Free survey sample size calculator using Cochran's formula. Find how many responses you need for 95% or 99% confidence at any population size. Table included.
Enter your population, pick a confidence level, set the margin. The required sample size updates live. All values use Cochran's formula with automatic finite population correction.
Total people you could survey: cohort, employee list, applicant pool. Leave blank for unknown.
How sure you want to be the sample reflects the whole.
Maximum gap between your sample result and the true value.
Use 0.5 if you don't know how responses will split: it is the most conservative.
278
completed responses
To detect a true proportion within ±5% at 95% confidence, survey at least 278 people out of 1,000.
Achievable for most programs. See response-rate planning below.
Formula Cochran 1977 · Distribution p = 0.5 · Z-score 1.960 · FPC on · Rounding ceil(n)
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Survey sample size is calculated using Cochran's formula: n₀ = Z² · p · (1 − p) / e². Z is the z-score for the chosen confidence level, p is the expected response distribution, and e is the margin of error as a decimal. For known populations under 5,000, apply the finite population correction n = n₀ / (1 + (n₀ − 1) / N). At 95% confidence with ±5% margin and unknown population, the required sample is 384.
Z · z-score
Confidence level dial
Z is determined by your confidence level. At 90%, Z = 1.645. At 95%, the program-evaluation default, Z = 1.96. At 99%, Z = 2.576. A higher z-score raises the required sample.
90% · 1.645
95% · 1.960
99% · 2.576
Funder or board policy, before fielding the survey.
p · distribution
Expected split of responses
p is the expected proportion of responses in one direction. Use 0.5 when the split is unknown: it gives the most conservative estimate. If prior research shows roughly 80% in one category, p = 0.8 reduces the required sample.
p = 0.5, maximum variability.
Use the observed proportion. Smaller required n.
e · margin
Acceptable error band
e is the maximum acceptable gap between sample result and true population value. At ±5%, a 70% finding means the true value is between 65% and 75%. Halving e quadruples the required sample, from 384 to 1,537.
±5 percentage points.
The decision needs precision. Cost compounds.
Plugging 95% confidence (Z = 1.96), p = 0.5, and ±5% margin into the formula: n₀ = 1.96² · 0.5 · 0.5 / 0.05² = 384. This is the number cited in virtually every survey research guide for unlimited populations. It is not a magic constant: it is the output of three specific parameter choices.
Cochran's formula computes the raw sample, then the finite population correction trims it for known populations. The two-step calculation is step-by-step below, with z-scores keyed to the confidence level you picked above.
Compute the infinite-population sample size from your z-score, response distribution, and margin of error. This is the headline 384 at 95% / ±5%.
If N is known and under 5,000, the correction shrinks the required sample. For a cohort of 1,000, n drops from 385 to 278: a 28% reduction.
Required n is completed responses, not invitations sent. Divide n by the channel response rate to get how many people to contact.
All values use Cochran's formula with p = 0.5 and finite population correction. Use the table to sense-check the calculator, or to skim a few cohort sizes before you commit. The ★ column marks the 95% / ±5% standard used in most program evaluations, customer satisfaction surveys, and employee engagement studies.
| Population (N) | 90% · ±10% | 95% · ±5% ★ | 95% · ±3% | 99% · ±5% | 99% · ±2% |
|---|---|---|---|---|---|
| 50 | 29 | 45 | 48 | 47 | 50 |
| 100 | 41 | 80 | 92 | 88 | 98 |
| 250 | 54 | 152 | 203 | 182 | 236 |
| 500 | 60 | 218 | 341 | 286 | 447 |
| 1,000 | 64 | 278 | 517 | 400 | 806 |
| 2,500 | 66 | 334 | 749 | 525 | 1,561 |
| 5,000 | 67 | 357 | 880 | 586 | 2,268 |
| 10,000 | 68 | 370 | 965 | 623 | 2,932 |
| 50,000 | 68 | 382 | 1,045 | 655 | 3,830 |
| 100,000 | 68 | 383 | 1,056 | 660 | 3,983 |
| N → ∞ | 68 | 385 | 1,068 | 664 | 4,148 |
All values rounded up to whole responses. The 95% / ±5% column is the standard for most program evaluations because it balances precision with feasibility: 384 completions is achievable for most organisations, while ±5 percentage points is tight enough for board reporting and funder review.
