Sample size calculator (survey)
Give the confidence you want, the margin of error you accept and, if you know it, the population size.
Result
370People to survey
- n₀ = 1.96² × 0.5 × (1 − 0.5) ÷ 0.05² = 384.15
- Without correction (infinite population)
- 385
- After correction (before rounding)
- 369.97
- z value used
- 1.96
Inputs
- Confidence level
- 95%
- Margin of error
- 5
- Expected proportion
- 50
- Population size (optional)
- 10000
How it is calculated
Cochran’s formula: n₀ = z² × p × (1 − p) ÷ e².
Result
People to survey
- Without correction (infinite population)
- 385
- After correction (before rounding)
- 369.97
- z value used
- 1.96
How it is calculated
- Cochran’s formula: n₀ = z² × p × (1 − p) ÷ e².
- z is 1.645 (90%), 1.960 (95%) or 2.576 (99%), from the normal law.
- Finite population N: n = n₀ ÷ (1 + (n₀ − 1) ÷ N).
- Always round up to the next whole number.
Example
95%, margin 5%, p = 50%: n₀ = 1.96² × 0.25 ÷ 0.0025 ≈ 384.1, so 385 people. For 10,000 people: 370.
Good to know
- The formula assumes random selection. A biased sample stays wrong, even when large.
- It is a normal approximation, valid for a simple survey of one proportion.
- Plan more contacts than n: not everyone answers.
Sources
- W. G. Cochran, Sampling Techniques (1977)
Frequently asked questions
What is this tool used for?
Give the confidence you want, the margin of error you accept and, if you know it, the population size.
How is the result calculated?
Cochran’s formula: n₀ = z² × p × (1 − p) ÷ e².
What should I check before using the result?
The formula assumes random selection. A biased sample stays wrong, even when large.