Free tool Sample size calculator for surveys
How many people need to answer your survey before the percentages mean something? Choose how precise the result should be and how confident you want to be. Add the population size if it is small, and your expected response rate to see how many invitations to send.
- Responses and invitations
- Finite population correction
- Runs locally
How precise should the result be?
Margin of error is the “± points” you can live with. Leave the population empty if it is very large or unknown.
Write 5 or 5% for ±5 percentage points. Smaller margins need many more responses: halving it roughly quadruples the sample.
95% is the usual choice.
The share you expect to answer a key question a certain way. Leave at 50% if unsure: it gives the largest, safest sample.
How many people you could survey: customers, employees, members. Leave empty for a large population.
The share of invited people you expect to answer, from your past surveys. Used to work out invitations.
Responses needed
377
Completed responses, after finite population correction.
Invitations to send
1,508
Responses needed ÷ response rate.
For a very large population
385
Without the population correction.
z value
1.960
For the chosen confidence level.
Responses needed by margin of error
Same proportion and population; your current margin is highlighted.
| Margin of error | 90% confidence | 95% confidence | 99% confidence |
|---|---|---|---|
| ±1% | 5,055 | 6,489 | 9,068 |
| ±2% | 1,560 | 2,144 | 3,435 |
| ±3% | 725 | 1,014 | 1,688 |
| ±4% | 415 | 583 | 986 |
| ±5% | 267 | 377 | 643 |
| ±7% | 138 | 195 | 333 |
| ±10% | 68 | 96 | 165 |
How it was calculated
| Step | Calculation |
|---|---|
| z for 95% confidence | z = 1.9600 |
| Sample for a very large population (Cochran) | n₀ = z² × p(1 − p) ÷ e² = 1.9600² × 0.5 × 0.5 ÷ 0.05² = 384.146 |
| Finite population correction | n = n₀ ÷ (1 + (n₀ − 1) ÷ N) = 384.146 ÷ (1 + 383.146 ÷ 20000) = 376.925 |
| Round up | ⌈376.925⌉ = 377 |
| Invitations at the response rate | 377 ÷ 25% = 1508 → 1508 |
Share these inputs: the values go after the # in the link, so they never reach a server.
https://tapcub.com/tools/survey-sample-size-calculator
Version v1.0Updated Update history
What the number guarantees, and what it does not
In the example, 377 completed responses from a customer base of 20,000 give a margin of error of ±5 points at 95% confidence.
Responses needed
If 377 randomly chosen customers answer and 62% say they are satisfied, the true share among all 20,000 is very likely between 57% and 67%. Count only completed responses; partial answers to the key question do not count.
Invitations to send
At a 25% response rate you need to invite 1,508 people. Use your own past response rate; if you have none, start with a pilot. The calculator does not assume a benchmark rate.
Very large population
Without the population correction the answer is 385. The population size matters less than people expect: 10,000 or 10 million customers both need about 370–385 responses. It only makes a real difference when the sample is a sizeable share of the population.
Margin-of-error table
Shows the cost of precision. Going from ±5% to ±3% takes you from 377 to 1,014 responses; ±1% would need 6,489. Pick the widest margin that still supports your decision.
The formula covers random sampling error only. If the people who answer differ from those who do not (non-response bias), a larger sample just gives a more precise wrong answer.
Four inputs, two numbers
Everything except the margin of error has a sensible default.
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1
Set the margin of error
±5% is common for business surveys, ±3% for published polls. Think about the smallest difference you need to see: if two options might be 4 points apart, ±5% is not enough.
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2
Keep 95% confidence and 50%
Change the expected proportion only if a previous survey tells you the answer is far from 50%, for example around 10%.
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3
Add population and response rate
Enter the population if it is a few thousand or less. Enter last time’s response rate to get the number of invitations, and check the table to see what a tighter margin would cost.
Cochran’s formula with a finite population correction
The sample size for estimating a proportion comes from inverting the margin-of-error formula. For small populations, the result is scaled down because every response removes a larger share of the remaining uncertainty.
