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 calculator works out how many completed responses a survey needs, using Cochran’s formula with the finite population correction. At 95% confidence and a ±5% margin of error, the answer for a large population is 385. It also gives the common minimum sample sizes for multiple regression and PLS-SEM, so you can see which rule sets your floor.
Every result shows its working. That matters at the pre-submission seminar, where “why 385?” is a common question and “the website said so” isn’t an answer.
Method
How this tool works
For a survey that estimates a proportion, Cochran’s formula gives the sample size for a very large population: n₀ = z² × p(1 − p) ÷ e². Here z is 1.96 for 95% confidence, p is the proportion you expect (50% if you don’t know, because that gives the largest sample) and e is the margin of error as a decimal.
When you can count the whole population and it is small, the finite population correction brings the number down: n = n₀ ÷ (1 + (n₀ − 1) ÷ N). With 1,000 teachers in a district, 385 becomes 278. The result is always rounded up, because 277.7 people can’t fill in a form.
The response-rate box answers a different question: how many questionnaires to send so that enough come back. At a 60% response rate, 385 completed responses means sending about 642.
The regression and SEM box applies two published rules of thumb. Green (1991) suggests at least 50 + 8m respondents to test a regression model with m predictors, and 104 + m to test the individual predictors. The 10-times rule for PLS-SEM asks for ten times the largest number of arrows pointing at any one construct. Both are minimums that examiners know, and both are weaker than a power analysis.
Limits
What this tool can’t do
FAQ
Frequently asked questions
Why is 385 the answer so often?
Because 95% confidence, a ±5% margin and p = 0.5 are the usual defaults, and with a large population they give 384.16, which rounds up to 385. Change any of the three and the number changes.
Should I use the population size if I know it?
Yes, if you can list the whole population and it is small (a few thousand or fewer). The correction makes a real difference below about 5,000. For a large or uncountable population, such as “farmers in Tamil Nadu”, leave the box empty.
What do I write in my methodology chapter?
Name the formula, give the values you used for confidence, margin and p, show the calculation, and cite Cochran (1977). Then say how you reached that many respondents. The sample size guide has a model paragraph.
My supervisor says 300 is enough. Who is right?
It depends on what the study does. For a descriptive survey, 300 gives a margin of about ±5.7% at 95% confidence, which may be acceptable if you say so. For SEM or subgroup comparisons, the requirement comes from the model, not from Cochran. Agree the justification in writing before data collection.
Does a higher response rate change the sample size?
No. The sample size is the number of completed responses you need. The response rate only tells you how many people to approach to get there.
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