Before sending a customer survey, you need to know how many replies make the results trustworthy. The standard formula uses the z score for your confidence level, the expected proportion and the margin of error you will tolerate. This recipe adds the finite population correction, which lowers the requirement when your customer list is small.
95% confidence, an unknown proportion of 50% and a 5% margin need 385 responses; with 5,000 customers that falls to 358.
The example
Three surveys. Tighter margins and higher confidence require far more responses.
| A | B | C | D | E | F | G | |
|---|---|---|---|---|---|---|---|
| 1 | Case | Z score | Proportion | Margin | Population | Sample | Adjusted |
| 2 | Customer survey | 1.960 | 50.0% | 5.0% | 5,000 | 385 | 358 |
| 3 | Staff survey | 1.645 | 50.0% | 3.0% | 2,000 | 752 | 547 |
| 4 | Member poll | 2.576 | 30.0% | 4.0% | 20,000 | 871 | 835 |
The formula
Infinite-population sample size first, then the correction for a finite list:
How it works
Here is the logic, one piece at a time:
B2^2is the squared z score: 1.96 for 95% confidence, 1.645 for 90%, 2.576 for 99%.C2*(1-C2)is the variance of a yes/no answer; 0.5 is the most conservative choice.- Dividing by
D2^2shrinks the sample as the margin widens. - The second formula scales the result down for a finite list of
E2customers.
The sample size is the number of completed responses, not the number of invitations.
Try it: interactive demo
Enter the z score, proportion, margin and population.
Variations
Estimate invitations from a response rate
Divide by the expected response rate to get invitations to send.
Use NORM.S.INV for z
Compute z from a confidence level instead of typing it.
Pitfalls & errors
The formula assumes random sampling; a self-selected survey can be biased regardless of size.
Entering the margin as 5 instead of 0.05 gives a sample size near zero.
Use p=0.5 when you have no prior estimate; it gives the largest, safest sample.
Practice workbook
Frequently asked questions
What z should I use?
When does the correction matter?
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