The most-used formula in student research
Slovin's formula sizes a survey sample from the population alone: n = N ÷ (1 + Ne²), with e the margin of error you will tolerate. Its footprint in theses and market studies across Asia and beyond is enormous, mostly because the inputs are two numbers anyone can state: how many people exist, and how precise the estimate must be. Enter N = 2,000 and e = 0.05 and it returns 334 respondents; tighten e to 0.03 and it asks for 715.
Rewrite it as 1/n = 1/N + e² and the structure shows: Slovin's is Cochran's formula at a fixed z of 2 (roughly 95.45% confidence) and the worst-case proportion p = 0.5, with the finite population correction folded in. Check: Cochran at z = 2, p = 0.5, e = 0.05 gives n0 = 400, corrected for N = 2,000 to 400 ÷ (1 + 399/2000) ≈ 333.5, which rounds up to the same 334. The two formulas are one formula wearing two names, which the side-by-side calculators on this site let you verify.
The honest criticism
No confidence level and no proportion appear in Slovin's formula, so two surveys with different confidence needs get the same n, and the user is never asked to choose. That silence is why methodology texts treat it cautiously: it hard-codes roughly 95% confidence and maximum variance without saying so. Used knowingly, it is a serviceable default for simple random sampling of a proportion. Used as a magic incantation ("Slovin said 334"), it hides the assumptions a reviewer will ask about. State the e you chose and the simple-random-sampling assumption next to the number, and the formula does its job.
Plugging the margin in as a percentage (e = 5 instead of 0.05). The formula expects the decimal: e = 5 would divide the population by 1 + 25N and return something near zero. If your sample size comes out under 10, check the units first.
Frequently asked questions
What is Yamane's formula, and is it the same?
Identical: n = N/(1 + Ne^2) appears in Taro Yamane's 1967 statistics text, and the two names denote the same equation. The attribution history is murky; what matters is the formula's assumptions, not its name.
What confidence level does Slovin's formula use?
It does not state one. Algebra shows it matches Cochran's formula at z = 2 (about 95.45% confidence) with the worst-case proportion p = 0.5.
Why does the sample stop growing as N gets huge?
Precision needs cap out: as N grows, n approaches 1/e^2 (400 at e = 0.05). Past a few thousand population, adding people adds almost no information per head.