Sample Size Calculator
Find the sample size you need for your survey or study. Enter the population size, confidence level, margin of error and expected proportion.
How sample size works
Sample size is the number of respondents or observations you need to collect so your results are precise enough to act on. The more people you sample, the smaller your margin of error — but the higher your fieldwork cost.
The calculation uses four inputs. The confidence level is how sure you want to be that the true value lies within your margin of error (95% is the standard). The margin of error is the maximum acceptable sampling error. The expected proportion is your best guess at the true percentage — 50% is the safest choice because it maximises the required sample. The population size is the total group you are sampling from; leave it blank when the population is effectively unlimited.
If you know the population size, the result is adjusted with the finite-population correction, which slightly reduces the sample you need.
The formula
n₀ = z²·p(1−p) ÷ e², then n = n₀ ÷ (1 + (n₀−1) ÷ N)
z is the z-score for the chosen confidence level (1.96 for 95%), p is the expected proportion, e is the margin of error, and N is the population size. The result is always rounded up to a whole number — you cannot interview a fraction of a respondent.
Worked example
A study with a population of 10,000
For 95% confidence, a 5% margin of error and an expected proportion of 50%: n₀ = 1.96² × 0.25 ÷ 0.05² = 384.16, so 385. With the finite-population correction: 384.16 ÷ (1 + 383.16 ÷ 10,000) = 370.0, so you need a sample of about 370.
Frequently asked questions
What confidence level should I use?
95% is the standard choice for most research and gives a z-score of 1.96. Use 90% for exploratory work or 99% when the stakes are high and you need more precision.
Why is 50% the default expected proportion?
p(1−p) is largest when p = 0.5, so 50% produces the biggest sample size. It is the safest assumption when you do not know the true proportion, because it never under-samples.
Why is the result rounded up?
The formula produces a minimum sample size. Rounding up guarantees you collect at least that many, since you cannot survey a fraction of a respondent.
Related tools
Related guides
- Sample Size and Margin of Error: A Practical GuideHow sample size controls margin of error, the formulas behind both, the finite-population correction, and the practical caveats researchers should not skip.
- Confidence Intervals ExplainedWhat a confidence interval is, how to interpret the 95% level correctly, how to calculate one for a mean or a proportion, and what changes its width.
- How to Calculate NPSThe Net Promoter Score formula, how to classify promoters, passives and detractors, a worked example, and the caveats about small samples and timing.
- Survey Research Statistics: A Practical GuideThe core statistics every survey researcher should understand — response, completion and incidence rates, sample size, margin of error and significance — and how they fit together.
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