Large population survey
For a broad audience with unknown population size, use the infinite-population formula.
95% confidence, 5% margin, p = 0.5
Required sample size: 385
Sample Size Calculator
Use this sample size calculator to determine the appropriate sample size for your research or survey with specified confidence level and margin of error. Get step-by-step solutions instantly.
Sample Size Calculator
Select the calculation type, enter the required parameters, and click Calculate to find the appropriate sample size for your research or survey.
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What is Sample Size?
Sample size refers to the number of individuals or observations included in a study or survey. It is a critical component of research design that affects the precision, reliability, and validity of your results.
A properly calculated sample size ensures that your research findings are representative of the entire population within your specified confidence level and margin of error. Too small a sample may lead to inaccurate results, while an unnecessarily large sample can waste resources.
Sample Size Formulas
Here are the key formulas used to calculate sample size for different scenarios:
For Unknown/Large Populations
When the population size is unknown or very large (typically when N > 100,000), use this formula:
$n = \frac{z^2 \times p \times (1-p)}{e^2}$
For Known/Finite Populations
When the population size is known and relatively small, use this adjusted formula:
$n = \frac{N \times z^2 \times p \times (1-p)}{(N-1) \times e^2 + z^2 \times p \times (1-p)}$
Z-Score Values
The z-score is determined by your desired confidence level:
$\begin{array}{|c|c|} \hline \text{Confidence Level} & \text{Z-score} \\ \hline 90\% & 1.645 \\ \hline 95\% & 1.96 \\ \hline 99\% & 2.576 \\ \hline \end{array}$
Applications of Sample Size Calculation
Market Research
Used to determine how many consumers to survey for product testing, market analysis, and customer satisfaction studies.
Medical Research
Essential for clinical trials, epidemiological studies, and healthcare surveys to ensure statistically significant results.
Social Sciences
Applied in psychology, sociology, and political polling to gather representative data from populations.
Quality Control
Used in manufacturing and production to determine appropriate inspection sample sizes for quality assurance.
How to Use This Calculator
- Select the calculation type (Unknown/Large Population or Known/Finite Population).
- Choose your desired confidence level (90%, 95%, or 99%).
- Enter your margin of error as a percentage (e.g., 5 for 5%).
- Specify the population proportion (default is 0.5, which gives the maximum sample size).
- If you selected Known/Finite Population, enter the population size, then click 'Calculate' to get your result.
Use a population proportion of 0.5 when you do not know the expected share. It produces the most conservative, largest sample size estimate.
Sample Size Examples
Finite population correction
When the full population is known, the required sample size usually decreases.
95% confidence, 5% margin, p = 0.5, N = 1000
Required sample size: 278
Higher precision study
A smaller margin of error increases the sample size needed for reliable conclusions.
95% confidence, 3% margin, p = 0.5
Required sample size: 1068
Sample Size Calculator FAQ
Why does a smaller margin of error require a larger sample size?
A smaller margin of error means you want tighter precision. To reduce uncertainty, the study needs more observations.
Why is 0.5 often used for population proportion?
A proportion of 0.5 produces the largest sample size requirement, so it is a conservative default when the true proportion is unknown.
When should I use the finite population formula?
Use the finite population formula when the full population size is known and not extremely large. It adjusts the estimate downward because sampling a larger share of the population gives more information.
Does a higher confidence level increase the required sample size?
Yes. Higher confidence levels use larger z-scores, which increases the sample size needed to maintain the same margin of error.