Taro Yamane Sample Size Calculator
Choose your margin of error, see every step of the substitution, and copy a paragraph for your methodology chapter.
1 Set your parameters
* You need an exact population count. If it is unknown, use Cochran’s formula (about 385 at 95% confidence) instead.
Margin of error (e)
💡 Which margin of error?
5% is the usual choice for theses and survey research (it corresponds to 95% confidence). The smaller e is, the more responses you need — at the same population, e = 1% needs several times more than e = 5%. Tap the options to compare.
Minimum sample size
Population of 1,000 at a 5% margin of error
Step-by-step substitution
Text for your report (Chapter 3)
ⓘ This free tool helps with a first calculation. Khontob does not guarantee the results or any outcome of using them. Before using them in your research, please check them against the original software or textbook and with your advisor.
Taro Yamane sample size table
Sample size from n = N / (1 + Ne²), rounded to the nearest whole number as in the commonly circulated Yamane tables.
| Population (N) | e = 3% | e = 5% | e = 10% |
|---|---|---|---|
| 100 | 92 | 80 | 50 |
| 200 | 169 | 133 | 67 |
| 300 | 236 | 171 | 75 |
| 400 | 294 | 200 | 80 |
| 500 | 345 | 222 | 83 |
| 1,000 | 526 | 286 | 91 |
| 2,000 | 714 | 333 | 95 |
| 3,000 | 811 | 353 | 97 |
| 5,000 | 909 | 370 | 98 |
| 10,000 | 1,000 | 385 | 99 |
| 50,000 | 1,087 | 397 | 100 |
| 100,000 | 1,099 | 398 | 100 |
How to read it: a population of 1,000 at a 5% margin of error needs 286 respondents. For other populations, use the calculator above.
Understanding the Taro Yamane formula
n = required sample size
N = total population size
e = acceptable margin of error (e.g. 0.05)
1. You need the exact population size
The formula only works when N is known, such as the number of employees in a company, students in a faculty or members of a community. If your population is something you cannot count, like “people who shop online”, use Cochran's formula for an unknown population instead.
2. How to round the result
This calculator rounds to the nearest whole number, following the ready-made Yamane tables commonly used in theses. For example, N = 500 at e = 5% gives 222.22, rounded to 222. Some supervisors prefer always rounding up (to 223), which is also fine — the unrounded value is shown in the step-by-step working, so follow whatever your supervisor asks for.
3. Yamane or Slovin?
The same expression, n = N / (1 + Ne²), is often called Slovin's formula in the Philippines and elsewhere. In published methodology sections it is usually cited as Yamane, whose statistics textbook presents it, so this page follows that citation.
! Good to know
Taro Yamane only takes population size into account, not statistical power or the number of variables in your model. If you plan a multiple regression or an SEM, your supervisor may ask you to confirm the sample with a G*Power calculation as well.
Source: Yamane, T. (1973). Statistics: An Introductory Analysis (3rd ed.). New York: Harper & Row.
Frequently asked questions
How is the Taro Yamane formula calculated?
The formula is n = N / (1 + Ne²), where n is the sample size, N is the population size and e is the margin of error. For example, a population of 1,000 at a 5% margin of error (e = 0.05) gives n = 1000 / (1 + 1000 × 0.0025) = 1000 / 3.5 = 285.71, which rounds to 286.
What margin of error should I use?
Most theses and survey studies use a 5% margin of error (e = 0.05), which corresponds to a 95% confidence level. Use 1% only if you need very high precision and can collect a much larger sample; 10% is sometimes used for pilot or exploratory surveys with limited resources. Always confirm the value with your supervisor.
Is the Yamane formula still accepted?
Yes, it is widely used in survey research when the population size is known exactly. Its limitation is that it only considers population size, not statistical power or effect size. If your analysis is a multiple regression or an SEM, supervisors often ask for a G*Power calculation instead or in addition.
What if I don't know the exact population size?
The Yamane formula cannot be used without N, because the population size is part of the equation. Use Cochran's formula for an unknown population instead, which gives about 385 respondents at 95% confidence, or the value of 384 from the Krejcie & Morgan table.
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