Running a survey, an A/B test, or a customer poll without enough responses is like fishing with a too-small net: you may catch something, but you cannot trust that it represents the whole pond. This sample size calculator tells you exactly how many responses you need before you start collecting data, so you do not waste money fielding 10,000 surveys when 384 would have done — or, worse, publish a result that a 200-response sample cannot actually support.
The math below follows Cochran's classic sample size formula for a proportion, the same method used by polling firms, market research agencies, and academic researchers. Enter your confidence level, margin of error, expected response distribution, and (optionally) the size of the population you are studying, and the calculator returns the minimum number of completed responses required.
How to Use
- Set your Margin of Error — the tolerance you are willing to accept, usually 5% (the default). A 5% margin means that if 40% of respondents pick option A, the true value in the whole population is likely between 35% and 45%. Smaller margins need larger samples.
- Choose your Confidence Level — 90%, 95%, or 99%. The default 95% means that if you ran the same survey 100 times, 95 of those surveys would produce a result within your margin of error. 95% is the standard for most business and academic work.
- Enter the Expected Response Distribution (p) — your best guess at the proportion you expect. If you have no idea, leave it at 50%. A 50/50 split produces the largest possible sample size, which is the safe, conservative choice.
- Fill in the Population Size only if the group you are studying is small and known — for example, all employees at a 500-person company, or all 2,000 existing customers. If your population is large or open-ended (a city, a social media audience, all website visitors), leave it at 0 to use the infinite-population formula.
- Read the result card. Required Sample Size is the number of completed surveys you actually need. The calculator also shows the infinite-population figure, whether finite population correction was applied, and the effective margin of error after rounding up to whole respondents.
The Sample Size Formula
The infinite-population sample size for a proportion is:
n₀ = Z² × p × (1 − p) / e²
Where:
- Z is the two-sided normal quantile for your confidence level — 1.645 for 90%, 1.96 for 95%, and 2.576 for 99%.
- p is your expected response proportion (0.5 for a 50/50 guess).
- e is your margin of error, expressed as a decimal (0.05 for 5%).
Plugging in the textbook defaults — 95% confidence, 5% margin, p = 0.5 — gives n₀ = 1.96² × 0.25 / 0.0025 ≈ 384 respondents. That is why the number 384 appears on nearly every survey methodology cheat sheet: it is the smallest sample that can support a ±5% result at 95% confidence when you have no prior estimate.
When your population is finite and small, the formula shrinks the required sample with the finite population correction (FPC):
n = n₀ / (1 + (n₀ − 1) / N)
where N is the population size. For a population of 1,000, the 384 figure drops to about 278 completed surveys. The FPC matters most when your sample would otherwise exceed roughly 10% of the population; for large populations, the correction is negligible.
Why p = 0.5 Is the Conservative Choice
The product p × (1 − p) is largest when p = 0.5 (it equals 0.25). When p = 0.1, the product falls to 0.09, and the required sample size drops by more than half. If you have pilot data or strong domain knowledge that says a response will land near 10% or 90%, plug that in and your sample needs shrink dramatically. But if you are truly guessing, 50% guarantees your sample is large enough regardless of what the real answer turns out to be.
A common mistake is to use a sample size calculated at p = 0.5 but then interpret a result near 10% with the same 5% margin. The math does not work that way: a 10% result in a 384-person survey actually carries a margin closer to ±3%, which is fine (it is tighter, not looser), but a 5% result in a sample sized for p = 0.5 carries a much wider real margin. When in doubt, over-sample by 10–20% to account for incomplete responses and screening filters.
Non-Responses and Incidence Rates
The 384 figure is the number of completed, valid responses. It is not the number of people you invite. If your survey has a 60% response rate, you need to invite 384 / 0.60 ≈ 640 people. If only 40% of the population fits your screening criteria (incidence rate), gross up again: 640 / 0.40 ≈ 1,600 invitations. Most online panel vendors quote cost per complete, so ask for the completed-survey number, not the impression number.
Examples
Example 1 — The textbook default. A startup wants to know what percentage of free users will upgrade to a paid plan. They set 95% confidence, a 5% margin of error, and p = 50% (no prior data), with no population cap. The calculator returns 384 completed surveys. That is the minimum; planning for a 40% response rate means inviting about 960 users.
Example 2 — Finite population correction at a small company. A 500-person company wants to run an employee engagement survey. At 95% confidence, 5% margin, p = 50%, and N = 500, the FPC brings the required sample down from 384 to about 218 completed responses. Surveying 218 of 500 employees (44%) is enough; surveying all 500 would be overkill unless response anonymity is the goal.
Example 3 — Tighter margin for an A/B test. An e-commerce team wants to detect a 3 percentage point lift in conversion between two checkout flows. They set 95% confidence, 3% margin, p = 50%, and no population cap. The required sample jumps to about 1,068 per variant, or roughly 2,136 visitors split across both arms. Halving the margin from 5% to 3% roughly triples the required sample, because sample size scales with the square of the margin.
Example 4 — Large population sanity check. A national pollster sets 95% confidence, 3% margin, p = 50%, and enters N = 330,000,000 (the US adult population). The FPC barely moves the number: the infinite-population figure is 1,068 and the corrected figure is 1,067. This is why national polls famously need only about 1,000 respondents to represent a country of 330 million people — the population size barely matters once it exceeds a few thousand.
FAQ
How many survey responses do I need for 95% confidence and a 5% margin of error?
With no prior estimate (p = 0.5) and a large population, you need 384 completed responses. This is the most commonly cited sample size in market research and is the default answer this calculator gives. If your population is under a few thousand people, the finite population correction lowers the number.
What is a good margin of error?
For most business surveys, 5% is the accepted standard. Political polls and academic studies often target 3%. Customer satisfaction tracking can tolerate 7–10% if the decisions being made are low-stakes. Remember that halving the margin roughly quadruples the required sample size, so tighten the margin only when the extra precision is worth the extra cost.
Does a larger population need a much larger sample?
Surprisingly, no. Once the population exceeds a few thousand people, the sample size barely changes whether the population is 100,000 or 330 million. The finite population correction only meaningfully reduces the required sample when your target group is small and well-defined — such as employees at a single company or members of a small association.
What if I already know the likely response percentage?
Plug your estimate into the Expected Response Distribution field. If you expect 15% of users to take an action, set p = 15% instead of 50%. Because p × (1 − p) is smaller away from 50%, the required sample drops. For example, at 95% confidence and a 5% margin, p = 15% requires about 196 responses instead of 384. If you are unsure, stick with 50% — it is the conservative choice.
What is the difference between confidence level and margin of error?
The confidence level says how often your method would produce a result within the margin if you repeated the survey many times. The margin of error says how wide that interval is. A 95% confidence level with a ±5% margin means: "If we ran this survey 100 times, 95 of them would give an answer within 5 percentage points of the true value." They are two separate knobs, and both feed the same formula.
Why do I need more responses than the calculator says?
The calculator returns completed, valid responses. Plan for non-responses (invite more people than the target), screening quotas (not everyone qualifies for your survey), and break-offs (some people start but do not finish). A common rule is to add 20–30% buffer on top of the calculated sample size.
Disclaimer
This sample size calculator is provided for informational purposes only and does not constitute statistical, research, marketing, or legal advice. Required sample sizes are estimates based on the standard normal-approximation formula for proportions; real-world survey design must also account for clustering, weighting, stratification, non-response bias, and the survey mode. Always confirm your sample plan with a qualified statistician or research professional before fielding a study whose conclusions will drive material business decisions.