Calculate exactly how many survey invites you need to send.
The total group you are studying.
90%
95%
99%
How certain you want to be.
Amount of error you can tolerate.
What percentage of people will reply?
Responses Needed
0
Total Invites to Send
0
Understanding Sample Size and Response Rate
When conducting research, one of the most common pitfalls is forgetting to account for the response rate. If your statistical formula says you need 385 responses, but you only send 385 emails, you will likely only receive 40 to 80 responses, rendering your data statistically insignificant.
Why Response Rate is Critical
The response rate is the percentage of people who actually complete your survey out of the total number of people invited. In modern digital surveys, response rates often hover between 10% and 30%. This calculator adjusts the standard Cochran formula to ensure your recruitment effort matches your data requirements.
How the Calculation Works
The calculator uses three primary steps:
Z-Score Calculation: Based on your confidence level (e.g., 1.96 for 95%).
Sample Size for Infinite Population: Determines the base number needed if the population was endless.
Finite Population Correction: Adjusts the number based on your specific population size.
Response Rate Adjustment: Divide the required sample by the response rate (decimal form) to find the final invitation target.
Example Calculation
Imagine you have a customer base of 5,000 people. You want a 95% confidence level and a 5% margin of error. Usually, you would need 357 responses. However, if you expect only 15% of customers to answer, you must send 2,380 invitations to reach that goal.
function calculateSurveySize() {
var N = parseFloat(document.getElementById('popSize').value);
var CL = parseFloat(document.getElementById('confLevel').value);
var e = parseFloat(document.getElementById('marginError').value) / 100;
var RR = parseFloat(document.getElementById('respRate').value) / 100;
// Validate inputs
if (isNaN(N) || N <= 0 || isNaN(e) || e <= 0 || isNaN(RR) || RR 1) {
alert("Response rate cannot be higher than 100%.");
return;
}
// Z-Score mapping
var z = 1.96;
if (CL === 90) z = 1.645;
if (CL === 95) z = 1.96;
if (CL === 99) z = 2.576;
// Sample Proportion (p) usually 0.5 for maximum variability
var p = 0.5;
// Cochran's formula for infinite population
var n0 = (Math.pow(z, 2) * p * (1 – p)) / Math.pow(e, 2);
// Finite Population Correction
var n = n0 / (1 + ((n0 – 1) / N));
// Required Responses (Rounded up)
var responsesNeeded = Math.ceil(n);
// Total Invitations needed based on Response Rate
var invitesNeeded = Math.ceil(responsesNeeded / RR);
// Update UI
document.getElementById('neededResponses').innerHTML = responsesNeeded.toLocaleString();
document.getElementById('totalInvites').innerHTML = invitesNeeded.toLocaleString();
var summary = "To achieve a margin of error of " + (e * 100).toFixed(1) + "% with " + CL + "% confidence in a population of " + N.toLocaleString() + ", you need " + responsesNeeded.toLocaleString() + " completed surveys. Given your " + (RR * 100).toFixed(0) + "% response rate, you must invite " + invitesNeeded.toLocaleString() + " participants.";
document.getElementById('summaryText').innerHTML = summary;
document.getElementById('resultsArea').style.display = 'block';
}