Raosoft Calculator

Raosoft Sample Size Calculator

The amount of error that you can tolerate. 5% is common.

90% 95% 99% The probability that the sample represents the population.

The total number of people in the group you are studying.

Expected outcome distribution. Use 50% for the most conservative estimate.

Recommended Sample Size

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Understanding the Raosoft Sample Size Calculation

The Raosoft calculator is an essential tool for researchers and survey designers. It determines the minimum number of respondents needed to ensure that survey results are statistically significant and representative of a larger population. Determining the correct sample size prevents wasting resources on excessive surveying while ensuring the data isn't too thin to draw conclusions.

The Key Parameters Explained

• Margin of Error: This is the "plus or minus" figure often reported in opinion polls. If you have a 5% margin of error and 60% of your sample picks an answer, you can be fairly confident that if you asked the entire population, between 55% and 65% would have picked that answer.
• Confidence Level: This expresses how certain you are that the population fits within your margin of error. A 95% confidence level is the industry standard, meaning if you conducted the same survey 100 times, the results would fall within the margin of error 95 times.
• Population Size: This is the total number of people in the group you are studying. If you are surveying employees at a company of 500 people, 500 is your population. If the population is extremely large (e.g., millions), the required sample size plateaus.
• Response Distribution: For many surveys, you don't know what the results will be beforehand. Setting this to 50% provides the most conservative (largest) sample size, ensuring your survey is robust regardless of the actual distribution.

Real-World Example

Imagine you want to survey a city with a Population Size of 50,000. You decide on a 95% Confidence Level and a 5% Margin of Error. Assuming a 50% response distribution, the Raosoft formula would calculate a recommended sample size of approximately 382 people. If you narrowed your margin of error to 2%, the required sample size would jump to over 2,200 people.

The Mathematical Formula

The logic follows the standard formula for sample size determination:

n = N x / ( (N-1) e^2 + x )

Where x is based on the Z-score of your confidence level and the response distribution. This calculator automates these complex logarithms to provide instant, actionable data for your research projects.

function calculateRaosoft() { var marginOfError = parseFloat(document.getElementById("marginOfError").value); var confidenceLevel = parseFloat(document.getElementById("confidenceLevel").value); var populationSize = parseFloat(document.getElementById("populationSize").value); var responseDistribution = parseFloat(document.getElementById("responseDistribution").value); if (isNaN(marginOfError) || isNaN(populationSize) || isNaN(responseDistribution)) { alert("Please enter valid numerical values."); return; } // Convert percentages to decimals var e = marginOfError / 100; var p = responseDistribution / 100; var N = populationSize; // Determine Z-score based on Confidence Level var z; if (confidenceLevel === 90) { z = 1.645; } else if (confidenceLevel === 95) { z = 1.96; } else if (confidenceLevel === 99) { z = 2.576; } else { z = 1.96; // Default to 95% } // Calculate critical value x // x = Z^2 * P * (1-P) var x = Math.pow(z, 2) * p * (1 – p); // Calculate sample size n // n = (N * x) / ((N-1) * e^2 + x) var sampleSize = (N * x) / ((N – 1) * Math.pow(e, 2) + x); // Round up to nearest whole person var finalResult = Math.ceil(sampleSize); // Display results var resultArea = document.getElementById("resultArea"); var sampleResult = document.getElementById("sampleResult"); var summaryText = document.getElementById("summaryText"); sampleResult.innerHTML = finalResult.toLocaleString(); summaryText.innerHTML = "To achieve a " + confidenceLevel + "% confidence level with a " + marginOfError + "% margin of error in a population of " + N.toLocaleString() + "."; resultArea.style.display = "block"; }