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.
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 a ±5% margin and an unknown population, the required sample is 384.
The calculator below runs that math live. Enter your population, pick a confidence level, set the margin, and the required sample size updates as you type, with the finite population correction applied automatically. Every value it returns is a count of completed responses, not invitations sent; the response-rate planning further down converts one into the other.
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)
Key takeaways
Three parameters drive everything. Z is set by your confidence level: 1.645 at 90%, 1.960 at 95% (the program-evaluation default), 2.576 at 99%. A higher z-score raises the required sample. p is the expected proportion of responses in one direction; use 0.5 when the split is unknown, because it gives the most conservative estimate, and use a prior observed proportion when you have one. e is the maximum acceptable gap between the sample result and the true population value: at ±5%, a 70% finding means the true value sits between 65% and 75%.
Plugging 95% confidence (Z = 1.96), p = 0.5, and a ±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 made by William Cochran's 1977 formulation, and changing any parameter changes the answer.
The sensitivity runs one direction you should know before negotiating with a funder: halving the margin of error quadruples the required sample. Moving from ±5% to ±2.5% takes the requirement from 384 to 1,537 completions. Tightening confidence from 95% to 99% adds roughly 73% more responses. Loosening to 90% cuts the requirement by about 30%.
Step 1, the raw sample. With Z = 1.960, p = 0.5, and e = 0.05: n₀ = 3.8416 · 0.25 / 0.0025 = 384.16, rounded up to 385. This is the unbounded-population sample size.
Step 2, the finite population correction. For a cohort of N = 1,000: n = 384.16 / (1 + 383.16 / 1000) = 384.16 / 1.38316 = 277.74, rounded up to 278. The correction trims the requirement by 28% because sampling from a bounded group carries less variance than sampling from an infinite one.
Step 3, invitations. Required n is completions, not contacts. At an expected 50% response rate, 278 completions means 556 invitations; at 25%, it means 1,112. The z-score reference for other confidence levels: 80% = 1.282, 85% = 1.440, 90% = 1.645, 95% = 1.960, 99% = 2.576, 99.9% = 3.291, all two-tailed.
All values below use Cochran's formula with p = 0.5 and the 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 are 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 organizations, while ±5 percentage points is tight enough for board reporting and funder review. For populations above 10,000, requirements are nearly identical regardless of total size; surveying 384 people from 100,000 provides the same precision as surveying 384 from one million, because you are measuring variance, not a percentage of the population.
For longitudinal designs 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 from a cohort of 1,000, enroll significantly more at baseline to absorb dropout. Longitudinal data collection software exists largely to keep that final wave connected to the first one.
The finite population correction reduces the required sample 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 requirement from 384 to 217, a 43% reduction.
The Cochran formula assumes an infinite or very large population. When the survey targets a defined group, a company's 400 employees, a program's 600 participants, a school's 1,200 students, 384 responses overshoots. Applied to a cohort of 500 it would demand 77% of the entire population; the corrected 218 hits the same ±5% precision at 95% confidence for roughly half the field cost. The scale of the effect across cohort sizes: N = 50 needs 45 (90% of the cohort), N = 250 needs 152 (61%), N = 1,000 needs 278 (28%), N = 100,000 needs 383 (0.4%).
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 organizations measuring outcomes on a fixed cohort.
For a statistically valid survey at 95% confidence with a ±5% margin, the minimum is 384 completed responses for unknown or very large populations, 278 for a population of 1,000, 217 for 500, and 80 for 100. These are minimum completions, not invitations sent. Validity is a quantity threshold, not a quality verdict.
"Statistically valid" means the results 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 samples only the most engaged participants may be statistically large but methodologically flawed. Four misreads account for most bad claims:
"We got 500, it's valid." Volume without context. 500 means nothing without the population, the channel, and the response rate; state N, required n, and actual completions side by side. Below 30 responses. The central limit theorem breaks down; report themes and patterns, not percentages with precision claims. The self-selected sample. An open link draws the most engaged or the most aggrieved; the size threshold is met while representativeness is not. Use a closed, invited sample from a known frame. The subgroup of 30. A total of 300 split across three sites gives 100 per site, and subgroup confidence intervals widen sharply; size each subgroup against its own Cochran minimum.
