Stratified Sampling Calculator
How many people to draw from each group so that the sample mirrors the population, with the rounding handled properly.
Results
What this tool does
A survey that draws everyone at random can easily end up with too few people from a small region or an uncommon age band, and then says nothing reliable about them. Stratified sampling fixes the shares in advance: each group contributes in proportion to its size, so the sample looks like the population by construction. List the groups and how many people are in each, say how many you can afford to ask in total, and this page hands out the places — including the awkward remainders, which it allocates by largest remainder so the column adds up exactly.
Formula
proportional allocation: each group takes total sample × group size ÷ population · the remainders go to the groups with the largest lost fraction
Variables
| Symbol | Meaning | Unit |
|---|---|---|
strata | The groups and their sizes, one per line | — |
sample_size | How many to sample in all | — |
OUT | How many from each | — |
PP | Everyone | — |
SM | The sample adds up to | — |
FR | Of everyone, that is | % |
NS | Groups | — |
BG | Largest group | — |
SA | Smallest group gets | — |
EQ | An equal split would give each | — |
Worked example
- The groups and their sizes, one per lineNorth = 12000 South = 8000 East = 5000 West = 3000
- How many to sample in all300
- How many from eachNorth 12000 129 42.9% South 8000 86 28.6% East 5000 53 17.9% West 3000 32 10.7%
- Everyone28,000
- The sample adds up to300
- Of everyone, that is1.071 %
- Groups4
- Largest groupNorth
- Smallest group gets32
- An equal split would give each75.0
Limitations
- The calculation runs entirely in your browser. The values you type are never sent to a server.
Frequently asked questions
Why do the numbers not divide evenly?
Because a proportion of a sample is almost never a whole number of people, and rounding each group on its own would leave the total one or two away from what you asked for. This page rounds every group down first, then hands the leftover places to whichever groups lost the most in the rounding. It is the same method used to allocate parliamentary seats, and it guarantees the column adds up to exactly the sample you wanted.
Is proportional always the right split?
No. Proportional allocation gives the best overall estimate for the population as a whole, and it is the right default. But it leaves small groups with very few people, and if you want to say something about each group separately, a handful is not enough to say anything at all. When that is the goal, an equal split — or something between the two — serves better, at the cost of a slightly less precise overall figure. The equal-split figure is shown here for that comparison.