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Sample Size Calculator

Work out how many completed responses a survey needs. Choose a confidence level and the margin of error you can accept, and optionally enter the population size; the calculator returns the minimum sample size, rounded up.

Quick examples
%

How far the survey result may sit from the true value, in percentage points.

%

Leave at 50% if unsure — it gives the largest, safest sample.

Leave at 0 if the population is very large or unknown.

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Sample size needed385
Before the population correction
384.15
Critical value (z*)
1.96

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      Formula

      n₀ = z*² × p × (1 − p) ÷ e²
      With a known population N: n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
      z* = critical value for the confidence level, p = expected proportion, e = margin of error (as a decimal)

      How to use it

      1. Choose the confidence level — 95% is the usual standard.
      2. Enter the margin of error you can accept, such as 5%.
      3. Leave the expected proportion at 50% unless you have a good reason to change it.
      4. Enter the population size if it is small enough to matter, or leave it at 0.

      Worked examples

      95% confidence and a ±5% margin of error, large population

      Sample size needed
      385
      Before the population correction
      384.15
      Critical value (z*)
      1.96

      The same survey in a company of 2,000 people

      Sample size needed
      323

      95% confidence and a ±3% margin of error

      Sample size needed
      1,068

      Reference values

      At 95% confidence with a 50% proportion and a large population: ±10% needs 97 responses, ±5% needs 385, ±4% needs 601, ±3% needs 1,068, ±2% needs 2,401 and ±1% needs 9,604. Halving the margin of error takes four times the sample.

      Population size matters less than you think

      For ±5% at 95% confidence, a population of 2,000 needs 323 responses and a population of 10,000 needs 370 — and the figure never rises above 385 however large the population gets. The correction only makes a real difference when the sample is a sizeable share of the whole group.

      Plan for non-response

      The result is the number of completed responses, not invitations. If you expect a 20% response rate and need 385, send about 1,925 invitations. The formula also assumes a random sample; a bigger sample does not fix a biased one.

      Questions people ask

      What sample size do I need for 95% confidence and a 5% margin of error?

      385 for a large population. The formula gives 384.15, which is rounded up.

      How many people should I survey in a population of 2,000?

      323 for 95% confidence and a ±5% margin of error.

      Why is the expected proportion set to 50%?

      Because p × (1 − p) is largest at 50%, it gives the biggest — and therefore safest — sample size. If you know the true figure is nearer 10% or 90%, a smaller sample will do.

      Related calculators

      Margin of Error CalculatorMargin of error of a survey percentage from its sample size.Confidence Interval CalculatorZ-based confidence interval for a mean.Z-Score CalculatorZ-score from a value, or z and value from a percentile.Standard Deviation CalculatorSample and population standard deviation, side by side.Point Estimate CalculatorBest single estimate of a proportion from successes and trials.