How many responses you needto actually trust the answer.
Send a survey to too few people and your results are noise wearing a percentage sign. This calculator gives you the exact number of completed responses you need for a margin of error and confidence level you can defend — plus the invite count to hit it once response rates take their cut.
Your survey
How many people are in the group you're trying to measure (customers, list size, market). Leave large if it's effectively unlimited.
The ± wiggle room you'll accept around each result. 5% means a 60% answer could really be 55–65%.
Your best guess at how answers will split. Unsure? Leave it at 50% — that's the worst case and needs the largest sample.
What you need
Responses needed
370
Infinite population
385
What the textbook formula asks for before correcting for your list size.
Invites to send (~2×)
740
Response rates take a cut — plan 2–3× the sample in invites.
Invites to send (~3×)
1,110
Sample vs. your population
Sensitivity · margin of error vs. sample
Precision isn't free
| Margin of error | Responses needed | Share of your list |
|---|---|---|
| ±3% | 965 | 9.7% |
| ±5% | 370 | 3.7% |
| ±7% | 193 | 1.9% |
| ±10% | 96 | 1.0% |
Confidence stays at 95% and the response split at 50% across this table — only the margin of error moves. Halving your margin roughly quadruples the sample you need, which is why a ±5% read is the practical default: it's tight enough to trust without demanding a sample you can't collect. A 50% split (not necessarily your current split) is the worst case and the safest assumption — it asks for the largest sample, so leaving it at 50% means you can't under-collect by guessing wrong.
Your move
You've got the sample size. I'll get you the answers worth measuring.
Need 370 responses at 95% confidence, ±5% margin (plan ~740–1,110 invites).
Numbers are only useful when they change a decision. Send me what you're trying to learn and I'll help you ask the right questions, hit the response rate, and turn the results into a move — not a slide nobody reads. Free 30-minute call, yours to keep either way.
Plain English
Sample size is a trade between cost and certainty.
Sample size is the number of completed responses you need before a survey result means anything. You're not trying to ask everyone — you're trying to ask enough people that the answer from your sample reliably matches the answer you'd get from the whole group. Get it wrong and you're making decisions on a coin flip dressed up as data.
Two dials control the number: margin of error (how precise you want the answer to be) and confidence level (how sure you want to be that the true answer falls within that margin). Tighten either one and the required sample climbs — often steeply. The research default is a 95% confidence level with a ±5% margin of error, which for most populations lands around 380 responses.
There's a third, sneakier input: the expected response split. When you have no idea how answers will land, you assume a 50/50 split, because that's the hardest case to measure and therefore needs the most responses. Plug in a number, and this calculator handles the finite-population correction too — so a 10,000-person list needs far fewer responses than the textbook 'infinite population' figure suggests.
The formula
n0 = z² × p × (1 − p) ÷ e², then n = n0 ÷ (1 + (n0 − 1) ÷ N)
At 95% confidence z = 1.96, with p = 50% (0.5) and a ±5% margin (e = 0.05): n0 = 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.16 → 385 responses for an infinite population. Correct that for a 10,000-person list and you only need 370. Drop to a 2,000-person list and it falls to 323.
The number came back bigger than your list. Now what?
Required sample is most of your population.
Your margin of error is too ambitious for a small group. Loosen it to ±7–10% for a directional read, or accept you'll need to survey nearly everyone. Small populations can't buy tight precision cheaply.
You can't hit the number with your response rate.
Don't lower the bar in secret. Either widen the margin of error on purpose and report it, or send more invites. Roughly 2–3× the sample in invites is normal for email surveys.
You only need a rough direction, not a decision.
Run at 90% confidence and ±10% margin. The sample drops dramatically and you'll still see clear signal vs. noise — just don't quote the result to two decimal places.
You're slicing results by segment.
Each segment needs its own adequate sample, not a share of the total. If you'll report findings for four groups, each group needs roughly the full sample size — plan invites accordingly.
How to actually get enough responses
01Send 2–3× your sample in invites
Email surveys convert at 10–30%. If you need 385 completes, plan for 1,300–3,800 invites depending on how warm the list is.
02Keep it under 5 minutes
Completion rate falls off a cliff after the five-minute mark. Cut every question that won't change a decision and watch your effective sample rise.
03Loosen the margin before you panic
Going from ±5% to ±7% can roughly halve the sample you need. For most internal decisions, ±7% is plenty precise.
04Use 50% split when unsure
It's the conservative assumption and guarantees your sample is large enough no matter how answers actually land. Only narrow it when you have real prior data.
05Lean on finite-population correction
If you're surveying a known, smallish list, the corrected number is far lower than the textbook figure. Don't over-collect against an infinite-population estimate you don't need.
06Send reminders to non-openers
A single reminder to people who haven't responded typically recovers 30–50% more completes. It's the cheapest sample you'll ever buy.
07Incentivize completion, not opening
A draw or small reward tied to finishing lifts your completion rate, which is what actually feeds the sample — not your open rate.
08Report your numbers honestly
Always state the sample size, margin of error, and confidence level alongside results. A clean ±5% at 95% disarms the 'is this even real?' question before it's asked.
The vocabulary
- Sample size (n)
- The number of completed responses you need. The finite-population-corrected figure for your specific group.
- Margin of error
- The ± range around a result. ±5% means a reported 40% could truly be anywhere from 35% to 45%.
- Confidence level
- How often the true value falls within the margin of error if you ran the survey repeatedly. 95% is the standard.
- Z-score
- The standard-normal value tied to your confidence level: 1.645 for 90%, 1.96 for 95%, 2.576 for 99%.
- Response split (p)
- The expected proportion choosing a given answer. 50% is the worst case and demands the largest sample.
- Finite-population correction
- The adjustment that lowers required sample size when the population is small and known, vs. effectively infinite.
Sample size questions, straight answers
For most purposes, 95% confidence with a ±5% margin of error is the bar, which works out to roughly 380 completed responses for a large population. That number drops if your population is small (finite-population correction) or if you accept a wider margin of error. There's no single magic number — it depends on how precise and how confident you need to be.
Keep going
A calculator tells you what. A call tells you what to do about it.
Send me the account behind these numbers. I'll tell you straight where the money's leaking and what I'd fix first — free, and you keep it whether you hire me or not.