Calculate the sample size needed for a survey to achieve your target margin of error and confidence level. Used in market research, opinion polls, A/B tests and quality control to know how many respondents you need.
Use 0.5 if unknown (most conservative)
Required sample size
385 respondents
Using z = 1.96 for 95% confidence at ±5% margin
Formula: n = z² · p(1−p) / e²
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Sample size determination is the first practical question in any survey, A/B test, clinical trial or market research study: 'How many respondents do I need to interview to get statistically meaningful results?' Sample too few and your results carry too much uncertainty to act on; sample too many and you waste time, money and goodwill. This calculator gives you the mathematically optimal sample size for a target margin of error and confidence level. It's the same calculation used by CSDS, Lokniti, Axis My India, CVoter and other Indian polling agencies when designing election surveys, and by product teams at Flipkart, Swiggy, Zomato, and Paytm when planning A/B tests.
Indian context: a national opinion poll with 1,200 respondents gives ~±3% margin at 95% confidence - sufficient for election predictions. State-level polls need 800-1,000 per state. Brand surveys for a city require 400-500 respondents for ±5% margin. A/B testing on websites can need 1,000-50,000 visitors per variant depending on baseline conversion rate and detectable difference. This calculator handles all these cases including finite population correction for small populations like 'survey all employees of a 500-person company'.
Pick your confidence level (95% is standard).
Enter your target margin of error (e.g. ±5%).
Enter the population proportion (use 0.5 for the most conservative estimate).
Optionally enter total population size for finite-population correction.
See the required sample size.
For a population proportion, the formula is n = (z² × p × (1−p)) / e². For a known finite population, the corrected sample size is n / (1 + (n−1)/N). Using p = 0.5 gives the largest required sample - safest if the true proportion is unknown.
n₀ = z² × p × (1−p) / e² n = n₀ / (1 + (n₀−1) / N) (finite population)
Core formula for infinite (large) population: n = z² × p × (1−p) / e², where z is the critical value for confidence level (1.96 for 95%, 2.58 for 99%, 1.645 for 90%), p is the expected proportion (0.5 if unknown - the worst case that maximises required sample), and e is the margin of error in decimal (0.03 for ±3%). The formula derives from the standard error of a proportion: SE = √(p(1-p)/n), set equal to e/z and solve for n.
Finite population correction: when sampling more than ~5% of a known finite population N, adjust: n = n₀ / (1 + (n₀-1)/N). For very large N, this barely changes n₀; for small N (like surveying 500-person company), it significantly reduces required sample. Example: n₀ = 384 (95% conf, ±5%, p=0.5) reduces to 217 for a 500-person population. The intuition: when you sample a large fraction, your sample contains more of the truth, so you need fewer to be confident.
Practical adjustments: factor in expected response rate. If you need 1,000 completed responses and response rate is 30% (typical for online surveys), you need to invite 3,300 people. For panel surveys, response rates can be 60-70%; for cold email, 5-15%. Multiply target n by 1/response_rate to get gross sample needed. Stratified sampling (separate samples by region, age, gender) may need larger total samples but produce more accurate sub-group estimates.
n = 1.96² × 0.5 × 0.5 / 0.03² = 3.8416 × 0.25 / 0.0009 = 1,067. Round up to 1,100. Standard CSDS-style poll size. Smaller margins (±2%) require 2,401; ±1% requires 9,604 - quickly impractical.
n₀ (uncorrected) = 384. Corrected for finite N: n = 384 / (1 + 383/500) = 384 / 1.766 = 217 employees. About 43% of the company. Manageable for an HR survey.
More complex - needs a power analysis tool. Rough estimate: with baseline p=0.03, lift to 0.03 × 1.02 = 0.0306, detectable at α=0.05 with 80% power, requires ~50,000 visitors per variant. A/B tests on small effects need large samples.
How far the sample estimate can stray from the true population value. ±3% margin means the result is within 3 percentage points of the truth (with the chosen confidence).
The product p × (1−p) is maximised at p = 0.5, giving the largest required sample. Safest when you don't know the true proportion in advance.
95% is the standard for opinion polls and most research. 99% is used for high-stakes decisions (medical, regulatory). 90% is sometimes used for quick estimates.
When sampling more than ~5% of a population, the variance is smaller than the simple formula suggests. The correction reduces required sample size for small populations.
1000-1100 respondents at 95% confidence gives ±3% margin. National polls typically use this as their floor.
Yes for fieldwork. If response rate is 25% and you need 1000 completes, you need to invite 4000 people. The math doesn't change but logistics do.
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