Slovin's formula table
| Population N | e = 0.10 | e = 0.05 | e = 0.03 | e = 0.01 |
|---|---|---|---|---|
| 100 | 50 | 80 | 92 | 100 |
| 200 | 67 | 134 | 170 | 197 |
| 500 | 84 | 223 | 345 | 477 |
| 1,000 | 91 | 286 | 527 | 910 |
| 2,000 | 96 | 334 | 715 | 1,667 |
| 5,000 | 99 | 371 | 910 | 3,334 |
| 10,000 | 100 | 385 | 1,000 | 5,000 |
| 100,000 | 100 | 399 | 1,099 | 9,091 |
The assumptions hidden inside Slovin
Slovin's formula is Cochran's formula with the finite population correction, simplified by fixing z² × p(1 − p) at 1. With z = 1.96 and p = 0.5 that product is 0.96, close enough to 1. So Slovin silently assumes roughly 95% confidence and maximum variability, and it only applies to estimating a proportion by simple random sampling.
That is why many thesis panels now ask for Cochran instead: it gives virtually the same number but shows the assumptions. If your study compares groups or tests a relationship, neither formula is right; use a power analysis.
How to cite it defensibly
If your institution requires Slovin, report it alongside the assumptions: “Sample size was computed with Slovin's formula (equivalent to Yamane, 1967) with a 5% margin of error, which assumes 95% confidence and p = .5.” Better still, report the Cochran figure next to it.
Frequently asked questions
What is Slovin's formula?
Slovin's formula is n = N / (1 + N·e²), where N is the population size and e the margin of error. It is widely taught in the Philippines and some other countries as a quick way to size a survey.
How do I use Slovin's formula?
Square the margin of error, multiply by the population, add 1, and divide the population by the result. For N = 1,000 and e = 0.05: 1,000 / (1 + 1,000 × 0.0025) = 1,000 / 3.5 = 285.7, so 286.
Who invented Slovin's formula?
Its origin is unclear. No verifiable publication by a statistician named Slovin has been found, and it does not appear in standard sampling textbooks such as Cochran (1977) or Lohr (2019). It is algebraically the Yamane (1967) formula.
Why do reviewers criticise Slovin's formula?
It fixes the confidence level at about 95% and the proportion at 0.5 without saying so, cannot be used for estimating means, and says nothing about power for hypothesis tests. Cochran’s formula with a finite population correction gives the same answer under those assumptions while stating them openly.