Determining the appropriate sample size is a critical step in any research, survey, or statistical analysis. An inadequate sample size can lead to unreliable results, while an excessively large sample size can be a waste of resources. This calculator helps you estimate the minimum number of participants or observations needed to achieve statistically significant and reliable results.
The Formula Explained
The most common formula for calculating sample size for proportions, assuming a normal distribution, is:
n = (Z^2 * p * (1-p)) / E^2
Where:
n: The required sample size.
Z: The Z-score corresponding to the desired confidence level. This value represents how many standard deviations away from the mean a data point is. Common Z-scores are:
90% confidence: Z = 1.645
95% confidence: Z = 1.96
99% confidence: Z = 2.576
p: The estimated proportion of the population that has the attribute in question. If you have no prior knowledge, it's common to use 0.5 (50%), as this yields the largest possible sample size, ensuring a conservative estimate.
E: The margin of error, expressed as a decimal (e.g., 5% = 0.05). This is the acceptable range of deviation from the true population value.
Finite Population Correction
If the population size (N) is relatively small, a correction factor can be applied to reduce the required sample size. The adjusted formula is:
n_adjusted = n / (1 + (n - 1) / N)
Where:
n_adjusted: The adjusted sample size for a finite population.
n: The sample size calculated using the initial formula.
N: The total population size.
If the population size is very large (often considered 20 times the calculated sample size or more), the correction factor has a negligible effect, and the initial formula is sufficient.
How to Use the Calculator
Confidence Level: Select how confident you want to be that your sample results reflect the true population value. Higher confidence (e.g., 99%) requires a larger sample size.
Margin of Error: Determine the acceptable range of error. A smaller margin of error (e.g., 3%) means your results will be more precise but require a larger sample size.
Estimated Population Proportion (p): If you have an estimate of how common the attribute is in your population, enter it here (as a decimal, e.g., 0.7 for 70%). If unsure, use 0.5 for the most conservative (largest) sample size.
Population Size (N): If you know the total number of people or items in your population, enter it. If the population is very large or unknown, enter 0.
Click "Calculate Sample Size" to get your recommended sample size.
When to Use This Calculator
Designing surveys and questionnaires.
Planning A/B testing for websites or marketing campaigns.
Conducting market research.
Setting up clinical trials or scientific experiments.
Estimating the proportion of defective products in a manufacturing batch.
Remember, this calculator provides a statistical estimate. Practical considerations, such as budget, time, and the complexity of data collection, should also factor into your final decision on sample size.
function getZScore(confidenceLevel) {
if (confidenceLevel >= 99.9) return 2.576;
if (confidenceLevel >= 99) return 2.576;
if (confidenceLevel >= 98) return 2.326;
if (confidenceLevel >= 95) return 1.96;
if (confidenceLevel >= 90) return 1.645;
if (confidenceLevel >= 80) return 1.282;
return 1.645; // Default to 90% if input is unusual
}
function calculateSampleSize() {
var confidenceLevel = parseFloat(document.getElementById("confidenceLevel").value);
var marginOfError = parseFloat(document.getElementById("marginOfError").value) / 100; // Convert percentage to decimal
var populationProportion = parseFloat(document.getElementById("populationProportion").value);
var populationSize = parseFloat(document.getElementById("populationSize").value);
var resultDiv = document.getElementById("result");
// Clear previous results
resultDiv.innerHTML = "";
// Input validation
if (isNaN(confidenceLevel) || isNaN(marginOfError) || isNaN(populationProportion) || isNaN(populationSize)) {
resultDiv.innerHTML = "Please enter valid numbers for all fields.";
return;
}
if (confidenceLevel 100) {
resultDiv.innerHTML = "Confidence Level must be between 1 and 100.";
return;
}
if (marginOfError <= 0) {
resultDiv.innerHTML = "Margin of Error must be a positive value.";
return;
}
if (populationProportion 1) {
resultDiv.innerHTML = "Population Proportion must be between 0 and 1.";
return;
}
if (populationSize 0) {
var n_adjusted = n0 / (1 + (n0 – 1) / populationSize);
finalSampleSize = Math.ceil(n_adjusted);
resultDiv.innerHTML = "Required Sample Size (adjusted): " + finalSampleSize + "";
} else {
finalSampleSize = Math.ceil(n0);
resultDiv.innerHTML = "Required Sample Size: " + finalSampleSize + "";
}
}