Sample size calculator
Work out how many completed survey responses you need for a chosen confidence level and margin of error, with or without a known population.
Sample size for a survey estimate uses Cochran's formula: z squared times p times one minus p, divided by the margin of error squared, then reduced for a small population. At 95 percent confidence, a margin of plus or minus 5 percent and an expected proportion of 50 percent, you need 385 completed responses.
How to use it
Choose a confidence level
95 percent is the convention for most business research. Use 90 percent for a quick directional read and 99 percent when a wrong call would be costly.
Set the margin of error
The margin is how far the result may sit from the true value. Plus or minus 5 percent suits most decisions; 3 percent suits results you will compare closely or publish.
Enter the expected proportion
If you do not know what share will answer a given way, leave it at 50 percent. It gives the largest sample, so it is the safe choice.
Add the population only if it is small
Enter a population when it is a few thousand people or fewer, such as a customer base. For a large population, leave it blank.
Read the result as completes
The result counts completed, valid responses. Divide it by the response rate you expect to see how many people to invite.
The formula
n₀ = z² × p × (1 − p) ÷ e², where z is 1.645, 1.96 or 2.576 for 90, 95 or 99 percent confidence, p the expected proportion and e the margin of error. For a population of N, n = n₀ ÷ (1 + (n₀ − 1) ÷ N). Round up.
Source: Cochran, Sampling Techniques, 3rd edition (Wiley, 1977)
A worked example
Example inputs, not a benchmark.
- Confidence level
- 95%
- Margin of error
- ±5%
- Expected proportion
- 50%
- Population size (leave blank if very large)
- Not set
- Completed responses needed
- 385
Common values
| Confidence | ±3% | ±5% | ±10% |
|---|---|---|---|
| 90% | 752 | 271 | 68 |
| 95% | 1,068 | 385 | 97 |
| 99% | 1,844 | 664 | 166 |
Sample size for interviews
Interviews are sized by saturation, not by this formula. The Nielsen Norman Group advises that there is no fixed number: start small, analyze as you go and stop when new interviews add little. A focused study with similar participants may need as few as five; a broad study across diverse groups may need 20 to 30 or more. Source: Nielsen Norman Group.
What the numbers show
- Halving the margin of error roughly quadruples the sample: at 95 percent confidence, plus or minus 5 percent needs 385 responses and plus or minus 2.5 percent needs 1,537.
- Raising confidence from 95 to 99 percent at a 5 percent margin takes the sample from 385 to 664.
- Beyond a population of a few tens of thousands, the population size barely changes the answer, which is why it can usually be left blank.
- Every segment you want to report on separately needs a sample of its own, and that is often what drives the total.
What the number leaves out
- It assumes a random sample. Online panels and opt-in lists are not random, and no sample size corrects for who chose to respond.
- It covers sampling error only. Unclear questions, missing groups and careless answers add error the formula cannot see.
- It sizes one estimate of a proportion. Comparing two groups, or detecting a change between survey waves, needs a larger sample sized with a power calculation.
- It does not apply to interviews, where the number depends on when new conversations stop adding new themes.
Related
More free research tools
- Incentive calculator Budget participant incentives, with an allowance for no-shows.
- Cost per insight calculator Add up what a study costs per completed interview.
- Time to insight calculator Plan how long a study takes from brief to findings.
- Research ROI calculator Weigh a study's cost against the decision it informs.