One boundary matters: for a qualitative survey, where open-ended responses are the primary data, Cochran's formula does not apply. Qualitative work operates on theoretical saturation, typically 15 to 50 in-depth responses, where the sample is sized by when new answers stop producing new themes.
A good survey sample size is the smallest number that meets the confidence level and margin of error for the cohort you are studying. Two knobs decide everything else, and knowing which one your funder, board, or LP actually cares about is half the work. 90% confidence suits exploratory research and internal pulse checks: at N = 1,000 it needs 214 completions, about 30% fewer than the default. 95% is the standard for program evaluation, board reports, and funder review at 278. 99% is for high-stakes decisions where being wrong carries serious cost, at 400, roughly 73% more than the default.
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 never launches at all. Collecting 50 when 278 are needed means a ±5% claim has an actual margin closer to ±14%, wide enough to make the finding useless for decisions. Confidence level is a policy decision, not a statistical one: set it before writing the survey, and make sure the sample also supports the breakdowns you plan to run in survey analysis, because a site-level comparison needs each site to clear its own minimum.
Every survey platform can tell you 384. SurveyMonkey publishes the same table; Qualtrics ships the same formula. The arithmetic was settled in 1977 and no vendor differentiates on it. What the form-centric era never solved is what happens to those 384 responses: each survey creates its own disconnected pool of respondents, so the intake wave, the exit wave, and the 90-day follow-up arrive as three separate spreadsheets matched by hand on names and emails, losing 20 to 30 percent of the pairs.
Sopact calls the alternative the Outcome Thread: one participant record, under a persistent Contact ID, that every wave lands on. A survey is not a new file of respondents; it is one more event on a record that already exists. That is why the sizing advice above keeps returning to the final wave: the 278 completions only measure change if they are the same 278 people you can trace back to baseline. Sizing the sample is step one; keeping it connected is the step the calculator cannot do for you, and the step the stakeholder intelligence layer exists to do.
A statistically valid response rate is not a fixed percentage: it is the rate at which invitations turn into the minimum required completions. If the Cochran calculation needs 278 completions from a cohort of 1,000, a 50% response rate requires contacting 556 people and a 25% rate requires 1,112. Confusing completions with invitations is the most common cause of under-powered surveys.
| Channel | Typical response rate | Invites for n = 278 | Invites for n = 384 |
|---|---|---|---|
| Cold email · external list | 15% – 25% | 1,112 – 1,854 | 1,536 – 2,560 |
| Embedded program touchpoint | 35% – 60% | 464 – 795 | 640 – 1,098 |
| Participant in active cohort | 40% – 70% | 397 – 695 | 549 – 960 |
| Mandatory funder follow-up | 70% – 90% | 309 – 397 | 427 – 549 |
| One-time anonymous link | 5% – 15% | 1,854 – 5,560 | 2,560 – 7,680 |
The real threat is non-response bias, not the rate itself. If the people who do not respond differ systematically from those who do, only the satisfied, only the English-fluent, only the most engaged, the results are biased regardless of whether the size threshold is met. Track the rate, report it beside n, and check that open-ended responses come from a representative subset, not just the most willing. The question sets that keep those completions comparable across waves live on the impact survey questions page.
A sample size is a promise about precision, and it only pays off if the responses are read while the survey is still in the field. That is the premise of the Loop, Sopact's method for continuous stakeholder data: collect clean at the source, analyze the moment each response arrives, and improve in time to act. Watching completions accumulate against the 278 target means a channel that under-delivers gets fixed in week one, not discovered in the post-mortem.
The same discipline protects the math itself. Duplicate submissions, orphaned records, and wording drift between waves all quietly shrink your effective n below the threshold you calculated. The same-answer-twice standard in Loop reliability is what keeps 278 collected responses worth 278 when the analysis runs.
One method, three moves that never stop
Then the cycle runs again, a little sharper each time. Read the method: the Loop methodology →
The number is the start of a field plan, not the end of one. Each prompt below is written to paste into Sopact Sense's Assistant, or to reason through with your team; the arrow above each links the Academy walkthrough with the expected output and tips.
