Krejcie & Morgan Sample Size Calculator

Determine the statistically appropriate sample size for your research study based on population size, confidence, and margin of error.

Configure Parameters

Target Population Size ($N$)

Total number of people in your target population.

Confidence Level

How sure you need to be that the sample reflects the population.

Margin of Error ($d$) 5%

The range of deviation allowed in your research results.

Target Response Proportion ($P$) 50%

Proportion expected to answer in a certain way. 50% gives the safest (maximum) sample size.

Required Sample Size

Minimum respondents needed for representativeness.

Sample Size Growth Curve

Calculation Step Breakdown

Pop. Size ($N$)

10,000

Chi-Square ($\chi^2$)

3.841

Margin ($d$)

Proportion ($P$)

50%

The Krejcie & Morgan Method

In 1970, statisticians **Daryle W. Krejcie** and **Evelle J. Morgan** published a paper titled "Determining Sample Size for Research Activities" in the journal Educational and Psychological Measurement. They calculated a formula to help researchers easily calculate representative sample sizes without complex manual probability derivations.

The formula is based on Chi-Square statistics assuming a target proportion of 0.50 (which yields the maximum sample size, representing the most conservative estimate).

The Formula Explained:

s = [ χ² * N * P * (1 - P) ] / [ d² * (N - 1) + χ² * P * (1 - P) ]

s = Required sample size

χ² = Chi-Square value for degree of freedom = 1 (determined by confidence level: 95% = 3.841, 99% = 6.635)

N = Target population size

P = Target response proportion (assumed to be 0.50 / 50% for maximum variance)

d = Degree of accuracy expressed as a decimal (Margin of Error, e.g. 5% = 0.05)

Why is the formula popular?

Prior to Krejcie & Morgan, researchers had to perform manual calculations or rely on charts. The creators calculated a reference table outlining representative samples for populations ranging from 10 to 1,000,000, which has since become an industry standard in sociological, academic, and business research.

Standard K&M Reference Table

Reference numbers at 95% Confidence Level and 5% Margin of Error ($P=50\%$):

Population ($N$)	Sample Size ($s$)	Population ($N$)	Sample Size ($s$)
10	10	1,000	278
50	44	5,000	357
100	80	10,000	370
250	152	50,000	381
500	217	100,000+	384

Note: As population approaches infinity, sample size stabilizes and caps out around 384 at 95% confidence level.