Sample Size Calculator

Required Sample Size
383
–

What Is a Sample Size Calculator?

This calculator determines how many survey responses you need to reach a statistically valid conclusion, given your population size, desired confidence level, and acceptable margin of error — essential for designing surveys, research studies, and A/B tests.

How to Use the Sample Size Calculator

  1. Enter your total population size.
  2. Choose a confidence level (95% is most common).
  3. Enter your acceptable margin of error.
  4. Enter expected response distribution (50% is the safest default if unknown).

Sample Size Formula

Sample Size (with finite population correction)
n = [Z²×p(1-p)/e²] / [1 + (Z²×p(1-p)/e² − 1)/N]
Z = z-score for confidence level
p = expected response distribution (decimal)
e = margin of error (decimal)
N = population size

Worked Example

Example: Population 100,000, 95% Confidence, 5% Margin of Error, 50% Distribution

Base sample size (infinite population): (1.96² × 0.5 × 0.5) / 0.05² ≈ 384.16

Adjusted for finite population of 100,000: approximately 383

Understanding Your Results

This is the minimum number of responses needed for your results to be statistically representative within your chosen confidence level and margin of error. Larger populations require diminishing additional sample size increases, which is why sample size requirements level off even for very large populations.

Common Mistakes to Avoid

  • Using an unrealistically small margin of error, which dramatically increases required sample size.
  • Assuming a larger population always needs a proportionally larger sample — this isn't the case beyond a certain point.

Frequently Asked Questions

Using a formula based on your desired confidence level (z-score), acceptable margin of error, expected response distribution, and total population size, with a finite population correction applied.

95% is the most commonly used standard for most research and surveys, balancing statistical rigor with practical sample size requirements.

50% produces the most conservative (largest) required sample size, ensuring your study is adequately powered even if you don't know the expected response split in advance.

Not proportionally — sample size requirements level off significantly for large populations, which is why national surveys often need only a few hundred to a couple thousand responses regardless of a population being in the millions.

5% is a common standard for many surveys, though more precise research may use 3% or lower margins, which require larger sample sizes.