Sample Size Calculator
Find the minimum sample size needed for your survey or experiment. Set confidence level, margin of error, and population size.
Private by design
Calculator results are estimates based on your inputs. They are useful for learning, planning, and comparison, but they are not professional advice.
Use responsibly
Use the result as a practical first pass, then verify any important decision with the appropriate source or professional.
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Why sample size matters
Sample size is the difference between a rough guess and a measurement you can defend. In surveys, it affects how reliable your estimate is. In experiments, it affects whether you can detect a meaningful difference at all. Teams often underestimate how quickly sample needs grow when they want tighter error margins or higher confidence.
Sample size formula
For an infinite population: n = (Z² × p × (1-p)) / e²
For a finite population: n_adj = n / (1 + (n-1)/N)
- Z = Z-score for confidence level.
- p = expected proportion.
- e = margin of error as a decimal.
- N = population size when using finite correction.
Common Z-scores
- 90% confidence -> 1.645
- 95% confidence -> 1.960
- 99% confidence -> 2.576
How to choose confidence and margin of error
95% confidence and a 5% margin of error are common because they balance quality and feasibility. Tighten the margin of error to 3% and the sample requirement rises sharply. Push confidence to 99% and it grows again. The right choice depends on how costly a wrong conclusion would be and how expensive data collection is.
Why people use p = 0.5
When you do not know the expected proportion, using p = 0.5 gives the most conservative sample size. It is effectively the safe default because it avoids underestimating what you need. If you already have historical data suggesting a more realistic proportion, you can use that to reduce oversizing.
What sample size does not solve
A large sample cannot fix poor sampling design, biased respondents, bad survey wording, or weak randomization. If the wrong people are answering, or the question is flawed, increasing the sample only gives you a more precise version of the wrong answer.
Related tools and guides
- Correlation Calculator for analyzing relationships once the data is collected.
- Standard Deviation Calculator to assess spread after sampling.
- Mean, Median & Mode Calculator for summary statistics after fieldwork.