Math

Sample Size Calculator

Calculate the sample size needed for your survey or study

Confidence level

%
%

Required Sample Size

385

respondents needed

95%
Confidence
Ā±5%
Margin of Error
1.960
Z-Score

What Is Sample Size?

Sample size is the number of observations or respondents you need to collect to make statistically valid inferences about a larger population. Too few and your results are unreliable; too many and you waste resources. The right sample size balances precision, confidence, and cost.

The Sample Size Formula

For estimating a proportion (e.g., a survey asking yes/no questions), the formula is:

n = zĀ² Ɨ p(1 āˆ’ p) / eĀ²

Where:

  • z = z-score for your confidence level (1.96 for 95%)
  • p = estimated proportion (use 0.5 if unknown ā€” most conservative)
  • e = desired margin of error as a decimal (0.05 for 5%)

For a 95% confidence level and 5% margin of error: n = 1.96Ā² Ɨ 0.5 Ɨ 0.5 / 0.05Ā² = 3.8416 Ɨ 0.25 / 0.0025 = 384 respondents.

Finite Population Correction

The formula above assumes an infinite population. For smaller populations (N), apply the finite population correction:

n_adjusted = n / (1 + (n āˆ’ 1) / N)

Example: you need 384 respondents for infinite population, but your total population is only 500. The adjusted sample size is 384 / (1 + 383 / 500) = 384 / 1.766 ā‰ˆ 217 ā€” nearly half as many.

Interpreting Z-Scores by Confidence Level

  • 80% confidence ā†’ z = 1.282
  • 90% confidence ā†’ z = 1.645
  • 95% confidence ā†’ z = 1.960 (most common)
  • 99% confidence ā†’ z = 2.576
  • 99.9% confidence ā†’ z = 3.291

The higher the confidence level, the larger the z-score, and the larger the required sample size. Moving from 95% to 99% confidence increases the required sample by roughly 75%.

Practical Guidance for Common Research Types

  • Consumer surveys: 95% confidence, 5% margin of error ā†’ ~384 respondents (infinite population)
  • Academic studies: 95% confidence, 3% margin of error ā†’ ~1,067 respondents
  • Employee surveys (company of 200): 95% confidence, 5% margin of error, N=200 ā†’ ~132 respondents
  • A/B tests: Use a power analysis calculator instead ā€” those use a different framework based on effect size and statistical power.

Frequently Asked Questions

What is sample size and why does it matter?
Sample size is the number of individuals or observations you include in your study or survey. A larger sample size reduces the margin of error ā€” giving you more precise estimates ā€” but costs more time and money to collect. If your sample is too small, your results may not be statistically meaningful. The minimum required sample size is determined by your desired confidence level, acceptable margin of error, and the estimated variability in your population.
What is confidence level in sample size calculations?
The confidence level tells you how sure you want to be that your sample results reflect the true population. A 95% confidence level means that if you ran the same survey 100 times with different samples, approximately 95 of those surveys would produce an interval containing the true population value. Common confidence levels are 90%, 95%, and 99%. Higher confidence requires a larger sample.
What is margin of error?
The margin of error (also called sampling error) is the maximum expected difference between your sample result and the true population value. For example, a poll with a 5% margin of error and a result of 52% means the true value is likely between 47% and 57%. A smaller margin of error requires a larger sample size. Most surveys use a 3ā€“5% margin of error.
What does the proportion setting do?
The proportion (p) is your best estimate of the percentage of the population with the characteristic you are measuring. Setting p = 0.5 (50%) gives the most conservative (largest) sample size because 50/50 is the highest variability possible. If you have prior research suggesting the proportion is closer to 10% or 90%, you can enter that to get a smaller required sample size.
What is the finite population correction?
The basic sample size formula assumes an infinitely large population. When your population is small (say, the 200 employees at your company), the required sample size is smaller than the infinite-population formula suggests. The finite population correction adjusts for this: n_adjusted = n / (1 + (n āˆ’ 1) / N). This can significantly reduce the required sample size for small populations.

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