Sample Size Calculator
Estimate the survey sample size needed for a confidence level and margin of error. Includes the finite population correction for India surveys.
Use 50% when unknown — it gives the largest sample.
Optional — applies the finite population correction.
Required sample size
385
Unlimited population
Corrected sample size
—
Enter a population size
Formula: n = z² × p(1 − p) ÷ e², rounded up. A 5% margin at 95% confidence needs 385 respondents.
Last updated: August 2026
How this calculator is verified
Checked by True Calculator automated test suite on
- Formula verified against a published worked example in the automated test suite
- Edge cases (zero, negative, boundary and unit-mismatch inputs) covered by unit tests
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When to Use This Calculator
Use the sample size calculator whenever you plan a survey, poll or experiment and need to know how many responses to collect — student projects, market research, customer satisfaction studies, exit polls and election surveys across India. The formula is the standard one used by polling agencies and journals: n = z² × p(1−p) ÷ e², with the finite population correction for small, well-defined groups such as employees of a single company or students of one college. Knowing the required sample before you start prevents both wasted spend on oversized surveys and useless undersized ones whose margins are too wide to support conclusions. The calculator also doubles as a margin-of-error checker: enter your actual response count afterwards to see the precision your collected data genuinely supports.
How to Use This Calculator
- Step 1: Choose the confidence level — 95% is the standard default for most surveys.
- Step 2: Enter the margin of error you can tolerate, for example 5% for a general survey.
- Step 3: Enter the expected proportion; keep 50% when you have no prior information.
- Step 4: Enter the total population size if it is small, to apply the finite population correction.
Worked Example
A political researcher in Lucknow wants to poll voter preference with 95% confidence and a 5% margin of error, with no prior estimate of vote share. Entering 95%, a 5% margin and a 50% expected proportion gives 385 respondents — the classic sample size for national-style polling. If the survey covers a constituency of only 1,000 voters, the finite population correction brings this down to 279. Tightening the margin to 3% at 99% confidence pushes the requirement to 1,843 respondents, which is why high-precision studies cost much more.
Tips and Common Mistakes
- •Tip 1: Use 50% proportion unless you have real prior data — it produces the largest, safest sample size.
- •Tip 2: Halving the margin of error quadruples the sample size, so choose the margin that matches the decision at stake.
- •Tip 3: Apply the finite population correction only when your sample would exceed about 5% of the population.
- ✗Mistake 1: Reporting a margin of error for a convenience sample — the formula assumes random sampling.
- ✗Mistake 2: Forgetting non-response: if 60% of people reply, you must invite about 1.7 times the required sample.
Frequently Asked Questions
What sample size do I need for a 95% confidence survey?
For a 95% confidence level with a 5% margin of error and an assumed 50% proportion — the most conservative choice — you need 385 respondents. If the total population is small, say 1,000, the finite population correction reduces this to 279. Enter your own margin of error to adjust.
Why use 50% as the expected proportion?
The sample size formula p(1−p) is largest when p = 0.5, so assuming 50% gives the biggest — and safest — sample. It guarantees your margin of error holds no matter what the true proportion turns out to be. If you have prior data suggesting a different proportion, say 30%, entering it produces a smaller required sample.
What is the finite population correction?
When your sample is a large fraction of the total population, sampling without replacement is more efficient than the infinite-population formula assumes. The correction n' = n / (1 + (n−1)/N) shrinks the required sample size. It matters most for small, well-defined groups like students in a single college or employees of a company.
Does this apply to market research in India?
Yes, it is the same formula used for election polling, brand studies and customer satisfaction surveys. For example, a pan-India online survey typically targets around 1,000–1,500 responses for a 2.5–3% margin at 95% confidence. Always state the margin of error alongside any headline percentage you publish.
How do I lower the required sample size?
You can accept a wider margin of error (say 7% instead of 5%), use a lower confidence level (90% instead of 95%), or enter an expected proportion closer to 0% or 100%. Each change trades precision for cost. The trade-off is direct: halving the margin of error quadruples the required sample size.
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