Sample Size Calculator for Thesis

How many respondents does your survey need? This calculator applies the two formulas most often cited in theses and dissertations, Cochran’s formula (with finite population correction) and Taro Yamane’s formula, shows the full working, and gives you a sentence you can put straight into your methodology chapter.

How to use this calculator

  1. Enter your population size N (for example, 1,000 students in a university). Leave it blank if the population is very large or unknown.
  2. Choose a confidence level (95% is standard).
  3. Enter the margin of error you can accept (0.05 = ±5%).
  4. Keep the expected proportion at 0.5 unless an earlier study suggests a different value. 0.5 gives the largest, safest sample.
  5. Click Calculate and add 10–20% to the result to allow for non-response.

Formula

Cochran (infinite population):  n₀ = z² · p(1 − p) / e²
Finite population correction:    n  = n₀ / (1 + (n₀ − 1) / N)
Yamane (1967):                   n  = N / (1 + N·e²)

z = z-score for the confidence level (1.96 for 95%)
p = expected proportion, e = margin of error, N = population size

Step-by-step example

  1. Population N = 1,000, 95% confidence, margin of error 5%, p = 0.5.
  2. Cochran: n₀ = 1.96² × 0.5 × 0.5 / 0.05² = 384.15 → 385.
  3. Finite correction: n = 384.15 / (1 + 383.15/1000) = 277.73 → 278.
  4. Yamane: n = 1000 / (1 + 1000 × 0.05²) = 285.71 → 286.

How to interpret the results

The result is the minimum number of completed responses you need. Always round up. If you expect only 70% of people to respond, divide the result by 0.7 to find how many questionnaires to distribute. Cochran’s formula with the finite population correction is the more flexible method (it lets you change confidence level and proportion); Yamane’s formula assumes 95% confidence and p = 0.5 and is popular in social science theses because it is simple to report.

How to report it in APA 7 style

The required sample size was calculated using Cochran’s (1977) formula with a finite population correction for a population of 1,000, assuming a 95% confidence level, a 5% margin of error, and an estimated proportion of .50. The minimum required sample size was 278.

Statistical symbols (t, F, p, r, M, SD, N, d) should be italicised in your thesis.

Assumptions

  • Participants are selected by probability (random) sampling. The formulas do not justify convenience samples.
  • The main outcome is a proportion or percentage (survey research).
  • For comparing groups or testing a hypothesis, use a power analysis instead.

How to do it in SPSS, R or Excel

Cite Cochran, W. G. (1977). Sampling techniques (3rd ed.). Wiley, or Yamane, T. (1967). Statistics: An introductory analysis (2nd ed.). Harper & Row. Many supervisors also accept the Krejcie and Morgan (1970) table, which gives the same values as Cochran’s formula with finite correction.

Roman Urdu mein khulasa

Sample size ka matlab hai ke aap ko kitne logon se questionnaire fill karwana hai. Agar population maloom hai (jaise university ke 1000 students) to N likhein, warna khali chhor dein. 95% confidence aur 5% margin of error sab se aam choice hai. Jo number aaye us se 10–20% zyada forms distribute karein kyun ke kuch log jawab nahi dete. Thesis mein formula ka naam (Cochran ya Yamane) aur reference zaroor likhein.

Frequently asked questions

Which is better, Cochran or Yamane?

Both are accepted. Cochran’s formula is more flexible because you can change the confidence level and expected proportion; Yamane’s is simpler and assumes 95% confidence and p = .5. Use whichever your supervisor or field prefers and cite it.

What sample size do I need if I don’t know the population size?

Leave N blank. With 95% confidence, a 5% margin of error and p = .5, Cochran’s formula gives 385 respondents.

Is Krejcie and Morgan’s table the same as this calculator?

The Krejcie and Morgan (1970) table is based on the same chi-square approach and gives almost identical numbers to Cochran’s formula with finite population correction at 95% confidence and a 5% margin of error.

Should I add extra respondents for non-response?

Yes. Increase the sample by your expected non-response rate. For example, if you expect a 20% non-response rate, distribute n / 0.8 questionnaires.

Can I use this for an experiment comparing two groups?

No. For experiments or group comparisons, use a power analysis, which bases the sample size on the expected effect size.

What margin of error should I use?

5% (0.05) is the most common choice in thesis research. A 3% margin gives more precise estimates but requires a much larger sample.

Related calculators

Cite this calculator

If ScholarCalc helped your analysis, you can cite it in APA 7 format:

ScholarCalc. (2026). Sample Size Calculator for Thesis [Web application]. https://scholarcalc.com/sample-size-calculator/

Written and maintained by the ScholarCalc team. Last reviewed: November 2026.

Accuracy: results are computed in your browser and were validated against Python scipy, statsmodels and pingouin on test datasets. See Methodology and accuracy.