Survey Sample Calculator
How many people must I survey? Cochran's n for a proportion — worst-case p = 0.5 by default — with the finite-population correction applied when your population is a real, countable one.
Survey Sample Calculator
Results recalculate instantly on every keystroke. Nothing you type is transmitted.
What this result does not account for
- Simple random sampling, single proportion — no design effects or stratification
- One question at a time: size to the tightest margin you actually need
In short: The classic question, answered: at 95% confidence and ±3.1% margin with the worst-case p = 0.5, Cochran's raw n is 1.959964²×0.25/0.031² = 999.338939 — 1,000 completed surveys, rounded up once at the end. That n covers ANY true split, because 0.5 maximizes p(1−p); planning on a believed 70/30 instead cuts it, at the risk of being wrong about the belief. Give a finite population and the correction bites: at N = 1,000 the same precision needs only 501 people; at a 5% margin the classic pair is 385 raw → 278 with N = 1,000, 218 with N = 500. The margin e is HALF the interval — the “±3.1%” under every poll.
Formula
n₀ = z*²·p(1−p)/e² · FPC: n = n₀/(1 + (n₀−1)/N)
Cochran's formula prices the worst-case variance at p = 0.5. The finite-population correction shrinks the requirement when the population is small enough that sampling a big share of it exhausts the uncertainty — applied to the UNROUNDED n₀, with the ceiling taken once at the end: round once, at the finish line.
Worked Example
- Set the margin e and confidence level — the claim you want to be able to print.
- Leave p at 50% unless you have solid prior knowledge; the worst case protects you from planning on a wish.
- Enter N only if the population is genuinely finite and countable — a company's workforce, a conference's registration list.
- Round up, then budget invitations against your expected response rate (a FAQ, not a field).
Defaults: ±3.1% at 95%, p = 0.5, no N — n₀ = 999.338939 → 1,000 surveys. With N = 1,000: correction → 501. At e = 5%: 385 raw → 278 (N = 1,000) and 218 (N = 500).
Strengths & Limits Of This Model
Where this engine is strong
- Worst-case p = 0.5 default with the belief trade-off stated
- FPC applied to the unrounded n₀, ceiling once
Where it stops
- No mean-flavour sizing (the ssz page's job)
- No clustering or design-effect multiplier
Practical Use Cases
Research
the fieldwork budget line, priced
HR
all-staff surveys with a countable roster
Customer programs
NPS-style panels sized honestly
Methodology & Editorial Standards
Computation runs in IEEE-754 double precision at full internal precision; rounding to two decimal places occurs strictly at the display layer, so no cumulative drift enters the result. All monetary outputs use accounting presentation — grouped thousands, two decimals, negatives in parentheses — so figures can be transcribed directly into a model or working paper. Division-by-zero and out-of-domain inputs return an em-dash rather than a misleading number.
This engine was reconciled against an independent reference implementation and hand-verified for the worked example above before release. Our full five-stage review process is published on the About Us page.
Disclaimer. This calculator is provided for informational and modelling purposes only and does not constitute financial, tax, legal, medical, or engineering advice. Verify all figures with a qualified professional before acting on them.
Survey Sample Calculator — 8 Expert FAQs
8 analyst-written answers to the questions practitioners actually ask — optimised for voice and answer-engine retrieval.
Why does p = 0.5 need the most surveys?
Because p(1−p) — the variance of a proportion — peaks at 0.25 exactly when the split is even. A 90/10 population is easy to pin down; a 50/50 one wobbles most. Planning at 0.5 means the resulting n is valid whatever the true split turns out to be — the safe default this page ships.
Why 1,000 surveys at ±3.1% and not the famous 384?
The famous 384 belongs to ±5%: at that margin the raw Cochran n is 384.145888, rounding to 385. At ±3.1% the same arithmetic gives 999.338939 → 1,000. Pollsters quote ±3% and field about a thousand completed interviews for exactly this reason; the page prices the pair you type.
When does the finite-population correction apply?
When the population is finite AND you would sample a meaningful share of it. N = 1,000 at ±5% cuts the requirement from 385 to 278; N = 1 million leaves it untouched. Blank N on this page means “large or unknown” — the correction stays off, which is the conservative reading.
Is the margin the full width of the interval?
No — e is HALF the width, the “plus or minus” itself. A ±3.1% margin is a 6.2-point interval around the estimate. Teams that type the full width as e double their fieldwork by accident; the help text keeps the definition one glance away.
How do response rates change the answer?
The n here is COMPLETED surveys, not invitations: at a 40% response rate, 1,000 completions take about 2,500 invitations — and non-response bias, unlike sampling error, is not fixed by more invitations. Budget the send, then fight the bias with design and reminders.
Does this page size an A/B test?
No, and the difference is structural: a survey ESTIMATES one proportion, an experiment DETECTS a difference between two — and detection is harder, so the experiment's n per arm runs larger. The power-analysis page owns that arithmetic; the sample-size page owns the mean-flavour version of this one.
Why is everything rounded up only at the end?
Rounding twice inflates: 999.34 → 1,000 is one honest ceiling, but 999.34 → 1,000 → corrected → rounded again compounds the padding and misstates the correction. The FPC runs on the unrounded n₀ and the ceiling lands once — the same round-once doctrine the site's other pages enforce.
What assumptions ride along with this n?
Simple random sampling, one question of interest, and independence between respondents. Stratified designs, clustering, or weighting change the arithmetic (usually upward, via a design effect) — the page prices the clean case and names the boundary rather than pretending the design effect away.