Sample size calculator

A sample size is the number of completed responses you need before your survey results say something reliable about the whole group you care about. You almost never survey everyone — you survey a slice, and use statistics to describe the rest.

The catch is that a slice is only useful if it's big enough. Ask ten customers and you learn about ten customers. Ask the right number and you can state, with a known level of confidence, what all of them think — within a known margin of error.

Those two phrases do the heavy lifting. Confidence level is how often this method lands on the right answer. Margin of error is how wide the answer is. Sample size is what you trade to tighten either one.

The standard starting point is Cochran's formula, which assumes an effectively infinite population:

What each part means

The finite population correction

Cochran's formula assumes you're drawing from an unlimited pool. When your population is countable — 4,000 customers, 250 employees — you need fewer responses than the formula suggests, because each one tells you proportionally more. The correction is:

This is why surveying a 200-person company needs far fewer than 385 responses. The calculator above applies the correction automatically whenever you enter a population.

These two inputs drive everything else, and the right answer depends entirely on what the results will be used for.

Confidence level

95% is the near-universal default and what most people will expect when you present results. Drop to 90% for exploratory or internal work where speed matters more than rigour. Move up to 99% only when a wrong call is expensive — regulatory, clinical, or safety-related research.

Margin of error

±5% is the standard for general business research. It means a result of 60% could reasonably be anywhere from 55% to 65% — fine for "most customers prefer A", useless for "A beat B by two points".

• ±10% — quick pulse checks, directional reads, small teams.
• ±5% — the default for customer satisfaction, market research, employee surveys.
• ±3% — when you need to detect smaller differences or split results by segment.
• ±1% — national polling and published research. Expect to need thousands of responses.

Precision gets expensive fast. Halving your margin of error roughly quadruples the sample you need, because n scales with 1/e². Going from ±5% to ±2.5% takes you from 385 responses to about 1,537.

Say you run a subscription business with 8,000 active customers and want to measure satisfaction. You settle on 95% confidence and a ±5% margin of error, and you have no prior data on how people will answer, so p stays at 0.5.

Step 1 — find the z-score. 95% confidence gives Z = 1.96.

Step 2 — apply Cochran's formula.

Step 3 — correct for your finite population.

Step 4 — round up. You need 367 completed responses. Not 367 invitations — 367 finished surveys.

Sometimes the target is simply out of reach — your list is small, or the response rate is poor. You have three honest options, and one dishonest one.

1. Widen the margin of error. Recalculate at ±8% or ±10% and report the wider range. The finding is less precise but still valid.
2. Lower the confidence level. Moving from 95% to 90% cuts the required sample by roughly 30%. Say so when you present.
3. Improve the response rate. Shorter surveys, mobile-friendly formats, a clear reason to respond, and one well-timed reminder typically move response rates more than any other lever.

The dishonest option is to collect 80 responses, report them as though they represented everyone, and say nothing about precision. That's how organisations end up making confident decisions on noise.

• Sizing for the whole survey, then analysing by segment. 385 responses gives you ±5% overall. Split it four ways and each segment has under 100 responses and a margin near ±10%. Size for the smallest group you intend to report on.
• Confusing sample size with response rate. A 60% response rate from a list of 100 is worse than a 12% response rate from a list of 5,000. What matters is the number of completions and whether they're representative.
• Assuming a big sample fixes bias. Sample size controls random error only. If only your happiest customers respond, 10,000 responses will give you a very precise measurement of the wrong thing.
• Ignoring the population correction. For small, defined groups it makes a real difference — and asking for more responses than you need burns goodwill.
• Reporting a single number with no interval. "72% are satisfied" is incomplete. "72%, ±5% at 95% confidence" is a result.

Once you know your target, the work shifts to actually collecting the responses. Divide your target by your expected response rate to get the size of your send, then build something short enough that people finish it.

You can start from a ready-made questionnaire in the SurveyKar template library, and once responses come in, check the precision you actually achieved with the margin of error calculator — it's the exact inverse of this one, so the numbers will line up.