Skip to content
SpirelightSpirelight
Sign inSign up free (opens in a new tab)
Main menu

Free · Cochran’s formula · In your browser

Sample size calculator with finite population correction

This sample size calculator uses Cochran’s formula to work out how many responses a survey needs for a chosen confidence level and margin of error. Add a population size and a response rate to adjust the number and see how many people to invite.

Above 0 and up to 50. Use a dot for decimals.

Keep 50 if you do not know. It gives the largest sample.

A whole number with no separators. Leave empty for a very large population.

The share of invited people you expect to answer.

Responses needed

385

Formula: n₀ = z² · p · (1 − p) / e²

With your numbers:

n₀ = 1.96² · 0.5 · (1 − 0.5) / 0.05² = 384.16

z is 1.645 for 90%, 1.96 for 95% and 2.576 for 99% confidence.

Assumes: simple random sampling and an estimate of one proportion. A sample of this size does not guarantee a representative result.

Sample size and invitations are rounded up to whole people.

The calculation runs only in your browser. Your numbers are not sent anywhere or saved.

How to use the sample size calculator

  1. 1

    Choose a confidence level

    Pick 90%, 95% or 99%. A higher level needs more responses.
  2. 2

    Set the margin of error

    This is how far your estimate may sit from the true value. A margin of 5 means plus or minus 5 percentage points.
  3. 3

    Keep the expected proportion at 50%

    Change it only if earlier data gives you a better figure. A proportion of 50% gives the largest sample, so it is the safe choice when you do not know.
  4. 4

    Add a population and a response rate

    Both are optional. A population size lowers the number when the group is small, and a response rate shows how many people to invite.

The formula behind the result

The calculator uses Cochran’s formula, n₀ = z² · p · (1 − p) / e². Here z comes from the confidence level, p is the expected proportion as a decimal, and e is the margin of error as a decimal. At 95% confidence, a margin of 5 points and a proportion of 50%, that is 1.96² · 0.5 · 0.5 / 0.05² = 384.16, rounded up to 385 responses.

With a known population N, the finite population correction n = n₀ / (1 + (n₀ − 1) / N) lowers the number. For a population of 1,000, 385 becomes 278. With an expected response rate of 30%, you would invite 278 / 0.3 = 926.67, rounded up to 927 people.

The z values are fixed at 1.645, 1.96 and 2.576. More decimals would move the answer by at most three responses at a margin of 1 point or wider.

What the result assumes

  • Simple random sampling. Everyone in the population has the same chance of being picked. A convenience sample, such as a link shared in a course group, does not meet this.
  • One proportion. The formula sizes a sample for estimating one share, such as the percentage who agree. It is not a power calculation for comparing groups, means or regression models.
  • Random non-response. A response rate only tells you how many to invite. People who answer can differ from those who do not.

A sample of this size does not guarantee a representative result. It tells you how many responses the margin of error needs if the assumptions hold.

Interviews and privacy

This formula is for surveys. The number of participants in a qualitative interview study rests on other arguments, so do not use it there. If you interview people, Spirelight’s interview transcription turns a recording you upload into a text draft that you review against the audio.

The calculation runs only in your browser, and your numbers are not sent anywhere or saved.

Questions and answers

How do I calculate sample size?
Use n₀ = z² · p · (1 − p) / e², then round up. At 95% confidence, a 5-point margin and a proportion of 50%, the answer is 385 responses.
What sample size do I need for a population of 1,000?
278 responses, at 95% confidence, a 5-point margin and a proportion of 50%. A tighter margin of 3 points needs 517 responses from the same population.
Why is the expected proportion set to 50%?
Because p · (1 − p) is largest at 50%, it gives the biggest sample and is the safe choice when you have no earlier figure. A proportion of 20% would need fewer responses.
Does a larger population need a much larger sample?
Not by much once the population is large. At 95% confidence and a 5-point margin, 10,000 people need 370 responses and 100,000 people need 383.
How many people should I invite?
Divide the sample size by the share you expect to answer, then round up. For 278 responses and a 30% response rate, invite 927 people.

More free tools