Sample Size Calculator
Calculate required sample size for surveys and studies.
Survey Parameters
Use 50% for maximum sample size (conservative)
Sample Size Result
Required Sample Size
385
respondents
Z-Score
1.960
Parameters:
Confidence: 95%
Margin of Error: 5%
Proportion: 50%
About This Calculator
The Sample Size Calculator helps you determine the required sample size for surveys, studies, and research. It calculates the minimum number of respondents needed to achieve a desired confidence level and margin of error.
The calculator uses statistical formulas to determine sample size based on confidence level (typically 90%, 95%, or 99%), margin of error (the acceptable error range), and population proportion (the expected percentage, often 50% for maximum variability).
Formula & Calculation Method
Sample Size Formula:
Infinite Population:
n = (z² × p × (1-p)) / e²
Finite Population:
n = (n₀ × N) / (n₀ + N - 1)
where n₀ is the infinite population sample size
Variables:
n = sample size
z = z-score for confidence level
p = population proportion (0.5 for maximum variability)
e = margin of error
N = population size
The z-score depends on the confidence level: 1.96 for 95%, 2.576 for 99%, etc. Using p = 0.5 (50%) gives the maximum sample size and is conservative when the true proportion is unknown.
How to Use This Calculator
- Set Confidence Level: Choose your desired confidence level (typically 95%).
- Set Margin of Error: Enter the acceptable margin of error (e.g., 5% means ±5%).
- Set Population Proportion: Enter expected proportion (use 50% if unknown for maximum sample size).
- Population Size (optional): Check the box and enter population size for finite population correction.
- View Results: See the required sample size and z-score used.
Frequently Asked Questions
What is a good sample size?
Sample size depends on your confidence level and margin of error. For a 95% confidence level with a 5% margin of error, you typically need about 385 respondents for an infinite population. Larger samples provide more precision but require more resources.
Why use 50% for population proportion?
Using 50% gives the maximum possible sample size, which is conservative and ensures your sample is large enough regardless of the actual proportion. If you know the expected proportion, you can use that instead for a smaller required sample size.
What is margin of error?
Margin of error is the range within which you expect your results to fall. For example, a 5% margin of error means if 60% of your sample says "yes," you can be confident that 55-65% of the population says "yes" (at your chosen confidence level).
When should I use finite population correction?
Use finite population correction when your sample size is a significant portion of your total population (typically more than 5%). This correction reduces the required sample size for smaller populations.
Calculator by
Prof. Emily Watson, PhD
PhD in Applied MathematicsStatistics Certification