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Stratified Sample Allocation Calculator

Calculate how to proportionally allocate a total sample size across population strata (subgroups).

Result

Region A
192 samples
Region B
128 samples
Region C
80 samples
StratumPopulationProportionAllocated Sample
Region A1200048%192
Region B800032%128
Region C500020%80

About the Stratified Sample Allocation

This calculator determines how many survey or sample participants should be drawn from each subgroup (stratum) of a population so that every subgroup is represented in proportion to its actual size. It is designed for planning stratified sampling, where the goal is a sample that mirrors the population's composition rather than one that is fully random or evenly split.

How It Works

You enter the total sample size you want, a comma-separated list of stratum labels, and a matching comma-separated list of each stratum's population size. The calculator sums the stratum sizes to get the total population, computes each stratum's proportion of that total, and multiplies the total sample size by each proportion to get that stratum's allocated sample count, rounded to the nearest whole number.

Proportion for stratum i = strataSize[i] / totalPopulation. Allocated sample for stratum i = round(totalSampleSize * proportion).

Formula & Methodology

The number of labels entered must match the number of stratum sizes entered, and the total population across all strata must be greater than zero, or the calculator returns an error. Each stratum's allocation is rounded independently with Math.round, so the individual allocated samples may not sum to exactly the requested total sample size due to standard rounding behavior.

Examples

Allocating a market research sample across three regions

With a total sample size of 400 and stratum populations of 12,000, 8,000, and 5,000 (total population 25,000), Region A gets round(400 * 12000/25000) = round(192) = 192, Region B gets round(400 * 8000/25000) = round(128) = 128, and Region C gets round(400 * 5000/25000) = round(80) = 80.

Allocating across two unequal strata

With a total sample size of 150 and stratum populations of 9,000 and 1,000 (total population 10,000), the larger stratum gets round(150 * 0.9) = 135 samples and the smaller stratum gets round(150 * 0.1) = 15 samples.

Advantages

  • Handles any number of strata at once through comma-separated lists, rather than requiring one calculation per subgroup.
  • Automatically shows each stratum's proportion of the total population alongside its allocated sample count in a single table.
  • Ensures the sample composition matches the population's actual subgroup structure rather than an arbitrary even split.

Common Mistakes

  • Splitting the total sample evenly across strata regardless of their actual size, which over-represents small subgroups and under-represents large ones.
  • Entering mismatched numbers of labels and stratum sizes, which the calculator will reject rather than silently misalign.
  • Expecting the allocated sample counts to sum exactly to the requested total, when independent rounding per stratum can cause small discrepancies.

Edge Cases to Watch For

  • If the count of labels doesn't match the count of population sizes, the calculator rejects the input rather than guessing an alignment.
  • A total population of zero across all strata triggers an error since the proportions would be undefined.
  • Because each stratum's allocation is rounded separately, the sum of all allocated samples can be off by a point or two from the requested total sample size, especially with many small strata.

Common Use Cases

  • Market researchers designing a survey that needs proportional representation across regions, age groups, or other segments.
  • Public health or social science researchers planning a stratified sample study across demographic subgroups.
  • Analysts auditing an existing sample to check whether it matches the population's true subgroup proportions.
Written & fact-checked by the Calculateus TeamLast updated August 5, 2026How we verify our formulas

Frequently asked questions

What is proportional stratified allocation?

It splits your total sample across subgroups (strata) in proportion to each subgroup's share of the total population - a stratum with 30% of the population gets roughly 30% of the sample, ensuring every subgroup is represented in the sample at a rate matching its true prevalence.

Related calculators

Confidence Interval CalculatorCalculate the confidence interval for a sample mean.Sample Size CalculatorCalculate the minimum sample size needed for a survey or study at a given confidence level and margin of error.Margin of Error CalculatorCalculate the margin of error for a survey result given sample size and confidence level.Correlation Coefficient CalculatorCalculate the Pearson correlation coefficient between two paired sets of numbers.

Conclusion

Proportional stratified allocation keeps each subgroup's representation in the sample consistent with its share of the overall population, which helps avoid over- or under-sampling any particular group. This calculator automates that proportional math across any number of strata from just population sizes and a target sample total.