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Sample Size Calculator

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Enter your population size, confidence level, and margin of error to find the sample size you need for a survey or study.

Sample Size Calculator

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Sample size needed
370
Uses the worst-case assumption of 50% response variability, the standard conservative choice when the true variability is unknown.

The formula

n₀ = (Z² × p × (1-p)) / E² n = n₀ / (1 + (n₀ - 1) / N) where Z = confidence z-score, p = 0.5 (worst case), E = margin of error, N = population
Example

A population of 10,000 at 95% confidence, 5% margin of error: n₀ = (1.96² × 0.25) / 0.0025 ≈ 384.16, adjusted for finite population: 370 respondents needed.

Step-by-step guide

  1. Enter your total population size (the full group you're studying).
  2. Choose a confidence level - 95% is the most commonly used standard.
  3. Enter your acceptable margin of error - smaller margins require larger samples.

Why the margin of error affects sample size so dramatically

Margin of error appears squared in the denominator of the sample size formula, which means cutting it in half doesn't just double the required sample - it roughly quadruples it. Going from a 5% margin to a 2.5% margin, for example, requires close to four times as many respondents, which is exactly why tightening precision requirements is often the most expensive lever to pull in survey design - far more costly than raising the confidence level from 95% to 99%.

Common mistakes

Confusing confidence level with margin of error - confidence level describes how sure you can be the true value falls within your result, while margin of error describes how wide that range is.
Assuming a huge population always needs a huge sample - past a certain point, sample size requirements level off and stop scaling proportionally with population size, which is why national surveys often need only slightly more respondents than city-level ones.

Frequently asked questions

Why does this use 50% as the assumed variability?

50% represents maximum uncertainty (an even split), which requires the largest possible sample size for a given margin of error - using it is a conservative, safe assumption when you don't already know the true response distribution.

Does population size matter much for very large populations?

Less than most people expect - once a population is large enough (in the hundreds of thousands or more), the required sample size stabilizes and barely increases further, since the formula's finite-population correction has diminishing effect at that scale.

What confidence level should I use?

95% is the most widely used standard across research and surveys, offering a reasonable balance between certainty and practical sample size - 99% is used when higher certainty is specifically required.

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