Determine the appropriate sample size needed for your research or survey.
90%
95%
99%
Required Sample Size:
Understanding Sample Size Calculation
Calculating the correct sample size is crucial for any research, survey, or statistical study. A sample that is too small may not be representative of the population, leading to unreliable conclusions. Conversely, a sample that is too large can be wasteful of time, resources, and money.
The Formula for Sample Size
A common formula used for calculating sample size for proportions, especially when the population size is unknown or very large, is:
n = (Z^2 * p * (1-p)) / E^2
Where:
n is the required sample size.
Z is the Z-score corresponding to the desired confidence level. Common Z-scores are:
90% confidence level: Z = 1.645
95% confidence level: Z = 1.96
99% confidence level: Z = 2.576
p is the estimated proportion of the population that has the characteristic you are interested in. If you have no prior information, using p = 0.5 (or 50%) will yield the largest possible sample size, making it the most conservative estimate.
E is the desired margin of error (expressed as a decimal). This is the acceptable difference between your sample result and the true population value.
Finite Population Correction
If your population size (N) is relatively small and known, and your calculated sample size (n) is a significant fraction of the population (typically more than 5%), you can adjust the sample size using the Finite Population Correction (FPC) formula:
n_adjusted = n / (1 + (n - 1) / N)
Where:
n_adjusted is the adjusted sample size.
n is the initial sample size calculated without considering population size.
N is the population size.
This adjustment reduces the required sample size when sampling from a finite population.
How to Use This Calculator
1. Confidence Level: Select how confident you want to be that your sample results reflect the true population value. Higher confidence levels require larger sample sizes.
2. Margin of Error: Decide how much error you are willing to tolerate. A smaller margin of error (e.g., 3% instead of 5%) means your sample is closer to the population, but requires a larger sample size.
3. Population Size: If you know the total number of people in your target group, enter it here. If the population is very large or unknown, leave this field blank. The calculator will use the formula for an infinite population.
4. Estimated Proportion: If you have an estimate of how common the characteristic you're studying is in the population (e.g., 60% of users prefer feature X), enter it as a decimal (0.60). If you have no idea, use 0.5 (50%) for the most conservative (largest) sample size.
5. Calculate: Click the button to see the recommended sample size. If a population size was entered, the calculator will also show the adjusted sample size.
When to Use a Sample Size Calculator
Market research surveys
Political polling
Scientific experiments
User feedback studies
Quality control inspections
function getZScore(confidenceLevel) {
var zScores = {
0.90: 1.645,
0.95: 1.96,
0.99: 2.576
};
return zScores[confidenceLevel] || 1.96; // Default to 1.96 if not found
}
function calculateSampleSize() {
var confidenceLevel = parseFloat(document.getElementById("confidenceLevel").value);
var marginOfError = parseFloat(document.getElementById("marginOfError").value);
var populationSize = parseFloat(document.getElementById("populationSize").value);
var estimatedProportion = parseFloat(document.getElementById("estimatedProportion").value);
var resultDiv = document.getElementById("result");
var resultValueDiv = document.getElementById("result-value");
// Validate inputs
if (isNaN(marginOfError) || marginOfError 0.5) {
alert("Please enter a valid Margin of Error between 0.01 and 0.5.");
return;
}
if (isNaN(estimatedProportion) || estimatedProportion 1) {
alert("Please enter a valid Estimated Proportion between 0 and 1.");
return;
}
if (!isNaN(populationSize) && populationSize 0) {
var n_adjusted = n_initial / (1 + (n_initial – 1) / populationSize);
finalSampleSize = Math.ceil(n_adjusted);
resultDiv.style.display = "block";
resultValueDiv.innerHTML = finalSampleSize + " (Adjusted for finite population)";
} else {
finalSampleSize = Math.ceil(n_initial);
resultDiv.style.display = "block";
resultValueDiv.innerHTML = finalSampleSize;
}
}