--- title: "Sample Size Calculator: Slovin's and Cochran's Formula" description: "Free sample size calculator for theses and surveys. Enter the population, margin of error and confidence level to get Slovin's and Cochran's sample size." canonical: https://formswrite.com/tools/sample-size-calculator last-updated: 2026-10-15 --- Free Sample Size Calculator # Sample Size Calculator for Your Thesis Find how many respondents you need with Slovin's formula or Cochran's formula. Enter the population, the margin of error and the confidence level; the worked formula shows under the result, ready for Chapter 3. Population size (N) Everyone you could survey, for example all 1,200 Grade 11 students. Leave it empty for a very large population. Margin of error (%) 5% is the usual choice for a thesis. Smaller margins need more respondents. Confidence level 90%95%99% Used by Cochran's formula. Slovin's formula assumes 95%. Slovin's formula300respondents Cochran (corrected)292respondents at 95% confidence How it was computed Slovin: n = N / (1 + N·e²) = 1,200 / (1 + 1,200 × 0.05²) = 300 Cochran: n₀ = z²·p(1−p) / e² = 1.96² × 0.5 × 0.5 / 0.05² = 385 Corrected: n = n₀ / (1 + (n₀ − 1) / N) = 292 Results are rounded up, because you cannot survey part of a person. Plan for a few extra in case some answers come back incomplete. ## How to Use the Sample Size Calculator Type the population size, the number of people your study is about, such as every Grade 11 student in the school or every registered member of a cooperative. Keep the margin of error at 5% unless your adviser says otherwise, and pick the confidence level. The calculator returns Slovin's sample right away and Cochran's sample with the finite population correction, each with the formula filled in so you can copy it into your methodology. ## Worked Example A researcher studies the study habits of 1,200 senior high school students with a 5% margin of error. Slovin's formula gives n = 1,200 / (1 + 1,200 × 0.05²) = 1,200 / 4 = 300 respondents. Cochran's formula at 95% confidence starts from n₀ = 1.96² × 0.5 × 0.5 / 0.05² = 384.16, rounded up to 385, and the finite population correction brings it to 385 / (1 + 384 / 1,200) ≈ 292 respondents. Either number is defensible; say which formula you used and why. ## Slovin or Cochran: Which One to Report Slovin's formula is simple and widely accepted in local theses, but it fixes the confidence level and assumes the most varied population. Cochran's formula states the confidence level and the expected proportion openly, which reviewers in journals tend to prefer. When the sample is set, draft the instrument from a [ready research questionnaire](/research-questionnaire), check its reliability with the [Cronbach's alpha calculator](/tools/cronbach-alpha-calculator) after the pilot test, and interpret the Likert results with the [weighted mean calculator](/tools/weighted-mean-calculator). ## More free tools for your thesis From the sample to the reliability test to the interpretation of the results. - [Cronbach's Alpha CalculatorCheck the reliability of a Likert scale from pasted scores or a CSV.](/tools/cronbach-alpha-calculator) - [Weighted Mean CalculatorLikert counts to weighted mean, SD and verbal interpretation.](/tools/weighted-mean-calculator) - [Research QuestionnairesReady thesis questionnaires by topic, with Likert scales and interpretation bands.](/research-questionnaire) - [Questionnaire MakerTurn your list of questions into a survey you can share.](/tools/questionnaire-maker) - [Field Research SurveysCollect answers on phones, offline, with SPSS and Excel export.](/solutions/field-research) Kiki: Round up, always. Half a respondent never answers the survey. ## Frequently Asked Questions What is Slovin's formula? Slovin's formula, n = N / (1 + N e²), gives a sample size from the population size N and the margin of error e. It is common in Philippine and Southeast Asian theses because it needs nothing but N and e. With 1,200 students and a 5% margin, n = 1,200 / (1 + 1,200 × 0.0025) = 300. When should I use Cochran's formula instead of Slovin's? Use Cochran's formula when your adviser asks for a confidence level, or when the population is very large or unknown. It starts from n₀ = z² p (1 − p) / e² (385 at 95% confidence and a 5% margin) and, when you know N, applies the finite population correction n = n₀ / (1 + (n₀ − 1) / N). What margin of error should I use for a thesis? Most undergraduate theses use 5%. A 10% margin is sometimes accepted for small pilot studies, and 3% or lower for studies that need precise estimates. A smaller margin always needs more respondents, so check what your adviser and the institution expect. Why is the result always rounded up? A sample size is a count of people. Rounding down would leave the margin of error slightly above the one you chose, so the calculator rounds every result up to the next whole respondent. What if I do not know the population size? Leave the population empty. Slovin's formula needs N, so it shows no result, but Cochran's formula still works: for a very large population, 385 respondents give a 5% margin at 95% confidence. Is this sample size calculator free? Yes. It runs in your browser, needs no sign-up and keeps nothing you type. When the sample is set, build the questionnaire in Formswrite and collect the answers on phones. ## Build your questionnaire and get Chapter 4 automatically Make the survey in Formswrite, share one link and collect answers on phones. The Thesis kit then writes your frequency tables, weighted means, Cronbach's alpha and tests of relationship, plus a Chapter 4 draft in Word. - Free to start - SPSS and Excel export - Chapter 4 in Word [Browse research questionnaires](/research-questionnaire)[Create a free account](/accounts/signup?source=sample-size-calculator)