Free tool · Chapter 3
Taro Yamane sample size calculator
Enter your population and get the sample size for your questionnaire — with the full working, ready to paste into Chapter 3.
Everyone your study could include, e.g. all 1,200 SS2 students in the selected schools.
Margin of error (e)
5% is the usual choice for undergraduate projects.
Your sample size
300
respondents from a population of 1,200
Working
- n = N / (1 + N(e)²)
- n = 1,200 / (1 + 1,200 × 0.05²)
- n = 1,200 / (1 + 1,200 × 0.0025)
- n = 1,200 / 4
- n = 300
For your Chapter 3
The sample size was determined using the Taro Yamane (1967) formula, n = N / (1 + N(e)²), where n is the sample size, N is the population (1,200) and e is the margin of error (0.05, i.e. 5%). n = 1,200 / (1 + 1,200 × 0.05²) = 1,200 / 4 = 300. The sample size for this study is therefore 300 respondents.
The Taro Yamane formula
n = N / (1 + N(e)²)
- n — the sample size you need
- N — the population (everyone your study could include)
- e — the margin of error, usually 0.05 (5%)
Worked example: 1,200 SS2 students
- n = N / (1 + N(e)²)
- n = 1,200 / (1 + 1,200 × 0.05²)
- n = 1,200 / (1 + 1,200 × 0.0025)
- n = 1,200 / 4
- n = 300
So you would give questionnaires to 300 students.
Quick reference at a 5% margin of error
| Population (N) | Sample size (n) |
|---|---|
| 100 | 80 |
| 200 | 134 |
| 500 | 223 |
| 1,000 | 286 |
| 2,000 | 334 |
| 5,000 | 371 |
| 10,000 | 385 |
| 50,000 | 397 |
Notice the sample levels off near 400 however large the population gets — that's why Cochran's formula gives 385 when the population can't be counted.
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Common questions
What is the Taro Yamane formula?
Taro Yamane's (1967) formula is n = N / (1 + N(e)²), where n is the sample size, N is the population and e is the margin of error. At a 5% margin of error, a population of 1,200 gives a sample of 300.
Should I round the answer up or down?
Round up. A sample can't include part of a person, and rounding up means your sample is never smaller than the formula requires. Also plan for questionnaires that won't come back: many students distribute about 10% more than the sample size.
What margin of error should I use?
5% (0.05) is the usual choice for undergraduate projects. A smaller margin such as 3% needs a much larger sample; use it only if your supervisor asks for it.
When should I not use Taro Yamane?
Yamane is for surveys of a known, countable population. Don't use it for interviews or focus groups (choose participants until you stop hearing new themes), for experiments (replicates or a power analysis decide the number), or when you can't count the population — use Cochran's formula instead.