How to Calculate Sample Size: Surveys, Power Analysis, Interviews
Reviewed by Prof. Dr. Alexander Holtermann · Updated 16 October 2026 · 6 min read
For a survey with 95% confidence and a ±5% margin of error you need about 385 responses. For group comparisons, a power analysis sets the size.
Key takeaways
- For estimating a proportion, use n = z² × p × (1 − p) / e². With 95% confidence (z = 1.96), p = 0.5 and e = 0.05 you get 384.16, rounded up to 385.
- If your population is small (for example 800 students in one program), the finite population correction lowers the target: here to 260.
- If you compare groups or test relationships, run a power analysis: for a medium effect (d = 0.5) in a two-sample t-test you need 64 participants per group at α = .05 and 80% power.
- In qualitative interviews the number is not calculated but justified: in a fairly homogeneous group most themes typically appear within about 12 interviews (Guest, Bunce & Johnson, 2006).
- Plan for attrition: online surveys often lose 20–30% of responses to dropouts and data cleaning, so invite more people than your target.
Why sample size matters
A sample lets you draw conclusions about many people from a few. If it is too small, your results are imprecise: a difference you find may be chance, and a real difference may go undetected (a Type II error). If it is needlessly large, data collection eats time you need for writing up, and you burden more participants than necessary, which ethics committees notice.
Supervisors and examiners check this point closely. A justified sample size in your methods chapter shows that you planned your study rather than taking whatever came in. Justified means you name the formula or the power analysis and every value you assumed: confidence level, margin of error, expected effect size, alpha and power.
The formula for proportions (“What percentage of …?”)
If you want to estimate a proportion, such as the share of students who work alongside their studies, use Cochran’s formula:
n = z² × p × (1 − p) / e²
z is the value for your confidence level (1.96 for 95%, 2.576 for 99%). p is the proportion you expect. If you have no idea, use 0.5: it is the worst case and gives the largest sample. e is the margin of error you are willing to accept, usually 0.05 (±5 percentage points).
| Confidence level | Margin of error | Required sample (p = 0.5) |
|---|---|---|
| 90% | ±5% | 271 |
| 95% | ±5% | 385 |
| 95% | ±3% | 1,068 |
| 99% | ±5% | 664 |
Small populations: the finite population correction
If you survey a clearly bounded group, for example all 800 students in a degree program or all 1,000 employees of a company, you may reduce the sample:
n_adjusted = n / (1 + (n − 1) / N)
N is the size of the population. With N = 800, the 385 shrinks to 260. The correction is worth applying once your sample would make up more than about 5% of the population. For very large populations (a whole country, all undergraduates in the US) it changes nothing, which is why national polls also work with roughly 1,000 respondents.
| Population size (N) | Required sample (95%, ±5%) |
|---|---|
| 500 | 218 |
| 800 | 260 |
| 1,000 | 278 |
| 2,000 | 323 |
| very large | 385 |
Comparing groups: power analysis instead of rules of thumb
If you want to test whether two groups differ or whether two variables are related, the proportion formula does not apply. Here you determine the size with a power analysis (also called an a priori power analysis). It needs four inputs: the statistical test, the expected effect size, the significance level (usually α = .05) and the desired power (usually .80, an 80% chance of detecting a real effect).
Estimate the effect size from previous studies on your topic, ideally a meta-analysis. If you find nothing, fall back on Cohen’s (1988) conventions for small, medium and large effects, and say so in your methods chapter.
| Test | Small effect | Medium effect | Large effect |
|---|---|---|---|
| Two-sample t-test (per group) | 394 (d = 0.2) | 64 (d = 0.5) | 26 (d = 0.8) |
| Correlation (total, Fisher approximation) | 783 (r = .1) | 85 (r = .3) | 30 (r = .5) |
Qualitative research: saturation instead of a formula
Interviews and focus groups aim to understand, not to generalize statistically, so there is no formula. The usual yardstick is saturation: you keep collecting data until new interviews no longer produce new codes or themes.
