Sample Size Calculator
Sample size calculator for surveys (Cochran formula with finite-population correction) and A/B tests (power analysis for proportions). Get the minimum n needed.
Sample Size Calculator
How to use the Sample Size Calculator
Pick mode: Survey or A/B test
Survey mode: estimating an unknown population proportion (% who like brand X, % planning to vote Y). Uses Cochran\'s formula with optional finite-population correction. A/B test mode: detecting a difference between two conversion rates (5% baseline → 6% target). Uses power analysis for the z-test of proportions.
For survey: set confidence, MOE, expected proportion
95% confidence is standard (±2 SE rule). ±5% MOE is typical consumer-survey precision (≈ 384 respondents). Use p=0.5 if you have no prior estimate (worst-case max sample). For finite populations < 50,000, enter population size for adjustment.
For A/B test: set baseline + target + power
Baseline = current conversion rate. Target = what you\'re trying to detect (e.g., 6% if you want to detect a 1pp improvement on 5% baseline). 80% power is conventional minimum. α = 0.05 is conventional significance. Two-tailed for safety.
Read minimum n needed
The result is the MINIMUM. Aim for 10-20% above to account for non-response (surveys) or unexpected dropoff (A/B tests). For multi-arm tests (A/B/C/D), use per-arm sample size from the calculator times the number of arms.
Sample size — getting it right before you run the test
Sample size is the single most-neglected pre-test decision in business research. Too few subjects + you\'ll miss real effects (Type II error / low power); too many + you waste time, money, or both. Proper sample-size calculation BEFORE running a survey or A/B test prevents both failure modes. The math is well-established — Cochran\'s formula for surveys (1953) + the z-test power analysis for proportions are the standard tools — but most product teams skip this step and run "until they see something." This calculator gives you the right number upfront so you know how long an A/B test must run or how many people you need to survey for the precision you want.
Survey sample size — Cochran\'s formula
n = z² × p(1-p) / e². z = confidence multiplier (1.96 for 95%); p = expected proportion (use 0.5 for max sample when unknown); e = margin of error (half-width of confidence interval). At 95% confidence + ±5% MOE + p=0.5: n = 1.96² × 0.5 × 0.5 / 0.05² = 384.16 → 385. Finite-population correction: when sampling > 5% of population, n_adjusted = n / (1 + (n-1)/N). For surveys of populations under ~50,000, this materially reduces required sample. Common targets: ±5% MOE at 95% confidence (n ≈ 384) for consumer surveys; ±3% MOE (n ≈ 1,067) for political polling; ±1% MOE (n ≈ 9,604) for census-grade precision.
At 95% confidence + ±5% MOE, you need 384 respondents to estimate any proportion. This holds for surveys of 1 million or 100 million people — the formula doesn't care about population size when n << N.
A/B test sample size — detecting lifts requires huge samples
A/B test sample size depends critically on the size of effect you want to detect. Sample size grows roughly with 1/lift². Detecting a 5% relative lift from a 10% baseline (10% → 10.5%, 80% power, α=0.05 two-tailed): 57,763 per variant. Detecting a 1% relative lift (10% → 10.1%): 1,419,073 per variant — a fifth of the lift, ~25× the sample. Both figures are what the calculator above returns; enter them and check. The implication: small lifts require enormous samples. Most product changes produce small lifts (1-5%) — and small platforms simply don\'t have the daily traffic to detect them. Practical wisdom: only test changes large enough to actually matter (10%+ relative lift typically). For smaller-scale platforms (under 5K DAU), plan for weeks of test duration or test bigger-bet changes.
Common ASEAN-specific sample-size pitfalls
Three errors common in ASEAN business contexts: (1) Cross-country surveys treating regional sample as one: a 1,000-respondent survey covering SG/MY/PH/ID/TH/VN has effective sub-samples of ~167 per country — only ±7% MOE per country, not ±3% as reported. For per-country claims, plan ~400 per country (n=2,400 total). (2) Under-sized A/B tests in early-stage products: testing on 1-2K MAU products and declaring winners — typically you can only detect very large lifts (30%+). Realistic expectation: most A/B tests fail to reach significance because the product simply doesn\'t have enough traffic. (3) Online survey panels with poor demographic coverage: large platforms (Cint, Toluna, Lucid in ASEAN) have specific demographic skews. A "nationally representative" sample requires expensive quota sampling, not just a panel sample. Check panel quality before accepting estimates.
10 Things to Know About Sample Size
±5% MOE at 95% confidence: only need 384 respondents — regardless of whether population is 1M or 100M.
A/B test sample size ∝ 1/lift². Detecting half the lift requires 4× the sample.
