Know your sample size, and how to explain it in Chapter 3.
Enter your population and pick a formula. You get the answer rounded up, the working with your own numbers, and a short paragraph you can adapt for your methodology chapter.
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Work out your sample size.
Why Chapter 3 needs a sample size
Most Nigerian project supervisors expect Chapter 3 to say how many people you studied and how you arrived at that number. A figure like 'about 200 students' with no reasoning invites the question 'why 200?'. A recognised formula, applied to your real population, gives you an answer you can defend.
The calculator above does the arithmetic for three widely used formulas, shows every step with your own numbers, and always rounds up, because a sample that is one respondent short is smaller than the formula asks for.
Which formula should you use
- Taro Yamane (1967): n = N / (1 + Ne²). A common choice in Nigerian project reports for a known, finite population such as the staff or students of one institution, usually run at a 5% margin of error.
- Krejcie and Morgan (1970): a formula built on the chi-square value (3.841) at 95% confidence, a 5% margin of error and P = 0.5. Often quoted through its printed table; this tool computes it directly from the formula.
- Cochran (1977): n₀ = z²pq / e². Suited to large or unknown populations, with an optional finite population correction when you do know N.
- Your department or supervisor may prefer one of these. If they have told you which to use, use that one.
Getting the inputs right
Population (N) is the number of people in the group you want to describe, not the number you hope to reach. Use a real figure you can point to, such as a registry, staff list or enrolment count, and say where it came from in Chapter 3.
The margin of error is how far your sample result can sit from the true value; 5% is the usual choice, and a smaller margin needs a larger sample. The confidence level (Cochran only) is how sure you want to be; 95% is the usual choice.
After you have the number
The sample size is the number of completed, usable responses you are aiming for. Many students distribute a few extra questionnaires to allow for ones that come back blank or incomplete; state in Chapter 3 how many you distributed and how many you analysed.
Also describe how you selected respondents (for example simple random or stratified), because the formula tells you how many, not who.
Frequently asked questions
Is the sample size calculator free?
Yes. It needs no account and no payment, and it runs entirely in your browser.
Why does the answer round up?
Rounding down would give a sample slightly smaller than the formula requires, so the usual convention is to round up to the next whole respondent.
Why can a Krejcie and Morgan table row differ by one from this tool?
Printed tables round to the nearest whole number, while this tool rounds up. For example the formula gives about 44.3 for a population of 50; the table shows 44 and this tool shows 45.
Can I cite the formulas?
Yes. They are usually credited to Yamane (1967), Krejcie and Morgan (1970) and Cochran (1977). Look up the full reference details in the source itself and format them in your department's referencing style.
What if my population is unknown?
Use Cochran's formula and tick that the population is unknown or very large. With 95% confidence, a 5% margin of error and p = 0.5 it gives 385.