📊 Sample Size Calculator
Find the sample size you need for a survey from confidence level, margin of error and population, or the margin of error for a sample you already have.
Leave the expected proportion at 50% if you do not know it — that gives the largest, safest sample size.
| z-score for 95% | 1.9600 |
|---|---|
| n₀ = z² × p(1 − p) ÷ e² | 1.960² × 0.50 × 0.50 ÷ 0.050² = 384.1 |
Sample sizes at 95% confidence (large population, p = 50%)
| Margin of error | Responses needed |
|---|---|
| ±10% | 97 |
| ±7% | 196 |
| ±5% | 385 |
| ±4% | 601 |
| ±3% | 1,068 |
| ±2% | 2,401 |
| ±1% | 9,604 |
What Sample Size Calculator Does
This sample size calculator tells you how many survey responses you need to estimate a percentage within a chosen margin of error at a chosen confidence level. Enter the population size if it is small and known — a company’s employees, a school’s parents — and the finite population correction lowers the requirement accordingly. The formula is shown with your numbers, so you can cite it in a report.
Switch to the reverse mode if you already have responses: it gives the margin of error for that sample size. Add an expected response rate to see how many people you need to invite, and use the reference table to see how the required sample grows as the margin of error shrinks.
How to Use Sample Size Calculator
- Choose a confidence level and margin of error
- Enter the population size if it is small and known
- Keep the expected proportion at 50% unless you know better
- Read the responses needed, with the formula shown
- Add a response rate to see how many people to invite, or switch to margin of error
Formula Used by Sample Size Calculator
Cochran’s formula
n₀ = z² × p(1 − p) ÷ e²
- z
- z-score for the confidence level (1.96 for 95%)
- p
- Expected proportion (0.5 when unknown)
- e
- Margin of error as a decimal (0.05 for ±5%)
Worked example
95% confidence, ±5%, p = 0.5.
- 1.96² × 0.5 × 0.5 = 0.9604
- 0.9604 ÷ 0.05² = 384.2
- Round up
Result: 385 responses.
Finite population correction
n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
Worked example
The same survey of a population of 1,000.
- 384.2 ÷ (1 + 383.2 ÷ 1,000)
- = 384.2 ÷ 1.383
Result: 278 responses.
Responses Needed (Large Population, p = 50%)
| Margin of error | 90% confidence | 95% confidence | 99% confidence |
|---|---|---|---|
| ±10% | 68 | 97 | 166 |
| ±5% | 271 | 385 | 664 |
| ±3% | 752 | 1,068 | 1,844 |
| ±2% | 1,691 | 2,401 | 4,147 |
| ±1% | 6,764 | 9,604 | 16,588 |
How to Read Your Result
Who you ask matters more than how many
The formula assumes a random sample. A thousand responses from a self-selected or convenience sample can be far less accurate than three hundred from a properly random one. Non-response also matters: if the people who reply differ from those who do not, a large sample does not remove that bias.
Subgroups need their own sample
If you plan to compare groups — regions, age bands, customers vs non-customers — each group needs enough responses on its own. The margin of error for a subgroup of 100 is about ±10% at 95% confidence, whatever the total sample.
Limitations & Accuracy Notes
- For estimating a proportion (a percentage); comparing two groups or estimating a mean needs different formulas, such as those in the A/B test calculator.
- Assumes simple random sampling; stratified or cluster designs need a design effect adjustment.