SAMPLE SIZE TABLE
Slovin's formula sample size table for populations from 50 to 100,000
Look up the minimum sample size for your population without calculating: find your population size (N) in the table and read across to your margin of error. Every value is rounded up, as thesis panels expect.Explore research statistics & data analysis →FORMULA OR CORE IDEA
n = N ÷ (1 + N × e²)WORKED EXAMPLE
For a population of 1,000 at a 5% margin of error: 1,000 ÷ (1 + 1,000 × 0.0025) = 285.71, rounded up to 286 respondents.QUICK REFERENCE
Slovin's formula sample size table
Minimum sample size n = N ÷ (1 + Ne²), rounded up. The last column shows Cochran's formula at 95% confidence, p = 0.5 and a 5% margin of error with the finite population correction, for comparison.| Population (N) | e = 1% | e = 3% | e = 5% | e = 10% | Cochran 95%, 5% |
|---|---|---|---|---|---|
| 50 | 50 | 48 | 45 | 34 | 45 |
| 100 | 100 | 92 | 80 | 50 | 80 |
| 150 | 148 | 133 | 110 | 60 | 109 |
| 200 | 197 | 170 | 134 | 67 | 132 |
| 250 | 244 | 205 | 154 | 72 | 152 |
| 300 | 292 | 237 | 172 | 75 | 169 |
| 400 | 385 | 295 | 200 | 80 | 197 |
| 500 | 477 | 345 | 223 | 84 | 218 |
| 600 | 567 | 390 | 240 | 86 | 235 |
| 700 | 655 | 430 | 255 | 88 | 249 |
| 800 | 741 | 466 | 267 | 89 | 260 |
| 900 | 826 | 498 | 277 | 90 | 270 |
| 1,000 | 910 | 527 | 286 | 91 | 278 |
| 1,500 | 1,305 | 639 | 316 | 94 | 306 |
| 2,000 | 1,667 | 715 | 334 | 96 | 323 |
| 2,500 | 2,000 | 770 | 345 | 97 | 334 |
| 3,000 | 2,308 | 811 | 353 | 97 | 341 |
| 4,000 | 2,858 | 870 | 364 | 98 | 351 |
| 5,000 | 3,334 | 910 | 371 | 99 | 357 |
| 10,000 | 5,000 | 1,000 | 385 | 100 | 370 |
| 20,000 | 6,667 | 1,053 | 393 | 100 | 377 |
| 50,000 | 8,334 | 1,087 | 397 | 100 | 382 |
| 100,000 | 9,091 | 1,099 | 399 | 100 | 383 |
STEP BY STEP
Find your population size
Use the total number of people who could be in your study, such as all Grade 11 students in the school. If your exact N is not listed, use the next larger row or the Sample Size Calculator for an exact answer.
Choose the margin of error
Most undergraduate and graduate theses use 5%. Use 3% when you need more precision and can survey more people, and 10% only for small exploratory studies your adviser approves.
Read the sample size
The value where your row and column meet is the minimum number of completed responses. Plan to distribute more questionnaires to allow for non-response.
Adjust for non-response
Divide the sample size by your expected response rate. If you need 286 responses and expect 80% to reply, distribute 286 ÷ 0.80 = 358 questionnaires.
Cite the formula in Chapter 3
Write the formula, the values of N and e, and the result, for example: “Using Slovin's formula with N = 1,000 and e = 0.05, the minimum sample size was 286.”
COMMON QUESTIONS
Frequently asked questions
What sample size do I need for a population of 1,000?
With Slovin's formula you need 286 respondents at a 5% margin of error, 527 at 3% and 91 at 10%. Cochran's formula at 95% confidence and a 5% margin gives 278.
What is the sample size for a population of 500 using Slovin's formula?
At a 5% margin of error the sample size is 500 ÷ (1 + 500 × 0.0025) = 222.2, rounded up to 223 respondents.
Why does the sample size stop growing for large populations?
As N gets very large, Slovin's formula approaches 1 ÷ e². At a 5% margin that limit is 400, so even a population of 100,000 needs only 399 respondents.
Should I round the sample size up or down?
Always round up. Rounding down would give a margin of error slightly larger than the one you chose.
Is Slovin's formula accepted for a thesis?
It is widely used in theses in the Philippines and parts of Asia, but some reviewers prefer Cochran's formula or a power analysis because Slovin's formula does not include a confidence level. Check with your adviser and cite the formula you used.