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

  1. Select the calculation type (Unknown/Large Population or Known/Finite Population).
  2. Choose your desired confidence level (90%, 95%, or 99%).
  3. Enter your margin of error as a percentage (e.g., 5 for 5%).
  4. Specify the population proportion (default is 0.5, which gives the maximum sample size).
  5. If you selected Known/Finite Population, enter the population size, then click 'Calculate' to get your result.