Sample size

Sample size is the number of completed, valid responses you analyze to draw conclusions about a larger group. For a typical survey reported at 95% confidence with a ±5% margin of error, you need about 385 responses from a large population, and fewer from a small one: about 323 from a population of 2,000.

Sample size counts completed responses, not invitations sent or surveys started. How many people you need to invite depends on your response rate (see below).

How many respondents you need: quick table

Responses needed at 95% confidence, assuming the most cautious 50/50 split of answers:

Above about 10,000 people, the population size hardly matters: a city and a whole country need nearly the same sample for the same precision.

The formula

For a percentage (such as the share of satisfied customers), the standard calculation (Cochran) is:

n₀ = z² × p × (1 − p) ÷ e²

• z: 1.645 for 90% confidence, 1.96 for 95%, 2.576 for 99%.
• p: the expected share. Use 0.5 when you don't know it; it gives the largest, safest sample.
• e: the margin of error as a decimal, such as 0.05 for ±5%.

For a population that isn't very large, apply the finite population correction:

n = n₀ ÷ (1 + (n₀ − 1) ÷ N), where N is the population size.

Worked example: an online store has about 20,000 customers a month and wants the share of satisfied customers at 95% confidence, ±5%. n₀ = 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.16. Corrected: 384.16 ÷ (1 + 383.16 ÷ 20,000) ≈ 377 responses. The sample size calculator does this for any inputs.

From sample size to invitations

Invitations = required responses ÷ expected response rate

If past surveys to the store's customers got a 10% response rate, 377 responses need about 3,770 invitations. Add a little extra for answers you will remove during cleaning (duplicates, speeders, blank text answers). The survey invitations calculator adds that buffer for you.

What changes the sample size

• Margin of error. Halving it roughly quadruples the sample: ±5% needs about 385, ±2.5% about 1,537.
• Confidence level. 99% needs more responses than 95%; 90% needs fewer.
• Expected split. If you expect 90% to choose one answer, fewer responses give the same precision as a 50/50 split.
• Subgroups. To report each region or age group with ±5%, each subgroup needs its own sample of that size. To compare two groups, plan with a power analysis and use the two-group sample size calculator.

Is there a minimum number of respondents?

There is no single minimum. You will often hear "30" or "100", but neither is a rule for surveys. What a sample of a given size buys you, as a margin of error at 95% confidence for a large population:

• 30 responses: about ±18 percentage points
• 100 responses: about ±10 points
• 200 responses: about ±7 points
• 400 responses: about ±5 points
• 1,000 responses: about ±3 points

Decide which margin your decision can live with, then read off the sample. The margin of error calculator works in the other direction, from responses to precision.

Qualitative research: saturation, not formulas

The formulas apply to quantitative research, where you estimate shares and averages. In interviews and focus groups, you stop when new participants no longer bring new themes, a point called saturation. In a well-known study of interviews with a fairly uniform group, Guest, Bunce and Johnson (2006) reached saturation within about 12 interviews. More varied groups need more.

Common mistakes

• Counting invitations or started surveys instead of completed, valid responses.
• Planning only the total and then reporting subgroups of 40 people as if they were precise.
• Expecting a large sample to fix a biased one. 5,000 responses from a link posted only for loyal customers still describe loyal customers. See selection bias.
• Paying for a round number. Going from 400 to 1,000 responses narrows the margin from about ±5 to ±3 points. Check whether that difference changes your decision.
• Using these formulas for a convenience sample. The margin of error assumes random selection.

Once you know your target, SurveyNinja can close a survey automatically when it reaches that number of responses or a closing date (Response Limit and Survey Deadline, from the Standard plan). For a longer walkthrough with more examples, see the guide Sample Size Calculator: The Complete Guide for Reliable Research.