What is the sample size formula this tool uses?

It uses n0 = z² · p(1 − p) / e², where z is the critical value for your confidence level, p is the expected proportion and e is the margin of error as a decimal. For a 95% confidence level z is about 1.96, so with p = 0.5 and e = 0.05 you get n0 = 1.96² · 0.25 / 0.0025 ≈ 384.1, which rounds up to 385. When you supply a population N, the finite-population correction n = n0 / (1 + (n0 − 1)/N) shrinks that figure.

Why does 95% confidence with a 5% margin need 384 to 385 people?

Plug the numbers in: z = 1.96, p = 0.5, e = 0.05. Then z² = 3.8416, p(1 − p) = 0.25, e² = 0.0025, so n0 = 3.8416 · 0.25 / 0.0025 = 384.16. You always round a sample size up, never down, because rounding down would leave your margin of error slightly wider than promised, so the answer is 385. This is why almost every national poll you read quotes a sample of roughly 1,000 to 1,200 (a 3% margin) or about 385 (a 5% margin).

Why is p = 0.5 the most conservative choice?

The term p(1 − p) in the formula is largest exactly at p = 0.5, where it equals 0.25, and it shrinks as p moves toward 0 or 1. So when you do not know the true proportion in advance, choosing 0.5 maximises the required sample and guarantees your margin of error will be met no matter what the real value turns out to be. If you have solid prior data, for example you expect about 20% to say yes, entering p = 0.2 lowers the needed sample (0.2 · 0.8 = 0.16 instead of 0.25), saving roughly a third of the responses.

When should I use the finite-population correction?

Use it whenever you are sampling from a known, countable group rather than an effectively infinite one. Surveying 500 employees, 2,000 customers or 30,000 alumni are all finite cases. With N = 1,000, a 95% / 5% survey drops from 385 to 278 responses, because once your sample is a large fraction of the whole population each extra response carries more information. For an open web poll, a national population or any group above roughly 500,000, the correction barely changes the number, so you can leave the field blank.

What happens to the sample size when I shrink the margin of error?

Sample size grows with the square of the precision, so it climbs fast. Halving the margin of error from 5% to 2.5% does not double the sample, it roughly quadruples it: 385 becomes about 1,537. Going to a 1% margin pushes the requirement near 9,600. This is the single biggest cost driver in survey design, which is why most commercial polls settle on a 3% to 5% margin rather than chasing 1%.

Why does the answer barely move once the population is very large?

The finite-population correction n = n0 / (1 + (n0 − 1)/N) approaches n0 as N grows, because (n0 − 1)/N shrinks toward zero. At N = 10,000 a 95% / 5% survey needs 370; at N = 100,000 it needs 383; at N = 1,000,000 it needs about 384, essentially the infinite-population answer of 385. This is the famous and counter-intuitive result that you do not need a bigger sample to poll a bigger country: 385 well-chosen people describe a city or a nation almost equally well.

Plan a customer survey before you send it

You run a 4,000-customer SaaS and want to know what fraction would recommend the product, accurate to within 5 points at 95% confidence. Enter confidence 95, margin 5%, leave p at 0.5, and set population to 4,000. The tool returns 351 completed responses. Now you can work backward: if your survey completion rate is about 20%, you need to email roughly 1,755 customers to land those 351 answers, and you have a defensible number to put in front of your boss instead of a guess.

Size an A/B test conversion sample

Your landing page converts around 12% and you want to detect whether a new design moves the needle. Enter p = 0.12 and a margin tight enough to matter for your decision, and the calculator tells you how many visitors each variant needs before the result is trustworthy. Because p is well below 0.5, the required sample is smaller than the worst-case 385, which means you can call the test sooner.

Defend a poll's accuracy to a skeptical reader

A reader objects that your 600-person poll "can't possibly" represent a city of two million. Switch to reverse mode, enter sample size 600 at 95% confidence with p = 0.5, and the tool returns a margin of error of about 4%. You can now say, with the math attached, that the poll is accurate to plus or minus four points 19 times out of 20, regardless of how big the city is.

Teach the confidence-margin-sample triangle in class

Demonstrating sampling theory to students, you toggle one input at a time: raise confidence from 90% to 99% and watch the sample jump, then tighten the margin from 5% to 2.5% and watch it quadruple. The URL updates on every change, so you can paste a link in the class chat that reopens the exact scenario each student should reproduce.

Sample Size Calculator for Surveys and A/B Tests

How many people to survey for a given confidence and margin of error — finite-population correction, reverse mode, one-click copy, browser-only

Runs locally
Category Calculator
Best for Getting a realistic range before a purchase, plan, workout, or schedule decision.

Confidence level

Two-sided z = 1.9600

Margin of error

Expected proportion p

Use 0.5 when unsure — it gives the largest, safest sample.

Population size N (optional)

Leave blank for a very large or unknown population.

