How Many People Do You Need to Survey? Sample Size and Margin of Error
October 21, 2026
For a survey measuring a proportion, the sample size needed is n = z² × p × (1 − p) ÷ e², where z is the confidence multiplier (1.96 for 95%), p is the expected proportion (use 0.5 if unknown, which gives the most conservative result), and e is the margin of error. For a 5% margin at 95% confidence, n = 1.96² × 0.25 ÷ 0.05² = 384.16, so you need about 385 respondents.
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The formula assumes a very large population. If your population is small, apply the finite population correction: n_adjusted = n ÷ (1 + (n − 1) ÷ N). For N = 2,000, n_adjusted = 384.16 ÷ (1 + 383.16 ÷ 2,000) ≈ 322.4, so about 323 respondents. For N = 500, it falls to about 218.
In a population of 10,000 or more, the correction hardly matters, which is why national polls of about 1,000 people can represent millions.
| Margin of error (95%) | Sample size (large population) |
|---|---|
| ±10% | 97 |
| ±5% | 385 |
| ±3% | 1,068 |
| ±2% | 2,401 |
| ±1% | 9,604 |
What the Margin Means
A 5% margin of error at 95% confidence means that if you ran the survey many times, the true population value would fall within ±5 points of your estimate in about 95% of the samples. If 60% of respondents say yes, the plausible range is about 55% to 65%.
The margin shrinks with the square root of the sample size. Halving it requires four times as many respondents, so extra precision gets costly quickly.
Practical Advice
The formula assumes a random sample. A biased sample, such as self-selected volunteers or people who answer an online poll, can be far off regardless of size. Aim for a random or well-designed sample before chasing a larger one.
Expect non-response: if only 20% of people you contact respond, you need to contact five times as many as your target sample. Also consider subgroup analysis, which needs enough respondents in each group.
Frequently Asked Questions
How many survey responses do I need?
About 385 for a ±5% margin at 95% confidence in a large population.
Why use p = 0.5?
It maximizes p × (1 − p), so it gives the largest, safest sample size when you do not know the true proportion.
Does a bigger population need a bigger sample?
Only up to a point. Beyond about 10,000, the required sample barely changes.
What is the finite population correction?
An adjustment that reduces the required sample size when the sample is a large fraction of the population.