Sample Size Calculator
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Other tools you may find usefulSample size calculator – how many respondents do you need?
A good statistical sample produces reliable results with minimal testing cost. Too small a sample = inaccurate results. Too big = unnecessary costs. The calculator calculates the minimum sample size based on your desired margin of error, confidence level, and population size.
Key statistical concepts
Margin of error(s): the allowable error of the results. ±3% = results may differ by 3 percentage points. Confidence level (z): 95% confidence → z = 1.96. 99% → z = 2.576. 90% → z = 1.645. Variance (p): the proportion of the expected response. Without knowledge: p = 0.5 (maximizes the sample). Population (N): total number of people.
Sample size formulas
Infinite population: n = z² × p(1-p) / e². For 95%, p=0.5, e=5%: n = 1.96² × 0.25 / 0.05² = 3.8416 × 0.25 / 0.0025 = 384.16 ≈ 385 people. Finite population: n_adj = n / (1 + (n-1)/N). For N=1000: n_adj = 385 / (1 + 384/1000) = 385/1.384 ≈ 278 people.
Popular configurations
Nationwide survey (38M): e=3%, confidence 95% → n = 1068. e=5% → n = 385. NPS (Net Promoter Score): 300-400 answers is enough. A/B website test: depends on the base conversion rate. Local study (10,000): e=5%, 95% → n = 370. Pilot study: 30-50 people (initial).
Survey planning
Attrition rate: assume 30-50% of survey failure. If you need 385, please send 600-770. Sampling method: random (representative) vs quota (stratified). Bias: online survey ≠ representative sample (selection bias). Survey fatigue: max 10-15 questions for good answers.
FAQ
How many respondents do I need for a reliable survey?
Minimum rule: 30 people (the law of large numbers comes into play). For simple tests: 100-200. For brand/product level research: 300-500. For nationwide research: 1000-1500 (used by Ipsos, CBOS). Medical/pharmaceutical research: hundreds to thousands (depends on effect and statistical power).
What is margin of error and how to interpret it?
Score 52% yes with ±3% error: true score 49-55%. At ±5%: 47-57% – majority or minority possible. The larger the margin of error: the less certainty the result is. The media often does not provide margins in election polls - always ask "what sample and what margin?"
How to conduct a study on a small budget?
Google Forms: Free, Basic Analytics. Typeform: up to 10 responses/month for free. SurveyMonkey: Free plan. Distribution: social media, email to database, FB groups. Recruitment targets: announcement in appropriate groups (e.g. "we are testing users for X"). Incentive: vouchers drawn among participants.
What is statistical power?
Power (1-β): probability of detecting an effect that exists. β = type II error (missing an effect). Standard: power = 0.8 (80%). Power 0.8, confidence level 95%, small eta² = large n. Power calculator (G*Power: free software) → plan n before the test. Low power = many research studies fail to detect true effects.
How to calculate sample size for A/B testing?
Conversion rate baseline: e.g. 2%. Expected increase: +0.5% (minimum detectable effect). Confidence level: 95%. Power: 80%. Calculator: abtestguide.com/calc. Result: e.g. 5,000 users per variant. Test time: depends on traffic. Trap: ending the test "when the result is visible" → invalid results (peeking problem).
Related tools: statistical calculator, percentage calculator and test data generator.