For populations above 10,000, sample size requirements are nearly identical regardless of total size. Surveying 384 people from 100,000 provides the same ±5% precision as surveying 384 from one million.
Key insight · you are measuring variance, not percentage of population
For longitudinal surveys where participants respond at multiple timepoints, size against the smallest expected wave: typically the final follow-up, where attrition is highest. If 278 post-survey completions are needed for a cohort of 1,000, enroll significantly more participants at baseline to account for dropout.
The finite population correction reduces the required sample size when surveying a known, bounded population under 5,000. The formula is n = n₀ / (1 + (n₀ − 1) / N), where n₀ is the initial Cochran sample and N is the total population. For a population of 500, the correction shrinks the required sample from 384 to 217, a 43% reduction.
The Cochran formula assumes an infinite or very large population. When the survey targets a defined, bounded group (a company's 400 employees, a program's 600 participants, a school's 1,200 students), 384 responses is more than needed.
Required completions at N = 500
384
The Cochran baseline for unbounded populations. Applied to a cohort of 500, it overshoots: 77% of the entire population would need to complete the survey.
Required completions at N = 500
218
The finite-correction adjustment. 218 completions out of 500 hits the same ±5% precision at 95% confidence. A 43% reduction in required completions and field cost.
For populations above 10,000, the correction has negligible effect and the Cochran baseline applies essentially unchanged. For populations under 200, the correction often shrinks required n into the dozens.
45
N = 50 · 90% of cohort
152
N = 250 · 61% of cohort
278
N = 1,000 · 28% of cohort
383
N = 100,000 · 0.4% of cohort
The practical implication: most nonprofit program evaluations, employee surveys, and cohort studies operate on populations under 2,000. The finite population correction is not an academic refinement: it is the difference between an achievable survey and an unachievable one for most organisations running pre and post surveys to measure program outcomes.
For a statistically valid survey at 95% confidence with ±5% margin, the minimum is 384 completed responses for unknown or very large populations. For smaller defined populations: 80 responses for N = 100, 217 for N = 500, 278 for N = 1,000. These are minimum completions, not invitations sent. Validity is a quantity threshold, not a quality verdict.
"Statistically valid" means results accurately reflect the broader population within the stated margin of error at the chosen confidence level. It does not mean the survey is free of bias. A survey with 500 responses that asks leading questions, reaches only English speakers, or surveys only the most engaged participants may be statistically large but methodologically flawed. Sample size answers the quantity question; survey design answers the quality question. Four common misreads:
Misread 01 · "We got 500, it's valid"
Volume without context
500 means nothing without knowing the population, the channel, and the response rate. Could be excellent or biased.
State N, required n, and actual completions side by side. Then state response rate.
Misread 02 · Below 30 responses
Directional only
With fewer than 30 responses, the central limit theorem breaks down. Findings are directional, not statistically inferential.
Report as "themes" or "patterns observed". Do not attach precision claims or percentages.
Misread 03 · Self-selected sample
Non-response bias
An open link that anyone can fill draws the most engaged or the most aggrieved. Sample size is met; representativeness is not.
Use a closed, invited sample from a known frame. Track and report response rate.
Misread 04 · Subgroup of 30
Wide confidence interval
A total sample of 300 split across three sites gives 100 per site. Subgroup confidence intervals widen sharply.
Size each subgroup against its own Cochran minimum. Report subgroup CIs alongside the headline number.
For qualitative surveys where open-ended responses are the primary data, Cochran's formula does not apply. Qualitative research operates on theoretical saturation: typically 15 to 50 interviews, where sample size is determined by when new responses stop producing new themes.