In dissertations, 8 to 15 semi-structured interviews are common. A widely cited study by Guest, Bunce and Johnson (2006) found that in a relatively homogeneous group most themes emerged within the first twelve interviews, and the basic elements of the key themes were present after about six. Heterogeneous groups, comparative designs or grounded theory studies usually need more.
In your methods chapter, do not just write “until saturation”. Explain how you recognized it, for example by tracking how many new codes each interview added, and mention practical limits such as access to participants.
- Homogeneous group, focused question: often 8–12 interviews
- Two or more subgroups you want to compare: plan per subgroup
- Expert interviews: often 5–10, because each expert covers a lot
- Focus groups: usually 3–5 groups per participant category
Dropouts, response rate and what goes in your methods chapter
Not everyone who opens your survey finishes it, and some responses fail attention checks. Divide your target size by the expected share of usable responses. If you expect 75% usable questionnaires and need 385, aim for about 515 completed starts. If you send personal invitations, also estimate the response rate: at a 20% response rate, 515 starts need around 2,600 invitations.
- the target sample size and how you calculated it (formula or power analysis, with all values)
- how you recruited participants (sampling method, e.g. convenience or stratified random sampling)
- the number actually achieved after data cleaning, and why cases were excluded
- what the sample means for generalizability (limitations section)
Tools that do the math for you
You do not need to do these calculations by hand. Our free sample size calculator applies Cochran’s formula with the finite population correction, and the power analysis tool covers t-tests, paired designs and correlations with the same approximations used in this article. Once you know your target, you can build and distribute your questionnaire at /umfragen and watch responses come in against that target.
Requirements differ between institutions: some departments expect a formal power analysis even for bachelor’s projects, others accept a reasoned convenience sample. Your university’s own guidelines take precedence. Upload them to Professor Digital and every recommendation is tailored to them.
Frequently asked questions
How many participants do I need for a survey in my dissertation?
For estimating proportions with 95% confidence and a ±5% margin of error, about 385. Many undergraduate dissertations work with 100–200 responses, which is usually accepted if you state the larger margin of error and the limits on generalizability.
Is a sample size of 100 enough?
For descriptive trends and simple comparisons it often is: with 100 responses the margin of error is about ±10 percentage points. For group comparisons it depends on the effect size, so check it with a power analysis.
How many interviews are enough for qualitative research?
Usually 8 to 15 semi-structured interviews, continuing until no new themes appear (saturation). What counts is the justification, not the number itself.
What is a power analysis?
A calculation of the sample size a statistical test needs, based on the expected effect size, the significance level (usually .05) and the desired power (usually 80%).
Why use 0.5 as the proportion in the sample size formula?
Because p × (1 − p) is largest at 0.5. If you do not know the true proportion, 0.5 is the conservative choice and guarantees your margin of error for any result.
Sources and further reading
- Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences (2nd ed.). Lawrence Erlbaum.
- Guest, G., Bunce, A., & Johnson, L. (2006). How many interviews are enough? An experiment with data saturation and variability. Field Methods, 18(1), 59–82.
- Clark, T., Foster, L., Sloan, L., & Bryman, A. (2021). Bryman’s Social Research Methods (6th ed.). Oxford University Press.
Your university’s examination regulations and style guide always take precedence.
Related articles
- Sampling methodsProbability sampling gives everyone a known chance of selection and supports generalization; non-probability sampling is quicker but limits it.
- Survey response rateThe response rate is the share of invited people who complete your survey. Short surveys, personal invitations and reminders raise it most reliably.
- Quantitative vs qualitativeQuantitative research measures and tests hypotheses with numbers; qualitative research explores meanings with words. Your research question decides.
- Effect sizeAn effect size tells you how large a difference or relationship is, independent of sample size. Cohen’s d of 0.2, 0.5 and 0.8 is small, medium, large.
- t-testA t-test checks whether two means differ significantly: two independent groups, two paired measurements, or one mean against a fixed value.
- Semi-structured interviewsA semi-structured interview follows an interview guide of open questions but lets you change order, follow up and probe. Typical: 8–15 interviews of 45–60 min.
