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 research methods
- Survey Sampling
- Hypothesis Testing
When to use this tool
Use this when you are planning data collection and need to decide how many responses or observations are required to estimate a population value within an acceptable margin of error.
Assumptions
- Random sampling or a sampling frame you can reason about.
- A specified confidence level (commonly 95%).
- A stated margin of error you are willing to accept.
Limitations
- A larger sample only reduces sampling error — it does not fix non-response bias, measurement error, or a biased sampling frame.
- The result is an estimate; the true value will usually differ by some amount within the margin of error.
How to interpret the result
The calculator returns the minimum sample size needed under your assumptions. Using fewer respondents increases the actual margin of error; using more narrows it, with diminishing returns.
How to report the result
Report the confidence level, the target margin of error, and the assumed expected proportion (or variability) alongside the resulting sample size.
Next steps in your analysis
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.
- AQL Sampling and Audit Sample Size: How Many to InspectAcceptable quality limits, sampling plans and audit sample sizing — how to decide how many units to inspect or records to audit to make a defensible decision.
- Effect Size and Statistical Power: Designing Studies That Can Detect EffectsWhy statistical significance is not enough — how to measure effect size with Cohen's d and design studies with adequate statistical power before you collect data.
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