Free Sample Size Calculator

See how many completed responses your survey needs for your confidence level and margin of error — and how many people to invite to get them.

Confidence level

Margin of error: ±5%

±1% (precise)±10% (rough)

Population size (optional)

Expected response rate: 30%

5%100%

Completed responses needed

385

for a 95% confidence level and ±5% margin of error.

Invitations to send

1,284

assuming a 30% response rate.

Uses Cochran's formula with a 50% proportion (the most conservative assumption), a finite population correction when you enter a population size, and rounds up to whole responses.

How to use the sample size calculator

Four settings decide the result, and a fifth is fixed in the background. Change one at a time and watch how much it moves the number — that is the quickest way to find a precision you can afford.

Confidence level: How sure you want to be that the true value lies inside your margin of error. At 95%, if you repeated the survey 100 times with fresh random samples, about 95 of the resulting ranges would contain the true value. 95% is the usual default; 99% needs about 70% more responses, 90% about 30% fewer.
Margin of error: The ± range around every percentage in your results. If 62% of respondents are satisfied and the margin is ±5%, the true share is most likely between 57% and 67%. Precision gets expensive quickly: ±3% needs about 2.8 times as many responses as ±5%.
Population size: The group your results should describe — all active customers, all employees, everyone who attended an event. Leave it blank when the group is very large or unknown, and the calculator treats it as unlimited. It only changes the answer noticeably when the population is small.
Expected response rate: The share of invited people you expect to complete the survey. It does not change how many completed responses you need, only how many invitations you send.
Population proportion: The share of people you expect to give a particular answer. The calculator fixes it at 50%, the value that requires the largest sample, so the result is safe before you know how the answers will split.

Sample size formula

The calculator uses Cochran's formula for estimating a proportion. It starts with the sample size for an unlimited population:

n_0 = \frac{z^2 \cdot p\,(1 - p)}{e^2}

z — the z-score for your confidence level (1.96 for 95%)
p — the expected proportion, 0.5 when you don't know it
e — the margin of error as a decimal (0.05 for ±5%)

When you enter a population size N, the finite population correction scales the result down, because each response covers a larger share of a small group:

n = \frac{n_0}{1 + \dfrac{n_0 - 1}{N}}

The result is always rounded up — rounding down would leave you just short of the precision you asked for. To turn completed responses into invitations, divide by the expected response rate r:

\text{invitations} = \frac{n}{r}

Z-scores and the responses they require at ±5% for a large population
Confidence level	Z-score	Responses needed
80%	1.282	165
85%	1.440	208
90%	1.645	271
95%	1.960	385
99%	2.576	664

The calculator uses unrounded z-scores (1.95996 rather than 1.96), so a hand calculation can occasionally differ from it by one response.

Worked example: 2,000 customers

A B2B software company has 2,000 active customers. It wants to run a customer satisfaction survey and report the results at 95% confidence with a ±5% margin of error. Its last email survey to the same customers had a 25% response rate.

Base sample size. With z = 1.96, p = 0.5 and e = 0.05:
$n_0 = \frac{1.96^2 \times 0.5 \times 0.5}{0.05^2} = \frac{0.9604}{0.0025} = 384.16$
Finite population correction. The customer base is small enough for N = 2,000 to matter:
$n = \frac{384.16}{1 + \dfrac{383.16}{2{,}000}} = \frac{384.16}{1.1916} \approx 322.4$
Rounded up, the company needs 323 completed responses.
Invitations. At a 25% response rate:
$\text{invitations} = \frac{323}{0.25} = 1{,}292$

Without the correction the team would have aimed for 385 responses — 62 more than it needs. Since 1,292 is well below 2,000, it can also invite every customer and keep some headroom in case the response rate comes in lower this time.

How to adjust sample size for response rate

The formula gives you completed responses. Most people you invite will not answer, so the number to plan around is invitations: the responses you need divided by the response rate you expect. For 385 responses, a 40% response rate means 963 invitations; a 10% rate means 3,850.

Take the rate from a comparable past survey — same audience, same channel — rather than an optimistic guess. With no history, send in waves: invite part of the list, count the completes, then size the next wave. Our guide to survey response rate covers what drives the rate and the changes that actually raise it.

