How many survey responses do you need?
You rarely get an answer from everyone you want to learn about. A sample size calculation tells you how many completed responses are enough to draw conclusions about the whole group, with a level of precision you choose in advance.
What the three inputs mean
- Confidence level is how certain you want to be. At 95%, if you repeated the survey many times, about 95 out of 100 results would fall within your margin of error.
- Margin of error is the precision you need. With a margin of 5%, a survey result of 60% means the true value most likely lies between 55% and 65%.
- Expected proportion is your best estimate of the answer. Results near 50% are the hardest to pin down, so 50% is the safe choice when you have no estimate.
A worked example
For 95% confidence (z = 1.96), a 5% margin of error and a 50% proportion: 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.2. Rounded up, you need 385 completed responses.
What changes the outcome most?
The margin of error has by far the largest effect. Halving it from 5% to 2.5% makes the required sample four times as large. Raising the confidence level from 95% to 99% increases the sample by about 70%.
What if my audience is small?
This calculator assumes a large population and does not apply a finite population correction. If the group you are studying is small, say a few hundred or a few thousand people, you need fewer responses than shown here. You can adjust the result yourself: divide it by 1 + (result − 1) ÷ population size. For a population of 1,000 people, 385 becomes 278.
From sample size to invitations
The sample size is the number of completed responses, not the number of invitations. Not everyone you invite will answer, so divide the sample size by the response rate you expect. The response rate calculator helps you estimate that.