- z: 1.645 for 90%, 1.960 for 95%, 2.576 for 99% confidence
- p(1 − p) is largest at p = 50%, so 50% gives the most conservative sample
- Finite population correction matters once the sample is more than about 5% of the population
- The result is always rounded up
- Same formula as Raosoft and SurveyMonkey: 385 for a large population, 370 for 10,000, 278 for 1,000 (95%, ±5%)
Large population (Cochran)
n₀ = z² × p(1 − p) ÷ e²
95%, ±5%, p = 50%: 1.96² × 0.25 ÷ 0.05² = 384.15 → 385
Finite population correction
n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
N = 20,000: 384.15 ÷ (1 + 383.15 ÷ 20,000) = 376.93 → 377
Invitations
invitations = n ÷ response rate
377 ÷ 25% = 1,508
How population size changes the answer
Responses needed at 95% confidence and p = 50% for different population sizes. Above a few thousand, the population barely matters.
| Population | ±5% margin | ±3% margin |
|---|---|---|
| 100 | 80 | 92 |
| 500 | 218 | 341 |
| 1,000 | 278 | 517 |
| 5,000 | 357 | 880 |
| 10,000 | 370 | 965 |
| 20,000 | 377 | 1,014 |
| 100,000 | 383 | 1,056 |
| Very large | 385 | 1,068 |
Calculated with the formula above (z = 1.95996). For a team of 100 you need 80 answers at ±5%: close to a census. Example values.
Why a big enough sample can still mislead
The calculator gets the arithmetic right. These are the decisions it cannot make for you.
Planning for the whole sample, then splitting it
If you will report results by region or plan, each subgroup needs its own sample. 385 responses overall gives about ±13% for a subgroup of 60.
Confusing invitations with responses
The formula counts completed answers. Sending 385 invitations with a 20% response rate leaves you with about 77.
Assuming a large sample removes bias
A self-selected sample (a pop-up only engaged users see, a link shared on social media) is not random. More responses make it more precise, not more representative.
Guessing a low proportion to shrink the sample
Entering 10% instead of 50% cuts the sample from 385 to 139, but if the true share is near 50% your margin will be about ±8%, not ±5%.
Know your population before you survey it
The population is the group you want to learn about. In TapCub that group is a segment with a live size, and you can reach it on the site.
Segments with live size
Define the population by rules on events and properties; the size updates as data arrives. Use it in reports, as a chat audience, or export it.
Learn moreProactive chat
Invite visitors by page, time on page or source with a rule, and send the first message yourself.
Learn moreBots counted separately
Population sizes from analytics only make sense without crawlers. TapCub keeps them out by default.
Learn moreSurvey sample size questions
Still have a question?
Chat with the team behind TapCub — we usually reply within a few hours on business days.
How many survey responses do I need?
For ±5% at 95% confidence, about 385 completed responses for a large population, fewer for a small one (278 for 1,000 people, 370 for 10,000). For ±3% you need about 1,068. If you will break results down by subgroup, each subgroup needs enough responses on its own.
What is the sample size formula for a survey?
n₀ = z² × p(1 − p) ÷ e², where z is 1.96 for 95% confidence, p is the expected proportion (0.5 if unknown) and e is the margin of error as a decimal. For a population of N, correct it with n = n₀ ÷ (1 + (n₀ − 1) ÷ N) and round up.
Does population size matter?
Much less than people expect. Once the population is above a few thousand, the required sample hardly changes: 370 for 10,000 and 384 for a million at ±5%. It matters for small groups such as a team of 100, where you need 80 responses.
Why use 50% as the expected proportion?
p(1 − p) is largest at 50%, so it gives the largest sample and guarantees the margin of error for every question in the survey. Use a different value only when you are confident about the answer from earlier data.
How do I account for response rate?
Divide the responses needed by your expected response rate. 377 responses at 25% means 1,508 invitations. Use the rate from your own previous surveys of the same audience; rates vary widely by channel and relationship.
Is this the same as an A/B test sample size?
No. This calculator sizes a sample to estimate one proportion with a given precision. An A/B test needs enough users to detect a difference between two groups with a given power, which usually takes more. Use the A/B test sample size calculator for that.
What confidence level should I choose?
95% is the convention for most surveys and polls. 90% needs about 30% fewer responses (271 instead of 385) but is wrong more often; 99% needs about 70% more (664).
Update history
New features, fixes and data refreshes for this tool, newest first.
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· v1.0
LaunchedFirst release.
Missing something or found an error? Tell us — requests that come up often go into the next update. All tool updates
After the responses come in
Once the survey closes, check the precision you actually achieved and compare groups properly.