Three things a longer send list cannot fix:

A small population. When the invitations you need exceed the number of people in the group, you cannot invite your way to the target. Invite everyone and work on the response rate, or accept a wider margin of error — the calculator shows the response rate you would need.
Non-response bias. Reaching the number does not make the sample representative. If the people who answer differ from those who don't — only your happiest or angriest customers reply — more invitations bring more of the same skew.
Unusable responses. Duplicates, speeders and incomplete submissions come out during data cleaning, so add a small buffer to the target.

Sample size table at 95% confidence

Completed responses needed by population size and margin of error. Every figure is rounded up and matches the calculator.

Responses needed at 95% confidence
Population	±1%	±2%	±3%	±5%	±10%
100	99	97	92	80	50
500	476	414	341	218	81
1,000	906	707	517	278	88
5,000	3,289	1,623	880	357	95
10,000	4,900	1,937	965	370	96
50,000	8,057	2,291	1,045	382	96
100,000	8,763	2,345	1,056	383	96
1,000,000	9,513	2,396	1,066	384	97
Unknown or very large	9,604	2,401	1,068	385	97

Two patterns stand out. Past about 10,000 people the population hardly matters: at ±5% the requirement only moves from 370 to 385, however large the group gets. And precision is costly: going from ±5% to ±3% multiplies the sample by about 2.8, and ±1% by about 25.

Before you rely on the number

The formula assumes a random sample. Everyone in the population needs a similar chance of being invited. A convenience sample — whoever clicks a link on your website — does not meet that assumption, however many responses it collects.
It sizes the sample as a whole. If you will compare regions, plans or customer tiers, each of them needs enough responses on its own, so run the calculator once per segment.
It is built for percentages. Yes/no questions and shares of respondents fit the formula. Sizing a study to compare averages between groups, or to detect a statistically significant difference between them, calls for a power analysis instead.

For a fuller walkthrough of choosing these settings and a sampling method, read our guide on how to determine survey sample size.

Ready to collect the responses you need?

Knowing the number is the easy part; reaching it is where most surveys fall short. With Responsly you build the survey once and send it wherever your audience answers — email, SMS, WhatsApp, your website, a link or a QR code. Quota limits on a screening question keep any one segment from taking more than its share, and Athena, our AI agent, groups the open-ended answers into themes so the numbers come with reasons.

Frequently Asked Questions

What sample size do I need for a survey?

For a large or unknown population at 95% confidence and a ±5% margin of error, you need 385 completed responses. Smaller groups need fewer: 278 for a population of 1,000 and 218 for a population of 500. A tighter ±3% margin raises the requirement for a large population to 1,068 responses.

How do you calculate sample size?

Use Cochran's formula: n0 = z² × p(1 − p) / e², where z is the z-score for your confidence level (1.96 for 95%), p is the expected proportion (0.5 when you don't know it) and e is the margin of error as a decimal. If you know the population size N, apply the finite population correction n = n0 / (1 + (n0 − 1) / N), then round up to a whole response.

Does population size affect sample size?

Only while the population is small. At 95% confidence and ±5%, a population of 1,000 needs 278 responses, 10,000 needs 370 and 1,000,000 needs 384. Past a few tens of thousands the population barely changes the answer, which is why a well-drawn sample of about a thousand people can describe an entire country.

Is 100 responses enough for a survey?

It depends on the precision you need. With 100 responses from a large population, the margin of error at 95% confidence is about ±9.8%, so a result of 60% means somewhere between roughly 50% and 70%. That is enough for a directional read or to spot a serious problem, but not to detect a change of a few points between two survey waves.

Why does the calculator assume a 50% proportion?

Because p = 0.5 produces the largest sample size, so the result holds however the answers split. If earlier research tells you the split will be closer to 20/80, the true requirement is lower — 246 instead of 385 responses at 95% confidence and ±5%. Most surveys ask several questions, though, and some of them will land near 50/50.

How many people should I send my survey to?

Divide the completed responses you need by the response rate you expect. If you need 385 responses and expect 25% of invitees to finish the survey, invite 1,540 people. Base the rate on a comparable past survey, and if the result is larger than your population, you need a higher response rate or a wider margin of error.

Do I need a separate sample size for each segment?

Yes, if you plan to report or compare segments on their own. A total of 385 responses gives ±5% for the whole group, but split evenly across four regions each region has about 96 responses and a margin of error close to ±10%. Size every segment you want to read with confidence, then add the numbers up.