A complete guide and tool for students computing sample sizes for quantitative research.
Use this for finite populations with a known total number of individuals.
Distribute your total sample proportionally across population subgroups (e.g., grade levels, departments, sections).
| Stratum | Sub-population (Ni) | Proportion (Ni / N) | Sample (ni) |
|---|
Everything a student needs to know before computing their sample — explained clearly.
The sample size is the number of individuals or units selected from a total population to participate in a study. Rather than surveying everyone (which is costly and time-consuming), researchers use a representative sample to draw conclusions about the whole population.
An undersized sample produces unreliable, misleading results. An oversized sample wastes time and resources. A properly computed sample size balances statistical rigor with practical feasibility.
Population (N): The entire group you want to study (e.g., all 800 students in a school).
Sample (n): The subset you actually survey (e.g., 267 students selected from those 800).
The margin of error (e) tells you how much your sample result might differ from the true population value. A 5% margin (e = 0.05) means your findings could vary by plus or minus 5%. A smaller margin requires a larger sample.
The two are directly linked — choose based on your study's required precision.
| Margin of Error (e) | Confidence Level | Common Usage | Sample Tendency |
|---|---|---|---|
| 0.01 (1%) | 99% | Medical / High-stakes research | Very large sample required |
| 0.02 (2%) | 98% | Policy research, Demographic studies | Large sample required |
| 0.05 (5%) | 95% | Social science, Thesis, Surveys | Moderate — most common |
| 0.10 (10%) | 90% | Exploratory or pilot studies | Smaller sample acceptable |
Every member of the population has an equal chance of being selected. Used when the population is homogeneous. Slovin's formula directly gives you n for this method.
The population is divided into subgroups (strata) such as year level, department, or gender. The total sample n is distributed proportionally so that each stratum is fairly represented.
Every k-th person from a list is selected, where k = N / n. For example, if N = 800 and n = 267, select every 3rd person from a numbered list of the population.
Respondents are chosen deliberately based on specific criteria relevant to the research. Common in qualitative research. Slovin's formula does NOT apply here.
Follow this walkthrough to understand exactly how the calculation is done by hand.
e² = 0.05 x 0.05 = 0.0025N x e² = 800 x 0.0025 = 2.01 + 2.0 = 3.0n = 800 / 3.0 = 266.67n = 267 respondents — Always round up to ensure sufficient sample coverage.Suppose your 800-person population is composed of 3 departments. You need to fairly distribute the 267 respondents.
Dept A: 300 / 800 = 0.375 Dept B: 250 / 800 = 0.3125 Dept C: 250 / 800 = 0.3125Dept A: 0.375 x 267 = 100.13 ≈ 101Dept B: 0.3125 x 267 = 83.44 ≈ 83Dept C: 0.3125 x 267 = 83.44 ≈ 83101 + 83 + 83 = 267 — Confirmed. Minor rounding adjustments are acceptable.Never round down your final sample size. A result of 266.2 becomes 267, not 266. Rounding down invalidates your margin of error.
The formula requires a decimal for e. Write 0.05, not 5. Using e = 5 instead of 0.05 will produce a wildly incorrect result.
Use the TOTAL accessible population, not an estimate or a subset. If your population is all enrolled students, count all of them as N.
After distributing proportionally, the sum of all strata samples must equal your total n. Always check this. Adjust the largest stratum by +1 or -1 if rounding causes a discrepancy.