Academy walkthrough → Analyze pre, mid, and post survey data
My program has [N] participants and I need pre and post readings at 95% confidence with a ±5% margin. Using Cochran's formula with the finite population correction, calculate the required completions per wave, then work backward through my expected response rates ([PRE %] pre, [POST %] post) to an invitation plan for each wave. Flag whether matched pre-post pairs, not totals, will clear the threshold.
Academy walkthrough → Survey attrition in longitudinal studies
Here is my cohort plan: [BASELINE N] at baseline, follow-ups at [WAVE SCHEDULE]. Assuming [X]% attrition per wave, project the completed responses at each wave and tell me the baseline enrollment I need so the FINAL wave still clears the Cochran minimum for a population of [N] at 95% / ±5%. Show the math per wave.
Academy walkthrough → How to build a data dictionary
Build a data dictionary entry for my survey's 3 core outcome measures: [PASTE QUESTIONS]. For each, lock the exact wording, scale, and denominator rule across waves, and state what would invalidate a wave-to-wave comparison, so the sample size I calculated keeps its precision instead of leaking it to wording drift.
Each walkthrough is practical and short: what to do, the prompt to run, the output to expect, and the tips that make it reliable.
Watch: collecting survey data that stays clean, connected, and analyzable from the first response.
Survey sample size is calculated using Cochran's formula: n0 = Z² · p · (1 − p) / e². Z is the z-score for the 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. Sopact's calculator on this page runs both steps live, at 95% / ±5% with an unknown population the answer is 384.
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 = 384. For finite populations, Sopact's calculator applies the correction n = n0 / (1 + (n0 − 1) / N) automatically.
For 95% confidence with a ±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. Sopact's guidance is to divide the required sample by the expected response rate to set the invitation count, and to size the final wave, not the first, when the survey repeats over time.
The finite population correction reduces the required sample when surveying a known, bounded population under 5,000: n = n0 / (1 + (n0 − 1) / N). For a population of 500 it shrinks the requirement from 384 to 217, a 43% reduction. Above 10,000 the effect is negligible. Sopact's sample size calculator applies the correction automatically whenever a population size is entered.
A good survey sample size is the smallest number that produces results accurate enough for the specific decision being made. For most program evaluations, 95% confidence with a ±5% margin (278 to 384 responses depending on population) is the standard. Collecting far beyond the threshold wastes budget without adding precision; Sopact recommends spending the surplus effort on response quality and wave-to-wave consistency instead.
Response rate alone does not determine validity; the absolute number of completed responses does. A 15% response rate from 3,000 contacts (450 responses) can be statistically valid, while a 60% rate from 60 contacts (36 responses) typically is not. The real threat is non-response bias. Sopact's Loop methodology reads completions as they arrive, so an under-delivering channel is caught while the survey can still be re-fielded.
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% at the chosen confidence. Halving the margin quadruples the required sample, from 384 at ±5% to 1,537 at ±2.5%. Sopact's advice: choose the margin by how much uncertainty the decision can absorb, before fielding.
95% is the default for program evaluation, board reporting, and funder-facing work. 90% suits internal, exploratory reads and cuts the required sample by roughly 30%. 99% is for decisions where being wrong is expensive and raises the requirement by roughly 73%. Sopact treats confidence level as a policy decision to lock before the survey is written, not a dial to adjust after responses arrive.
No. Cochran's formula sizes samples for quantitative claims about proportions. Open-ended, qualitative research operates on theoretical saturation, typically 15 to 50 in-depth responses, sized by when new answers stop producing new themes. Sopact's approach pairs the two: size the quantitative strand with Cochran, then confirm the open-ended responses come from a representative subset of the same respondents on the same record.
At 99% confidence with a ±5% margin and an unknown population: 664 responses. At 99% with ±2%: 4,148. For smaller populations: 87 for 100, 286 for 500, 400 for 1,000. The jump from 95% to 99% raises the requirement by roughly 73% across most scenarios, which is why Sopact recommends reserving 99% for high-stakes decisions and putting the saved field effort into follow-up waves instead.
Next: the number decides how many people you ask; how to analyze survey data decides what the answers are worth, and best survey software compares the tools that keep every wave on one record.