A statistically valid survey response rate is not a fixed number: it is the rate at which expected invitations turn into the minimum required completions. If a Cochran calculation needs 278 completions from a cohort of 1,000, a 50% response rate requires contacting 556 people; a 25% rate requires 1,112. Sample size is the completed-response count. Response rate is the invitation-to-completion ratio. Confusing them is the most common cause of under-powered surveys.
| Channel | Typical response rate | Invites for n = 278 | Invites for n = 384 | Where it works |
|---|---|---|---|---|
| Cold email · external list | 15% – 25% | 1,112 – 1,854 | 1,536 – 2,560 | Market research, prospect surveys |
| Embedded program touchpoint | 35% – 60% | 464 – 795 | 640 – 1,098 | In-product, SMS, post-event push |
| Participant in active cohort | 40% – 70% | 397 – 695 | 549 – 960 | Workforce training, fellowships |
| Mandatory funder follow-up | 70% – 90% | 309 – 397 | 427 – 549 | Grant-required, exit surveys |
| One-time anonymous link | 5% – 15% | 1,854 – 5,560 | 2,560 – 7,680 | Open web link, social share |
Sample size is the count of completed responses. Response rate is the share of invitations that turn into completions. Those two are not the same number. The real threat is non-response bias, not response rate itself. If people who do not respond differ systematically from those who do (only satisfied participants, only English-fluent participants, only the most engaged), results are biased regardless of whether the sample size threshold is met.
For program evaluation using mixed method surveys, size around the quantitative strand, then confirm that open-ended responses come from a representative subset, not only the most willing respondents. For tactics that move the response rate dial, see how to increase survey response rates.
A good survey sample size is the smallest number that meets the confidence level and margin of error for the cohort you are studying. For most program evaluations, employee engagement, and customer satisfaction studies, 95% confidence with ±5% margin (278 to 384 responses, depending on population size) is the right standard. For high-stakes decisions affecting major budget allocations or policy, 99% confidence or ±3% margin is appropriate, requiring 400 to 1,068 responses.
Two knobs decide everything else: confidence level and margin of error. Tightening either one raises the required sample. Knowing which one your funder, your board, or your LP actually cares about is half the work.
90% confidence
Exploratory · internal · pulse
Appropriate for exploratory research, preliminary needs assessments, and pulse checks where the goal is direction, not validation. The smaller required sample makes the survey faster and cheaper to run.
214 completions
~30% smaller
95% confidence ★
Program evaluation default
The standard for program evaluations, customer satisfaction, employee engagement, and most published research. The 1.96 z-score yields sample sizes that balance rigour with practical feasibility.
278 completions
Board reports, funder review
99% confidence
High-stakes only
Justified when errors carry serious financial or operational consequences: regulatory compliance, pre-launch validation, clinical or health outcomes research. Sample size is roughly 73% larger than at 95%.
400 completions
~73% larger
The most common error is treating sample size as a credibility signal rather than a precision instrument. Collecting 1,000 responses when 278 would suffice wastes budget, delays results, and often means the survey does not launch at all. Collecting 50 responses when 278 are needed means a ±5% finding has an actual margin closer to ±14%, wide enough to make the result meaningless for decisions.
Confidence level is a policy decision, not a statistical one. Set it before writing the survey, not after the responses come in.
Field rule · program evaluation
For survey analysis to produce actionable findings, the sample must also support the breakdowns the team plans to run. A total of 300 split across three sites gives 100 per site, which at a site population of 200 yields a ±8% margin: potentially too wide for site-level comparisons.
Pulled from search-console data for this page. Each answer leads with the bottom-line answer, followed by the supporting context.
Survey sample size is calculated using Cochran's formula: n₀ = Z² · p · (1 − p) / e². Z is the z-score for the chosen confidence level (1.96 for 95%), p is the expected response distribution (0.5 for maximum variability), and e is the margin of error (0.05 for ±5%). For known populations under 5,000, apply the finite population correction n = n₀ / (1 + (n₀ − 1) / N). At 95% confidence with ±5% margin and unknown population size, the required sample is 384.
