Written by Dackohn; last reviewed November 2026.
For a proportion, n = z² × p(1 − p) / E². For a mean, n = (z × σ / E)². Always round up. A survey with a ±5% margin of error at 95% confidence needs 385 responses. If you are comparing groups, you need a power calculation instead.
First: estimating or comparing?
This page covers estimating a single value to a chosen precision. If you want to compare groups, the question is about power, so use the power calculator and see statistical power explained.
Sample size for a proportion
You want to estimate a percentage to within ±5 points with 95% confidence (z = 1.96). If you have no prior estimate, use p = 0.5, which gives the largest and safest answer:
n = 1.96² × 0.5 × 0.5 / 0.05² = 384.15, so round up to 385.
This is why 385 appears in so many survey plans. If you expect about 30%, then n = 1.96² × 0.3 × 0.7 / 0.05² = 322.7, so 323 is enough.
Sample size for a mean
You want to estimate a mean to within ±3 points at 95% confidence, and earlier data suggest an SD of about 15:
n = (1.96 × 15 / 3)² = 96.04, so round up to 97.
The hardest part is estimating the SD. Use a pilot study or earlier research, and lean towards the larger value if unsure.
Small populations
If you are sampling a large share of a small population, apply the finite population correction: nadj = n / (1 + (n − 1) / N). For a population of 2,000 people, 385 falls to 384.15 / (1 + 383.15 / 2000) = 322.4, so 323. For populations much larger than about 20 times your sample, the correction hardly matters. A national survey needs about the same sample as a city survey.
Allow for non-response
Divide by the expected response rate. To get 97 usable answers when you expect 90% to complete, invite 97 / 0.90 = 107.8, so 108 people. With a 20% response rate, a survey needing 385 responses must reach 1,925 people.
How precision costs
| Margin of error (p = 0.5, 95%) | Sample size |
|---|---|
| ±10% | 97 |
| ±5% | 385 |
| ±3% | 1,068 |
| ±1% | 9,604 |
Halving the margin of error needs four times the sample.
Common mistakes
- Rounding down, which misses the target precision.
- Assuming a large sample fixes a biased one. The formulas assume random sampling. A volunteer poll of a million people can still be badly wrong.
- Using an overall sample size for subgroups. If you plan to report on subgroups, each one needs enough people.
Try it yourself
Sample Size Calculator →Get the sample size for a mean or proportion. Survey Sample Size Calculator →With margin of error, confidence and population size. Statistical Power Calculator →For studies comparing groups.See also: Margin of error explained
Frequently asked questions
Why is 385 such a common sample size?
It is the size needed for a margin of error of plus or minus 5% at 95% confidence with p = 0.5, the most conservative assumption.
Does population size affect sample size?
Barely, unless the sample is a noticeable share of the population. Then the finite population correction reduces the requirement.
What sample size do I need to compare two groups?
It depends on the effect size and the power you want. For d = 0.5 and 80% power, you need 64 per group.
Related reading: Statistical power explained · How to calculate a confidence interval · Confidence intervals explained
Sources & further reading: NIST/SEMATECH e-Handbook of Statistical Methods · OpenStax Introductory Statistics. How we compute & validate: methodology. Written & reviewed by Dackohn; last reviewed August 2026.