Required sample size

385

z-score: 1.9600

What this tool does

Free sample size calculator for surveys, polls and A/B tests. Tell it the confidence level you want (90%, 95%, 99% or any custom value), the margin of error you can tolerate (say 5%), and the proportion you expect (use 0.5 when you have no idea, because it gives the largest and safest sample), and it returns the number of responses you need. It uses the standard formula n0 = z squared times p times (1 minus p) divided by e squared, then applies the finite-population correction n = n0 / (1 + (n0 minus 1)/N) when you enter a population size, so a survey of a 1,000-person company asks for far fewer responses than an open web poll. A reverse mode works the other way: enter the sample size you already collected and it tells you the margin of error you actually achieved. The z-score for your exact confidence level is computed with an inverse-normal approximation, not a lookup table, so a custom 92.5% is just as precise as 95%. Every result is one click to copy and the inputs live in the URL, so a shared link reopens the same calculation. 100% client-side, nothing is uploaded.

Tool details

Input: Numbers; The page exposes text boxes, numeric controls, file pickers, or structured inputs depending on the tool.
Output: Live result + Copy; The result area focuses on usable output, with copy, download, or preview actions when supported.
Privacy: Browser-side processing; The main tool logic does not call an external API, so inputs normally stay in the current tab.
Save / share: Shareable URL state; Key settings are encoded in the URL so another person can reopen the same setup.
Performance budget: Initial JS <= 9 KB; No WASM budget is declared, keeping the tool quick to open on mobile.
Best fit: Calculator · Marketer; Category and role tags drive related tools, internal links, and quick fit checks.

How to use

1. Input

Paste or drop your content into the tool panel.
2. Process

Click the button. All processing is local in your browser.
3. Copy / Download

Copy the result or download to disk in one click.

How Sample Size Calculator fits into your work

Use it for fast estimates, comparisons, and planning numbers before you make the final call.

Calculation jobs

Getting a realistic range before a purchase, plan, workout, or schedule decision.
Comparing scenarios by changing one input at a time.
Turning rough assumptions into a number you can discuss.

Calculation checks

Double-check units, dates, rates, and rounding assumptions.
Treat health, finance, tax, and legal outputs as planning aids, not professional advice.
Save the inputs that produced an important result so you can reproduce it later.

Good next steps

These links move the current task into a more complete workflow.

Real-world use cases

Plan a customer survey before you send it
You run a 4,000-customer SaaS and want to know what fraction would recommend the product, accurate to within 5 points at 95% confidence. Enter confidence 95, margin 5%, leave p at 0.5, and set population to 4,000. The tool returns 351 completed responses. Now you can work backward: if your survey completion rate is about 20%, you need to email roughly 1,755 customers to land those 351 answers, and you have a defensible number to put in front of your boss instead of a guess.
Size an A/B test conversion sample
Your landing page converts around 12% and you want to detect whether a new design moves the needle. Enter p = 0.12 and a margin tight enough to matter for your decision, and the calculator tells you how many visitors each variant needs before the result is trustworthy. Because p is well below 0.5, the required sample is smaller than the worst-case 385, which means you can call the test sooner.
Defend a poll's accuracy to a skeptical reader
A reader objects that your 600-person poll "can't possibly" represent a city of two million. Switch to reverse mode, enter sample size 600 at 95% confidence with p = 0.5, and the tool returns a margin of error of about 4%. You can now say, with the math attached, that the poll is accurate to plus or minus four points 19 times out of 20, regardless of how big the city is.
Teach the confidence-margin-sample triangle in class
Demonstrating sampling theory to students, you toggle one input at a time: raise confidence from 90% to 99% and watch the sample jump, then tighten the margin from 5% to 2.5% and watch it quadruple. The URL updates on every change, so you can paste a link in the class chat that reopens the exact scenario each student should reproduce.

Common pitfalls

Confusing the margin of error with the confidence level. The confidence level (95%) is how often the interval would contain the truth across repeated samples; the margin of error (5%) is the half-width of that interval. They are independent inputs. Bumping confidence from 95% to 99% does not shrink your margin, it grows the required sample to keep the same margin.
Forgetting to round the sample size up. n0 comes out as 384.16, and people sometimes truncate to 384. Always ceiling it to 385, because using 384 leaves your true margin of error a hair above the 5% you promised. The tool always rounds up for you, but if you compute by hand, never round down.
Entering a population for an effectively infinite group. If you are polling a national audience or an open web form, leaving the population blank is correct. Typing a huge number like 50,000,000 wastes effort because the finite-population correction changes the answer by less than one response at that scale.

Privacy

Every number you type and every result the tool produces stay inside your browser tab. The sample-size formula, the z-score lookup and the finite-population correction are all plain JavaScript running locally, with no server call and no logging of what you entered. The one thing to know: your inputs (confidence, margin, proportion, population) are encoded in the page URL so a shared link reopens the same calculation, which means those values appear in the recipient's browser history and any server log that sees the link. These are not sensitive values, but if you would rather not share them, use the copy button to paste the plain-text result instead.

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Sample Size Calculator for Surveys and A/B Tests

What this tool does

Tool details

How to use

1. Input

2. Process

3. Copy / Download

How Sample Size Calculator fits into your work

Calculation jobs

Calculation checks

Good next steps

Real-world use cases

Plan a customer survey before you send it

Size an A/B test conversion sample

Defend a poll's accuracy to a skeptical reader

Teach the confidence-margin-sample triangle in class

Common pitfalls

Privacy

FAQ

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