For 95% confidence with ±5% margin: 80 responses for a population of 100, 217 for 500, 278 for 1,000, 370 for 10,000, and 384 for unknown or very large populations. These are minimum completed responses, not invitations sent. Divide the required sample by the expected response rate to determine how many people to invite. A 50% response rate doubles the invitation count required.
A good survey sample size is the smallest number that produces results accurate enough to support the specific decision being made. For most program evaluations, 95% confidence with ±5% margin (278 to 384 responses) is appropriate. For high-stakes decisions, use 99% confidence or ±3% margin. The most common mistake is treating larger as always better. Collecting twice the needed responses wastes resources without improving precision.
Cochran's formula is n₀ = Z² · p · (1 − p) / e², developed by statistician William Cochran. Z is the z-score for the chosen confidence level (1.645 for 90%, 1.96 for 95%, 2.576 for 99%), p is the expected proportion (use 0.5 for maximum variability), and e is the margin of error. At 95% confidence and ±5% margin, n₀ = 1.96² · 0.5 · 0.5 / 0.05² = 384. For finite populations, apply the correction n = n₀ / (1 + (n₀ − 1) / N).
The finite population correction reduces the required sample size when surveying a known, bounded population under 5,000. The formula is n = n₀ / (1 + (n₀ − 1) / N), where n₀ is the initial Cochran sample size and N is the total population. For a population of 500, the correction shrinks the required sample from 384 to 217, a 43% reduction. For populations above 10,000 the correction has minimal effect.
Response rate alone does not determine validity. The absolute number of completed responses does. Plan invitations so that even at a conservative 20 to 30% completion rate the required n is cleared. A 15% response rate from 3,000 contacts (450 responses) can be statistically valid; a 60% rate from 60 contacts (36 responses) typically is not. Non-response bias is the real threat, not response rate itself.
Margin of error is the maximum acceptable gap between the sample result and the true population value. At ±5%, a finding of 72% satisfaction means the true value lies between 67% and 77% with the chosen confidence. Halving the margin of error quadruples the required sample: moving from ±5% (384 responses) to ±2.5% (1,537 responses). Choose the margin based on how much uncertainty the decision can absorb.
95% confidence is the default for program evaluation, board reporting, and most funder-facing work. Use 90% when the decision is internal and a wider margin is acceptable. That choice cuts the required sample by roughly 30%. Use 99% only for high-stakes decisions where the cost of being wrong is severe. It pushes the required sample size up by roughly 73% versus 95%.
Statistical significance for hypothesis testing differs from descriptive survey sample size. For descriptive surveys, use Cochran's formula: typically 278 to 384 responses. For testing whether group differences are statistically significant (t-test, chi-square), each subgroup must meet its own minimum threshold. If comparing two program sites, each needs its own Cochran-calculated minimum, not just the aggregate.
At 99% confidence with ±5% margin and unknown population: 664 responses. At 99% with ±2% margin: 4,148 responses. For smaller populations: 87 responses for a population of 100, 286 for 500, 400 for 1,000. The jump from 95% to 99% confidence increases the required sample by approximately 73% across most scenarios. Reserve 99% for decisions where being wrong has serious cost.
Sample size is step one of four. The guide covers question type selection, response-rate uplift tactics, and longitudinal design: the four decisions that determine whether the data survives funder scrutiny.
The four decisions that determine whether the survey survives funder scrutiny: who you ask, what you ask, how you analyse, and how you keep the cohort over time.
Tactics that move the response-rate dial: channel, timing, length, incentives, follow-up cadence.
03 · Before the fieldWhich question type matches which decision. Closed, open, scaled, ranked, and when each one fails.
04 · After the fieldFrom completed responses to a board-ready answer. Quant, qual, and the mixed methods funders ask for.
Across timeHow to size baseline, midline, and endline. Why attrition forces the math earlier than most teams plan.
Quant + qualCombining closed and open responses without losing either one to the other.
Before / afterOutcome measurement at the participant level. Why per-respondent matched pairs beat aggregate deltas.
Open-endedWhen Cochran does not apply: theoretical saturation, interview sizing, and code stability.
Engine pillarThe category these guides fall under. The persistent layer beneath every survey, application, and follow-up.
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