The Slovin Formula Calculator helps researchers determine the minimum sample size from a population.
Enter the population size and desired margin of error to get the sample size. Includes a comparison table at various error levels and an explanation of when the Slovin formula is appropriate.
Calculator information
📋 How to use this calculator
- Enter the population size (N) for your study, e.g., total students, total employees, or total residents.
- Enter the desired margin of error (e) as a percentage (1%, 5%, or 10% are most common).
- Click Calculate to get the minimum representative sample size.
- Compare with the reference table showing sample sizes at different error levels.
- Round results up for safety (never round down).
- Tip: Slovin's formula suits homogeneous populations; for heterogeneous populations consider stratified random sampling.
🧮 Slovin's Formula (1960)
n = N / (1 + N x e²)
- n = minimum sample size
- N = population size
- e = margin of error as a decimal (e.g., 0.05 for 5%)
Slovin's formula assumes a 95% confidence level and a finite population. For very large populations (>100,000), consider Cochran's or Lemeshow's formula instead.
💡 Worked example: Determining a sample size of high school students
Given:- Student population (N): 1,200
- Margin of error (e): 5% = 0.05
Steps:- Compute e² = 0.05 x 0.05 = 0.0025.
- Compute denominator = 1 + 1,200 x 0.0025 = 1 + 3 = 4.
- n = 1,200 / 4 = 300.
- Round up: n = 300 students.
Result: Minimum sample size is 300 students out of 1,200 (about 25% of the population).
❓ Frequently asked questions
When is Slovin's formula appropriate?
Slovin's formula fits descriptive or correlational research with a finite, known population, a 95% confidence level, and a relatively homogeneous population. It is widely used in social science, management, and education thesis work. It is not suitable for highly heterogeneous populations or experimental research.
What margin of error should I use?
Generally 5% for academic research with high confidence, 10% for preliminary surveys, and 1% for high-quality census-grade studies. The smaller the margin of error, the larger the required sample. Federal statistical agencies typically use 1-3% margins for large national surveys, while public opinion polls use 3-5%.
What are the limitations of Slovin's formula?
Slovin's formula does not account for population proportions (p, q), confidence levels other than 95%, or population variance. For studies with complex proportion assumptions, Cochran's formula (n = z² x p x q / e²) or Lemeshow's formula is more accurate. Slovin is also less valid for N < 100 or for heterogeneous populations.
What if the population is very large or unknown?
For unknown populations, use Cochran's formula without the finite population correction: n = z² x p x q / e². With z = 1.96 (95% CI), p = q = 0.5, and e = 5%, the minimum sample is 385. For very large populations (>100,000), Slovin's formula returns a sample size similar to Cochran's.
Do I still need random sampling after using Slovin's formula?
Strongly recommended. After determining sample size with Slovin's formula, use a probability sampling technique (simple random, systematic, stratified, or cluster) to ensure representativeness. Non-probability sampling (purposive, convenience) is only valid for qualitative or exploratory research, not for statistical generalization.
📚 Sources & references
Last updated: May 11, 2026