Sample Size Calculator
Choose a confidence level, a margin of error and the proportion you expect. If your whole population is small, enter its size. You get the number of responses you need.
Your numbers
How we calculate it
Cochran’s formula gives n0 = z² × p × (1 − p) ÷ e², where z is the critical value for your confidence level, p is the expected proportion and e is the margin of error, both as decimals. At 95%, p = 50% and e = 5%, n0 is 384.15, which rounds up to 385.
If the population N is known and small, the finite population correction reduces it: n = n0 ÷ (1 + (n0 − 1) ÷ N). For a population of 1,000 that gives 277.7, which rounds up to 278. The answer is always rounded up and is never more than the whole population.
Assumptions and limits
- Using 50% for the expected proportion gives the largest, safest sample size.
- The formula assumes a simple random sample. Surveys with low response rates need more invitations than the sample size you need.
- The correction only matters when the sample is a noticeable share of the population.
Frequently asked questions
How many people do I need to survey?
For a 95% confidence level and a 5% margin of error, you need about 385 responses when the population is large. A smaller margin of error needs many more.
Why is 50% used for the expected proportion?
The sample size is largest when the proportion is 50%, so it is the safe choice when you do not know it. If you have a good estimate, such as 20%, the sample you need is smaller.
When should I enter the population size?
When you are sampling from a small group, for example 1,000 customers or students. The correction lowers the sample you need. For a very large or unknown population, leave it empty.
Related calculators
- Confidence Interval CalculatorEnter the sample mean, the sample standard deviation, the sample size and the confidence level.
- Percentage CalculatorThree common percentage problems in one place.
- Probability CalculatorEnter the chance of event A and event B as percentages, and the number of times you try A.
- Z-Score CalculatorChoose whether you know a value with its mean and standard deviation, or you already have a z-score.
Worked example (a fixed example using the starting numbers, it does not change as you type)
Inputs: Confidence level = 95%; Margin of error (%) = 5; Expected proportion (%, use 50 if unsure) = 50.
- Sample size needed 385
- Without population correction 385
- Critical value (z) 1.960
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