Lloyd's Register Foundation Global Safety Evidence Centre · Tools
Internal Foundation tool

Study Design Calculator.

Work out how many people you need to survey or interview, and how confident you can be in what you find — for a poll, an evaluation, or a qualitative study. Plain-language by default; the statistics are there if you want them.

3
Calculators: survey, comparison, qualitative
0
Stats degree required
What are you planning?
Estimate a single figure — like "what share of people agree with X" — from a sample, within a margin of error you choose.
Your best guess at the answer
iThis is "p" in the formula. If you have no idea, leave it at 50% — that's the most conservative assumption and gives the largest (safest) sample size. If a previous wave found 30% agreement, use that.
%
Roughly what proportion do you expect to find? Unsure — leave at 50%.
How precise do you need to be?
iThe "±" you'd report alongside your headline figure, e.g. "62% ± 3pp". Smaller margins need bigger samples — halving the margin roughly quadruples the sample size needed.
pp
How many percentage points of wobble can you live with either side of your result?
iHow often you'd expect this margin of error to hold up, if you repeated the survey many times. 95% is the standard choice across social research and polling.
95% is the usual default for surveys and polling.
Adjustments (optional)
iLeave blank for a large or effectively unlimited population (a country, a general public). Only fill this in when you're sampling from a small, known, finite list — e.g. all 400 grantees the Foundation has ever funded.
Only matters if you're drawing from a small, fixed list — not a general population.
iInflates the sample size to account for clustering or complex sampling (e.g. sampling companies, then ships within a company, then crew on board — rather than drawing seafarers independently at random). A design effect of 1.0 = a pure random sample. Multi-stage or clustered surveys like the World Risk Poll typically run 1.3–2.0; ask your sampling statistician if unsure.
Above 1.0 if your sample is clustered (e.g. by company, ship, or region) rather than a pure random draw. Leave at 1.0 for a simple random sample.
Result
How it works

Notes, formulas and caveats

Click to expand for the maths behind each calculator, and where the numbers come from.

Survey sample size

Uses the standard formula for estimating a proportion within a margin of error: n = z²×p×(1−p) / e², where z comes from your confidence level, p is your expected result and e is the margin of error. If you give a population size, a finite population correction is applied afterwards; if you give a design effect above 1.0, the result is inflated to account for clustering or complex weighting. Numbers are always rounded up to the next whole person.

Comparing two groups

For two percentages, this uses the normal-approximation formula for comparing two independent proportions: n = (zα + zβ)² × (p₁(1−p₁) + p₂(1−p₂)) / (p₁−p₂)². For two averages, it uses n = 2 × (zα + zβ)² × σ² / δ², assuming both groups share roughly the same spread (standard deviation) and are the same size. "Power I already have" runs the same formula backwards to tell you the power of a sample size you've already fixed on. All values use exact normal-distribution quantiles (Acklam's inverse-CDF approximation), not rounded textbook z-values, so results will be close to but may not exactly match older printed tables.

This is the normal-approximation method, standard for planning purposes; it can be optimistic when a group's expected proportion is very close to 0% or 100%, or with very small planned samples (under ~20 per group) — get a statistician to check the exact method (e.g. Fisher's) in those cases.

Qualitative sample size

Unlike the two quantitative calculators, this isn't a formula — qualitative adequacy is judged by saturation (you stop hearing new themes), not statistical power. The ranges shown come from Hennink & Kaiser's 2022 systematic review of empirical saturation studies (Social Science & Medicine, 292): most studies with a fairly uniform population and a narrowly defined question reached code/theme saturation at 9–17 interviews or 4–8 focus groups, while deeper meaning saturation needed closer to 24 interviews or 8 focus groups. Studies looking for patterns that hold across several sites or very different sub-groups should plan for 20–40 interviews. Case-study guidance follows Yin's case study design logic rather than saturation: a single case suits a revelatory or critical case, while comparative claims need multiple cases (commonly 4–10) for replication.

Treat every range here as a starting point, not a target to hit exactly — plan to check for saturation as you go, and stop once two or three additional interviews add nothing new to your themes.

Caveats

These calculators plan a study; they don't replace a statistician for anything unusual — stratified designs, rare-event outcomes, non-inferiority tests, or multiple comparisons all need extra care beyond what's modelled here. Treat every result as a planning estimate, and build in a buffer for non-response and dropout on top of the number shown.

✓Copied