Sample Size Calculator
How many responses you need for a reliable survey.
Enter your values
Enter the margin of error in %.
Choose one of: 90%, 95%, 99%.
Enter the population size (0 for unlimited) you are working with.
Enter the expected proportion in %.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- Required sample size
- 385
- Unadjusted (infinite population)
- 385
- Margin of error achieved
- 5%
- Responses needed at 60% response rate
- 641
Working
- 1n₀ = 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.2
Quick answer
Required sample size is z²·p(1−p) ÷ e², adjusted downward when the population is small.
n = z²·p(1−p) ÷ e²
At a glance
| What it does | How many responses you need for a reliable survey. |
|---|---|
| Category | Statistics |
| Inputs needed | Margin of error, Confidence level, Population size (0 for unlimited), Expected proportion |
| Main output | Required sample size |
| Formula | n = z²·p(1−p) ÷ e² |
| Cost | Free — no sign-up, no download |
How to use the Sample Size Calculator
- 1Set the margin of error you can live with.
- 2Choose a confidence level.
- 3Enter the population size if it is small and known.
Inputs explained
- Margin of error(%)
- Enter the margin of error in %.
- Confidence level
- Choose one of: 90%, 95%, 99%.
- Population size (0 for unlimited)
- Enter the population size (0 for unlimited) you are working with.
- Expected proportion(%)
- Enter the expected proportion in %.
Worked example
Using the values the calculator loads with:
Inputs
- Margin of error5 %
- Confidence level95%
- Population size (0 for unlimited)0
- Expected proportion50 %
Results
- Required sample size385
- Unadjusted (infinite population)385
- Margin of error achieved5%
- Responses needed at 60% response rate641
- n₀ = 1.96² × 0.5 × 0.5 ÷ 0.05² = 384.2
Frequently asked questions
Why use 50% as the proportion?
It maximises variance, giving the most conservative (largest) required sample when you have no prior estimate.
Does population size matter?
Only for small populations. Beyond about 20,000 the required sample barely changes.
What do I need to enter into the Sample Size Calculator?
Just 4 values: margin of error, confidence level, population size (0 for unlimited), expected proportion. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Sample Size Calculator work out the answer?
Required sample size is z²·p(1−p) ÷ e², adjusted downward when the population is small. It applies the formula n = z²·p(1−p) ÷ e² and shows the working so you can check each step by hand.
Is the Sample Size Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.