Most product A/B tests are underpowered. Realistic effects (1-5% lift) need 100K+ users per variant.
80% power is conventional minimum. Below that, you frequently miss real effects.
Use p = 0.5 in survey sample-size formula for worst-case (maximum sample needed) when no prior estimate exists.
Finite-population correction matters when sampling > 5% of population. Reduces required sample.
Cross-country ASEAN surveys often under-sample per-country — n=1,000 across 6 countries = only ±7% MOE per country.
One-tailed tests need ~20% smaller sample than two-tailed, but require pre-registered direction.
Multi-arm A/B/C/D tests need full per-arm sample for each arm. Total = per-arm × n_arms.
Always add 10-20% buffer for non-response (surveys) or unexpected dropoff (A/B tests).
Frequently Asked Questions
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Sample size scales with desired precision, not population size, when n << N. The Central Limit Theorem says the sampling distribution\'s standard error = SD / √n — depends only on sample n, not population N. Counterintuitive but mathematically correct. Finite-population correction only kicks in when you\'re sampling a meaningful fraction of the population (>5%).
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Use p = 0.5. This gives the maximum sample size needed (variance p(1-p) is maximised at p=0.5). If your true p is 0.1 or 0.9, you\'d actually need fewer respondents — but sizing for worst case ensures you have enough regardless. Sample-size estimates done before you have data should default to p=0.5.
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Because typical effect sizes are small. Most product changes produce 1-5% relative lifts, requiring tens to hundreds of thousands of users per variant. This is why large platforms (Grab, Shopee, Sea) can A/B test effectively while small startups (~1K DAU) often can\'t — their math demands far more users than the product has. Practical answer: small-scale products should test bigger-bet changes (substantial UX redesigns, new categories) where effects are large enough to detect with available users.
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Statistical power = 1 − probability of Type II error (failing to detect a real effect). 80% power means: if the true effect IS what you\'re sizing for, you\'ll detect it 80% of the time + miss it 20%. 80% is conventional minimum (Cohen 1988). 90% is stricter; below 80% is considered underpowered. Higher power requires larger samples: 90% power needs ~30% more sample than 80% power. Most product teams default to 80%.
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Two-tailed is the safe default. One-tailed: more powerful (smaller sample for same effect) BUT requires pre-registering the direction of effect before seeing data. If you set up the test as "test will improve conversion" and conversion actually decreases significantly, one-tailed would NOT detect this — it can only "see" improvements. Two-tailed catches both directions. Use one-tailed only when you genuinely care only about one direction (regulatory non-inferiority testing, etc.).
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Plan per-arm sample size using the calculator (for the smallest difference you want to detect between any two arms). Then total sample = per-arm × number of arms. Plus multiple-comparison correction: with k arms, you have k(k-1)/2 pairwise comparisons. Adjust α (Bonferroni: α_adjusted = α / k(k-1)/2). Adjusted α means higher z-scores in the formula → larger per-arm sample. Practical rule: 4-arm test (A/B/C/D) ≈ 1.5× per-arm sample vs 2-arm; 6-arm ≈ 2×.
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This tool sizes for binary outcomes (proportions, conversion rates). For continuous outcomes (revenue per user, time on page, etc.) use t-test power analysis with Cohen\'s d effect size. Rough rule: detecting d = 0.2 (small effect) needs ~394 per group at 80% power; d = 0.5 (medium) needs ~64; d = 0.8 (large) needs ~26. Most A/B tests on revenue have small effect sizes — need large samples. Use specialised software (R pwr package, G*Power, Python statsmodels) for precise continuous sample sizing.
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Don\'t. Repeatedly checking results before reaching the calculated sample size dramatically inflates false-positive rates. If you peek 10 times during a test, your effective α can be 20-30% even though each "check" used α = 0.05. Solutions: (1) Commit to the calculated sample size + don\'t stop early; (2) Use sequential testing methods (group sequential designs, Bayesian methods) designed to handle peeking — but these need expert setup. Most A/B testing tools (Optimizely, VWO, etc.) include sequential testing options.
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No. All calculations run in your browser via JavaScript. Open DevTools → Network and confirm zero outbound requests. Parameters stay on your device. Safe for confidential product planning.
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Pair with: T-Test (RT-CNV-090) for continuous A/B; Chi-Square (RT-CNV-091) for testing conversion-rate differences post-test; ANOVA (RT-CNV-092) for multi-arm continuous; Confidence Interval (RT-CNV-083) for interval estimation. External: G*Power (free, gold-standard sample-size tool); R pwr package; Python statsmodels; Optimizely + VWO built-in sample-size calculators for A/B testing.
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