Enter the population size, confidence level and margin of error to get the sample size from Cochran's formula and the Krejcie & Morgan table, plus a methodology paragraph you can copy. Everything is calculated in your browser.
Cochran's formula is the most widely used way to set the sample size in questionnaire research. For a known population, the form found in most research-methods textbooks is:
n = N·z²·p·q / (N·d² + z²·p·q)
For an unknown or very large population the formula simplifies to n = z²·p·q / d², which gives 384.16 with the usual values and is rounded up to 385. Sample sizes are always rounded up.
The Krejcie & Morgan (1970) table is built from a formula that uses the chi-square value (3.841 for 95%) and gives almost the same number as Cochran for a known population. This tool shows both side by side, so you can report whichever your supervisor prefers. Some examples at 95% confidence and a 0.05 margin of error:
Some questionnaires never come back or are incomplete. If you enter an expected non-response rate, the tool calculates how many to distribute: sample size ÷ (1 − non-response rate). For a sample of 278 with 10% non-response, you need 309 questionnaires.
Put the responses in Excel or a Google Forms export (first row item names, one respondent per row). If you would rather not wrestle with SPSS, Kajino's questionnaire statistical analysis prepares Cronbach's alpha, hypothesis tests, APA tables and a written interpretation in one go.
At 95% confidence, a 0.05 margin of error and p = 0.5, Cochran's formula gives 278 and the Krejcie & Morgan table also gives 278.
Leave the population field empty; the sample size is calculated with Cochran's formula for an infinite population, which is 385 with the usual values.
The Morgan table comes from a chi-square based formula and gives almost the same result as Cochran for a known population, usually within one or two respondents.
When the proportion in the population is unknown, p = 0.5 gives the largest sample size, so it is the most conservative choice.
No. The calculation runs entirely in your browser and nothing is sent to the server.