Everyone you want the results to speak for. Leave empty if it's large or unknown.
Keep 50% if unsure.
The share of invited people you expect to answer.
Responses you need
385
For ±5% at 95% confidence.
Invitations to send at a 20% response rate
1,925
- z-score
- 1.960
- Before population correction
- 384.1
The formula
First, the sample size for a very large population (Cochran's formula):
Then, for a known population N, the finite population correction:
Example: 95% confidence, ±5%, p = 50%. n₀ = 1.960² × 0.25 / 0.05² = 384.1. For a population of 10,000: 384.1 / (1 + 383.1 / 10,000) = 370.0, so you need 370 responses. At a 20% response rate, invite 1,850 people.
Choosing the inputs
Confidence level. 95% is the usual choice. 99% needs about 70% more responses for the same margin; 90% needs about 30% fewer.
Margin of error. ±5% is common for general surveys. Halving the margin needs four times the responses: ±2.5% needs 1,537 instead of 385.
Proportion. 50% is the safe default because it needs the largest sample. Only change it if a past survey tells you roughly what to expect.
Already have your responses? Check how precise they are with the margin of error calculator.
Questions about sample size
- Why does the sample barely grow for large populations?
- Past a few thousand people, the population size hardly matters. 95% confidence and ±5% needs 370 responses from 10,000 people and 384 from a million.
- What response rate should I expect?
- It depends on how warm the audience is. Customers who know you might answer at 20 to 30%; a cold list can be under 5%. Use a past survey's rate if you have one.
- I need results for each group. Does this cover that?
- No. If you'll report on groups separately (say, each region), each group needs its own sample. Run the calculator once per group.