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Free sample size calculator

Sample size calculator: how many responses do you need?

Choose your confidence level and margin of error, add your population size if you know it, and see how many completed responses your survey needs. Add your expected response rate to see how many people to invite.

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How do you calculate sample size for a survey?

Square the z-score for your confidence level, multiply by p × (1 − p), and divide by the squared margin of error. At 95% confidence, ±5% margin and p = 50%, that gives 385 responses for a very large population. For a smaller population, apply the finite population correction. Claform’s free calculator does both steps.

Calculator

Sample size calculator: how many responses do you need?

Runs in your browser. Nothing you enter is sent or stored.

95% is the usual choice for surveys.
How far the result may be from the true value, e.g. 5 for ±5%.
Leave empty if the population is very large or unknown.
Keep 50% if unsure; it gives the largest, safest sample.
Share of invited people you expect to complete the survey.

Completed responses needed

385

Assumes a simple random sample. The result is rounded up to the next whole response.

Formula

The sample size formula

The standard formula for estimating a proportion has two parts: the sample size for a very large population, then a correction when the population is small.

n₀ = z² × p × (1 − p) ÷ e² n = n₀ ÷ (1 + (n₀ − 1) ÷ N)

  1. Pick a confidence level and look up its z-score: 80% = 1.2816, 85% = 1.4395, 90% = 1.6449, 95% = 1.96, 99% = 2.5758.
  2. Pick a margin of error e as a decimal, for example 0.05 for ±5%.
  3. Choose the expected proportion p. If you do not know it, use 0.5, which gives the largest sample and is the safe default.
  4. Calculate n₀ = z² × p × (1 − p) ÷ e². This is the sample size for a very large population.
  5. If you know the population size N, apply the finite population correction: n = n₀ ÷ (1 + (n₀ − 1) ÷ N).
  6. Round up to the next whole number. That is the number of completed responses you need.

Worked example

Worked example: 95% confidence, ±5% margin

Use 95% confidence (z = 1.96), a ±5% margin of error (e = 0.05) and p = 0.5.

n₀ = 1.96² × 0.5 × 0.5 ÷ 0.05² = 3.8416 × 0.25 ÷ 0.0025 = 384.16. Rounded up, that is 385 completed responses for a very large population.

If your whole population is 1,000 people, apply the correction: 384.16 ÷ (1 + 383.16 ÷ 1,000) = 277.7, which rounds up to 278 responses.

If you expect 20% of invited people to respond, invite 385 ÷ 0.20 = 1,925 people to reach 385 completes.

For comparison, ±3% at 95% confidence needs 1,068 responses, and ±5% at 99% confidence needs 664. Tighter margins cost far more responses.

How to use your sample size

The number tells you how many completes to aim for, if the sample is chosen well.

  • It counts completed responses

    The result is the number of finished surveys you need, not the number of invitations. Use the response rate field to estimate how many people to invite.

  • Plan for each subgroup

    If you want to compare groups, such as regions or customer types, each group needs enough responses on its own, not just the total.

  • Random beats large

    The math assumes a simple random sample. A large sample from a biased list, such as only your happiest customers, will not fix the bias.

  • Margin covers sampling only

    The margin of error reflects random sampling. It does not account for non-response, unclear wording or people answering untruthfully.

Sample size questions

What sample size do I need for a survey?

It depends on how precise you need to be. For a large population, 95% confidence and a ±5% margin of error need 385 completed responses. A ±10% margin needs 97, and ±3% needs 1,068. Use the calculator to try your own settings.

Why do people say you need 385 responses?

385 is the answer for the most common settings: 95% confidence, a ±5% margin of error, an expected proportion of 50% and a very large population. Change any of those and the number changes.

Does population size matter?

Less than most people expect. Once the population is in the tens of thousands, the required sample barely changes: at 95% and ±5% it is 370 for 10,000 people and 385 for a very large population. Population size matters most when it is small, such as a team of a few hundred.

What confidence level should I use?

95% is the usual choice. It means that if you ran the same survey many times with new random samples, about 95 out of 100 of the intervals you calculate would contain the true value. Use 90% for quick, low-stakes checks and 99% when an error would be costly.

Why use 50% as the expected proportion?

p × (1 − p) is largest when p is 50%, so it gives the biggest sample size. If you are unsure what result to expect, 50% guarantees your sample is large enough. If you are confident the answer is near 20% or 80%, you can use that value and need fewer responses.

How many people should I invite to my survey?

Divide the responses you need by your expected response rate. If you need 385 completes and expect 20% to respond, invite 1,925 people. Response rates vary a lot by audience and channel, so use your own past rates when you have them.

Is this sample size calculator free?

Yes. It is free, needs no sign-up and runs in your browser. Nothing you enter is sent or stored.

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