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Sample Size Calculator Guide
How many responses you need for a survey to be meaningful, at a given confidence level and margin of error.
n₀ = z² × p(1−p) ÷ e²
where z is the confidence z-score, p the expected proportion and e the margin of error.
At 95% confidence, p = 0.5 and e = 5%: n₀ = 1.96² × 0.25 ÷ 0.05² = 385.
For a known population, apply the correction: n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
Why 385 Keeps Appearing
385 is the answer for 95% confidence and a 5% margin of error at the most conservative proportion. It's the number behind most "nationally representative" polls of a thousand people, and it's why survey sizes cluster where they do.
The Part That Surprises Everyone
Population size barely matters. Sampling 385 people tells you roughly as much about a country of 60 million as about a town of 60,000.
It feels wrong, but it's real: precision comes from the absolute number of responses, not the fraction of the population. The correction only bites when your sample is a large share of a small population — surveying 385 from a population of 500 needs only 218, because at that point you're nearly counting everyone.
The Cost of Precision Is Brutal
| Margin of error | Sample needed (95%) |
|---|---|
| ±10% | 97 |
| ±5% | 385 |
| ±3% | 1,068 |
| ±1% | 9,604 |
Halving your margin of error quadruples the sample, because e is squared in the denominator. Going from ±5% to ±1% costs 25 times the responses. This is why almost everyone settles at ±5% — not because it's ideal, but because ±1% is unaffordable.
Why 50% Is the Safe Default
The p(1−p) term peaks at p = 0.5. If you have no idea what proportion to expect, using 50% gives the largest sample — you can't accidentally under-sample. If you have solid prior data suggesting 10%, using it cuts the required sample substantially, but you're betting on that prior being right.
The Assumption Everyone Breaks
All of this assumes a random sample. The maths does not know or care whether your sample is representative — it just assumes it is.
A survey of 10,000 self-selected respondents from your own mailing list has a beautiful margin of error and can still be completely wrong, because the people who answer differ from the people who don't. Non-response bias has sunk far more surveys than small samples ever have. Sample size is the easy problem; sampling method is the hard one.
Related: conversion rate calculator, standard deviation calculator, percentage calculator.
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