Free tool, data and statistics
Sample size calculator
A survey sample size with the working shown, ready for Chapter 3.
Give the confidence level and margin of error, and you get how many filled questionnaires to collect for your thesis survey, as per Cochran’s formula.
Many scholars are asking us how they should justify the sample size in Chapter 3, and many times the guide has simply said “take 385” without saying why. That is the reason we kept the working visible. If you know the exact count of your population and it is a small one, the tool brings the number down with a correction, and if you think some people won’t send the form back, it adds extra forms for them. Lower on the page there is one more box, which is for multiple regression and PLS-SEM, and it gives you the minimum sample as per two common rules of thumb. We show all the steps under every result. You can paste them in your methodology chapter as it is, and if a committee member asks where the figure came from, you have the answer ready with you.
Not sure the answer fits your study? WhatsApp us or call, and we’ll look at it with you.
How the tool works
Cochran made this formula for surveys which are trying to estimate a proportion, for example what share of farmers in a district have taken crop insurance. When the population is very large, the formula is n₀ = z² × p × (1 − p) ÷ e². The z you take from whatever confidence level you picked. We put 1.645 when it is 90%, and 1.96 when it is 95%. At 99% it becomes 2.576. Then p is the proportion you are expecting to find in the field. The e is your margin of error, but in decimal form, so the ±5% you wrote in the proposal goes into the formula as 0.05.
Most of the scholars who send us their proposals have kept 95% confidence, ±5% margin and p = 0.5. With these values the formula comes to 384.16, and our calculator always rounds up, so it shows 385. We round up because you cannot survey 0.16 of a person, and also because rounding down to 384 makes your margin slightly wider than what you promised in the proposal.
In some studies the whole population is small enough that you can actually count every person, and then the finite population correction pulls the figure down with n = n₀ ÷ (1 + (n₀ − 1) ÷ N). One example we use is a study on 800 primary school teachers in one block, where 385 comes down to 260 after the correction. If your population is in lakhs the correction hardly makes any change, so better leave that box empty.
The response rate box does the opposite. It works out how many forms you should give out so that enough filled forms come back to you. Suppose you need 385 and you think only 70% will reply, then you should approach 550 people, not 385.
In the second box we have used two rules of thumb. Green (1991) suggested 50 + 8m as minimum for a regression model, where m is the number of predictors you have. For PLS-SEM there is the older “ten times” rule, where you look in your model for the construct which has most arrows coming into it and multiply that count by ten. Please take both these numbers as a lower limit only, not as the target. When the study is testing differences or effects, a power analysis gives you a much stronger justification, and our choosing a statistical test guide will help you find out which test you will be running. What exactly to write about all this in your method chapter, we have covered in the sample size guide.
Questions scholars ask
Why does almost every thesis end up with 385?
It happens because most scholars leave the default values as they are, which is 95% confidence, ±5% margin and p = 0.5. For a large population these values give 384.16, and after rounding up you get 385. Change even one of the three and the answer will move.
Do I need the population size?
You need it only when the population is small and countable, say a few thousand people or less. For groups like “college students in Tamil Nadu” or “small retailers in Hyderabad”, keep the box empty, since the correction makes no real difference for such big groups.
How do I report this in Chapter 3?
Write that you used Cochran’s formula and cite Cochran (1977). Then mention the confidence level, the margin and the p value you took, and give the result you got. After that explain how you actually reached that many respondents during data collection. If you applied the population correction or a response rate, show those steps also, the same way the calculator shows them.
My guide says 200 is enough. Who is right?
It is possible that both of you are right. With 200 responses a descriptive survey has a margin of around ±6.9% at 95% confidence, and many times that is acceptable provided you report it openly in the thesis. For SEM or for comparing subgroups, though, it is your model which decides the number. Sit with your guide and agree on the reasoning before you start the data collection.
Is anything I type here saved?
Nothing you type here is stored by us. The calculation runs inside your own browser itself, and our server only comes to know that somebody pressed the button. It never gets the informations you typed into the boxes.
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Call or WhatsApp, say where you are in your thesis, and we’ll tell you plainly what kind of help makes sense, if any.