Stratified Sampling Calculator
Find a stratum's proportional sample size.
How proportional stratified sampling works
Proportional stratified sampling allocates your total sample across subgroups (strata) in proportion to each stratum's real share of the population — the standard allocation method for a probability-based stratified design.
Enter one stratum's population, the total population across all strata, and your overall desired sample size. The calculator returns that stratum's proportional sample size.
Repeat this calculation once per stratum. Because allocation is proportional, larger strata automatically receive proportionally larger samples — no manual balancing required.
The formula
Stratum sample = Total sample × (Stratum population ÷ Total population)
Divide the stratum's population by the total population to get its share, multiply by the total desired sample size, then round to the nearest whole respondent.
Worked example
A stratum of 4,000 within a population of 10,000, total sample 500
4,000 ÷ 10,000 = 40% share. 500 × 0.40 = 200 respondents from that stratum.
Frequently asked questions
What if a small stratum needs a minimum sample for its own analysis?
Proportional allocation can under-sample small strata for standalone reporting. If you need reliable estimates within every stratum, consider disproportionate (equal or oversized) allocation instead — see the Sample Size Calculator for each stratum's own minimum requirement.
Do the stratum samples need to add up exactly to the total?
Rounding each stratum independently can leave the sum a little above or below the target total sample size — a normal, expected effect of rounding, not an error.
Why stratify at all instead of a simple random sample?
Stratification guarantees representation of every subgroup and typically reduces sampling error compared to a simple random sample of the same size, when the strata differ meaningfully on the outcome you're measuring.
Next steps in your analysis
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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.
- 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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