Free tool · Data & statistics
Sample size calculator
Cochran’s formula, the small-population correction and the regression rules of thumb, with every step shown so you can defend the number.
This sample size calculator tells you how many completed survey responses you need, using Cochran’s formula with the finite population correction. If you go with 95% confidence, ±5% margin of error and a large population, you will get 385. A second box gives the usual minimum for multiple regression and PLS-SEM, so you can see which rule sets your floor.
All the working is shown with the result, so note it down for pre-submission seminar. Somebody in the committee will ask “why 385?”, and “the website gave it” is not going to work.
Method
How this tool works
Suppose your survey is estimating a proportion and the population is very large. Then Cochran’s formula is n₀ = z² × p(1 − p) ÷ e². z is 1.96 if you have chosen 95% confidence. e is the margin of error as a decimal, and p is the proportion you expect. Many scholars don’t have any clue about p at the start. No problem, put 50%, it gives the largest sample.
Your population is small and you have counted it? Then the finite population correction n = n₀ ÷ (1 + (n₀ − 1) ÷ N) brings the number down. Take one district with 1,000 teachers. For them 385 becomes 278. It is rounded up always, because 277.7 people cannot fill your questionnaire.
Response rate is a separate thing. That box tells how many questionnaires to send so enough filled ones come back. If you expect 60% to reply, for 385 completed responses you send around 642.
The regression and SEM box has two published rules of thumb. Green (1991) gave 50 + 8m respondents as the minimum for testing a regression model having m predictors, and 104 + m if you are testing the predictors one by one. For PLS-SEM it is the 10-times rule. Find the construct with the maximum arrows pointing into it and multiply that count by ten. Examiners are aware of both, but if you can do a proper power analysis for your model, that one carries more weight with them.
Limits
What this tool can’t do
FAQ
Frequently asked questions
Why is 385 the answer so often?
It comes from the defaults most people use, 95% confidence with ±5% margin and p = 0.5. For a large population that calculation gives 384.16, which you round up to 385. Change any input and the number changes.
Should I use the population size if I know it?
Yes, if you have the full list of your population and it is small, maybe a few thousand or below. Under roughly 5,000 the correction changes the answer quite a bit. If it is large or uncountable (“farmers in Tamil Nadu”, for example), keep that box empty.
What do I write in my methodology chapter?
Start with the formula name and the values you used for confidence, margin and p, then put the calculation step by step and cite Cochran (1977) there. Then explain about how you actually got that number of respondents. A model paragraph is there in our sample size guide.
My supervisor says 300 is enough. Who is right?
Honestly it depends on your study. If it is a descriptive survey, then 300 responses means a margin of about ±5.7% at 95% confidence, and that may be acceptable if you clearly state it. With SEM or subgroup comparisons the sample size has to come from your model, Cochran’s formula doesn’t apply there. Before collecting data, sit with your guide once and agree the justification in writing.
Does a higher response rate change the sample size?
It does not. Your sample size is the number of completed responses you need. Response rate just helps in planning how many people to approach.
Keep reading
Related guides and services
Sample size calculation for research
Cochran, power analysis and SEM rules of thumb, and how to justify the number you choose.
Statistical test chooser
Up to five questions about your data, then the test to use, its non-parametric alternative and why.
Statistics Training and Analysis Review (SPSS, R, AMOS, SmartPLS)
Learn the right tests on your own data, run them yourself, and get your output and interpretation checked.
Talk it through with a specialist for free
Send us where you are and what you need. We’ll reply within one working day with clear advice, a written scope and a fixed quote. No obligation.
Book a free consultation