RESEARCH STATISTICS GUIDE
Slovin's formula for sample size, with worked examples
Slovin's formula (also cited as Taro Yamane's formula) estimates the minimum sample needed from a known population for a chosen margin of error. It is one of the most used sample size formulas in thesis research.Explore research statistics & data analysis →FORMULA OR CORE IDEA
n = N ÷ (1 + N·e²)WORKED EXAMPLE
A school has 2,500 students and you accept a 5% margin of error. n = 2,500 ÷ (1 + 2,500 × 0.05²) = 2,500 ÷ 7.25 = 344.83, so you survey 345 students.QUICK REFERENCE
Slovin sample sizes at a glance
Minimum sample sizes from n = N ÷ (1 + N·e²), rounded up.| Population N | e = 5% | e = 10% |
|---|---|---|
| 100 | 80 | 50 |
| 500 | 223 | 84 |
| 1,000 | 286 | 91 |
| 5,000 | 371 | 99 |
| 10,000 | 385 | 100 |
| 100,000 | 399 | 100 |
STEP BY STEP
Find the population size N
N is the total number of people who meet your inclusion criteria, such as all enrolled nursing students or all registered SMEs in a district. Cite where the number came from.
Choose the margin of error e
Write e as a decimal: 5% becomes 0.05. A 5% margin is standard; 10% is sometimes accepted for small or exploratory studies; 3% needs a much larger sample.
Square e and multiply by N
With N = 2,500 and e = 0.05, N·e² = 2,500 × 0.0025 = 6.25.
Add 1 and divide
n = 2,500 ÷ (1 + 6.25) = 2,500 ÷ 7.25 = 344.83.
Round up
Always round up to the next whole respondent, giving 345. Rounding down would leave you below the minimum the formula requires.
Adjust for non-response
If you expect only 80% of invited people to respond, invite 345 ÷ 0.80 = 432 people so that you still reach the minimum.
COMMON QUESTIONS
Frequently asked questions
Is Slovin's formula the same as Yamane's formula?
Yes. Both are n = N ÷ (1 + N·e²). Taro Yamane published it in 1967, and the name 'Slovin' is widely used in Philippine and Southeast Asian research. Cite the name your institution uses.
What are the limitations of Slovin's formula?
It does not let you choose a confidence level or expected proportion, and it assumes simple random sampling. Critics argue it is often used without justification, so Cochran's formula or a power analysis can be more defensible.
How do I write Slovin's formula in my methodology?
For example: 'Using Slovin's formula with a population of 2,500 and a 5% margin of error, the minimum sample size was 345 respondents.' Include the formula and the substituted values.