margin of error trade off?
They multiply: moving from 95% to 99% confidence (z from 1.96 to 2.576) raises the required sample about 70% for the same margin. Halving the margin of error quadruples the sample — precision gets expensive fast. Most surveys settle on 95% ±5% as the cost-accuracy balance.
Does a bigger population need a proportionally bigger sample?
No — the most counterintuitive result in sampling. Ten million people need essentially the same sample as 100,000 for the same margin (about 384 at 95% ±5%). Sample size depends on the precision wanted, not the population size — until the population is small enough for the finite correction.

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