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How to calculate sample size for your project (with examples)

October 31, 2026

Your sample size is one of the first things a supervisor checks in chapter three. You need a number that is large enough to trust, and a recognised method to justify it. Here are the three methods most often used in Nigerian projects.

First, know your population

Your population is everyone your study is about: for example, all 2,000 final year students in a faculty. If you know that number, use Taro Yamane's formula or Krejcie and Morgan's table. If the population is very large or unknown, use Cochran's formula.

Method 1: Taro Yamane's formula

The formula is n = N / (1 + N × e²), where n is the sample size, N is the population and e is the margin of error (usually 0.05, meaning 5%).

Example: a population of 2,000 students with a 5% margin of error. First, 2,000 × 0.05² = 2,000 × 0.0025 = 5. Then 1 + 5 = 6. Finally, 2,000 ÷ 6 = 333.3, so the sample size is 333.

Method 2: Krejcie and Morgan's table

Krejcie and Morgan (1970) published a table that gives the sample size for a known population at a 95% confidence level. You simply look up your population. For a population of 2,000, the table gives 322. Cite the table in your methodology, and include it in your appendix if your department expects that.

Method 3: Cochran's formula (large or unknown populations)

When you don't know the population size, Cochran's formula is common: n = Z² × p × q / e², where Z is 1.96 for 95% confidence, p is the expected proportion (use 0.5 if you don't know it), q = 1 − p, and e is the margin of error.

Example: 1.96² × 0.5 × 0.5 / 0.05² = 3.8416 × 0.25 / 0.0025 = 384.16, so the sample size is 385 (always round up).

Plan for non-responses

Not everyone will return your questionnaire. Many researchers add 10% or more to the calculated sample to allow for this. If you do, say so and explain why.

How to write it up in chapter three

State the population and where the number came from.
Name the method and give the formula or table, with a citation.
Show the calculation step by step.
State the final sample size and any adjustment for non-response.
Explain how you'll select respondents (your sampling technique).

If your study uses a different design, such as an experiment or interviews, the rules are different. A research methodology tutor can help you choose and justify the right approach.

Find a research methodology tutor

Method 1: Taro Yamane's formula

The formula is n = N / (1 + N × e²), where n is the sample size, N is the population and e is the margin of error (usually 0.05, meaning 5%).

Example: a population of 2,000 students with a 5% margin of error. First, 2,000 × 0.05² = 2,000 × 0.0025 = 5. Then 1 + 5 = 6. Finally, 2,000 ÷ 6 = 333.3, so the sample size is 333.

Method 2: Krejcie and Morgan's table

Method 3: Cochran's formula (large or unknown populations)

Example: 1.96² × 0.5 × 0.5 / 0.05² = 3.8416 × 0.25 / 0.0025 = 384.16, so the sample size is 385 (always round up).

How to write it up in chapter three

State the population and where the number came from.

Name the method and give the formula or table, with a citation.

Show the calculation step by step.

State the final sample size and any adjustment for non-response.

Explain how you'll select respondents (your sampling technique).

If your study uses a different design, such as an experiment or interviews, the rules are different. A research methodology tutor can help you choose and justify the right approach.