Sample Size Calculator
Find how many survey responses you need for a margin of error and confidence level, or the margin of error for a sample size.
Change the values and press Calculate to work out your own figures.
Sample size needed
Enter the confidence level, margin of error, expected proportion and (optionally) the population size.
Show the working
- n₀ = z² p(1 − p) ÷ e² = 384.1458821
- Round up: 385
Margin of error for a sample
Enter the confidence level, sample size, proportion and (optionally) the population size.
Show the working
- MOE = z × √(p(1 − p) ÷ n) = 0.09601823353
How to use it
Enter the confidence level, margin of error, expected proportion and (optionally) the population size. Enter the confidence level, sample size, proportion and (optionally) the population size.
Probabilities can be typed as decimals, fractions or percentages. Show the working gives the formula with your numbers in it.
Key facts
n₀ = z² p(1 − p) ÷ e²; n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
Why 385?
For ±5% at 95% confidence with p = 50%, n₀ = 1.96² × 0.25 ÷ 0.05² = 384.16, which rounds up to 385. Smaller populations need fewer responses.
Questions
How many responses do I need?
385 for ±5% at 95% confidence from a large population.
What proportion should I use?
50% if unsure; it gives the most cautious (largest) size.
Formulas
n₀ = z² p(1 − p) ÷ e²; n = n₀ ÷ (1 + (n₀ − 1) ÷ N)
Sources
Limitations
- Probabilities can be typed as decimals (0.25), fractions (1/4) or percentages (25%).