Sample Size Calculator
Determine the necessary sample size for your study based on desired confidence and margin of error.
Enter the total number of individuals in your target population. If unknown or very large, use a large number (e.g., 1,000,000) or leave blank for infinite population assumption.
80%
85%
90%
95%
99%
The probability that your sample statistic will be within the margin of error. Common values are 90%, 95%, 99%.
The acceptable range of error around your sample estimate. A smaller margin of error requires a larger sample size. Express as a percentage (e.g., 5 for 5%).
Your best estimate of the proportion of the population that has the characteristic you are studying. If unknown, use 0.5 (50%), as this yields the largest sample size.
Your required sample size will appear here.
Understanding Sample Size Calculation
Determining the appropriate sample size is a critical step in research and statistical analysis. A sample that is too small may not provide reliable results, while a sample that is too large can be unnecessarily costly and time-consuming. This calculator helps you find the minimum sample size needed to achieve statistically significant results, taking into account your population size, desired confidence level, margin of error, and an estimated proportion of the population.
Key Concepts:
- Population Size (N): The total number of individuals or items in the group you are interested in studying. If the population is very large or infinite, a simplified formula can be used.
- Confidence Level: This represents how certain you want to be that the results from your sample accurately reflect the population. A 95% confidence level means that if you were to repeat the study many times, 95% of the time the results would fall within your margin of error. It's often represented by a Z-score.
- Margin of Error (e): This is the acceptable amount of error in your study's results. It's the "plus or minus" range around your findings. For example, a margin of error of 5% means your results could be off by up to 5 percentage points in either direction.
- Estimated Proportion (p): This is your best guess at the proportion of the population that exhibits the trait you're studying. If you have no prior information, using 0.5 (50%) is the most conservative approach, as it maximizes the required sample size, ensuring your sample is large enough regardless of the true proportion.
The Math Behind the Calculator:
The calculator uses a common formula for sample size calculation, which can be adjusted for finite or infinite populations.
1. For an Infinite Population (or a very large population where N is much larger than n):
The basic formula is:
n = (Z^2 * p * (1-p)) / e^2
Where:
n= Required sample sizeZ= Z-score corresponding to the desired confidence level (e.g., 1.96 for 95% confidence, 1.645 for 90%, 2.576 for 99%)p= Estimated proportion (0.5 for maximum sample size)e= Margin of error (expressed as a decimal, e.g., 0.05 for 5%)
2. Adjusting for a Finite Population (Cochran's formula adjusted):
When the population size (N) is known and relatively small, the initial sample size (n0) calculated above can be adjusted:
n = n0 / (1 + (n0 - 1) / N)
Where:
n= Adjusted sample sizen0= Sample size calculated for an infinite populationN= Population size
This adjusted formula yields a smaller sample size than the infinite population formula when N is finite, as sampling from a smaller population is more efficient.
How to Use This Calculator:
- Population Size (N): Enter the total number of individuals in your target population. If you don't know this number or it's very large (e.g., millions), you can enter a large placeholder like '1000000' or leave it blank and the calculator will assume an infinite population.
- Confidence Level: Select your desired confidence level from the dropdown menu (e.g., 95%).
- Margin of Error: Input the acceptable margin of error as a percentage (e.g., 5 for 5%). A smaller margin means more precision but requires a larger sample.
- Estimated Proportion (p): Provide your best estimate for the proportion. If you have no idea, use 0.5 (or 50%).
- Click "Calculate Sample Size" to see the recommended number of participants for your study.
When to Use This Calculator:
This calculator is valuable for researchers, market analysts, students, and anyone conducting surveys or studies where data is collected from a subset of a larger group. It helps ensure that the conclusions drawn from the sample are likely to be representative of the entire population.