Morgan Calculator
Access specialized Morgan calculator. Built for accuracy, speed, and mobile responsiveness.
Krejcie & Morgan Calculator
Determine the representative sample size ($s$) required for your research study based on population size ($N$). Computes automatically with standard confidence levels and margins of error.
Centimorgan (cM) Calculator
Input shared DNA centimorgans (cM) or share percentages to calculate potential family relationships and probabilities. Perfect for genetic genealogists mapping ancestor lineages.
De Morgan's Laws Calculator
Simplify boolean logic equations using De Morgan's Laws. Automatically generates mathematical step-by-step transformations and full digital truth tables for variables A and B.
Understanding the Three Pillars of "Morgan Calculator"
The term "Morgan Calculator" spans three completely independent academic and scientific fields: statistical research, genetic genealogy, and digital computing. Below, we break down what each tool represents, how they are formulated, and how they assist professionals and students daily.
1. Krejcie & Morgan Formula
Developed in 1970 by Daryle W. Krejcie and Evelle J. Morgan, this formula simplified sample size determination for research models. It ensures that the selected subset of a target population represents the whole accurately within standard confidence intervals.
2. Centimorgan (cM) DNA
Named after American geneticist Thomas Hunt Morgan, a centimorgan is a unit measuring genetic linkage. In genetic ancestry, it quantifies how much DNA segments two individuals share. The higher the shared cMs, the closer the family relation is.
- • ~3400 cM: Parent / Child
- • ~1750 cM: Grandparent / Aunt / Uncle
- • ~875 cM: 1st Cousin
3. De Morgan's Logic
Formulated by British mathematician Augustus De Morgan, these laws form the backbone of boolean algebra and mathematical set theory. They demonstrate how to negate combined statements in logic circuits and program code.
NOT (A AND B) ≡ (NOT A) OR (NOT B)
NOT (A OR B) ≡ (NOT A) AND (NOT B)
Frequently Asked Questions
What is the Krejcie & Morgan sample size calculator used for?
It is used by researchers to determine the minimum number of respondents required for a survey to accurately reflect the views of a larger population. It calculates this using a chi-square distribution value based on a 95% or 99% confidence level.
How accurate is the centimorgan (cM) relationship estimation?
The estimation utilizes peer-collected probability tables showing genetic ranges. While highly indicative for close relatives (like first and second cousins), distant relationships are subject to natural recombinational variance.
Are De Morgan's laws useful in coding?
Yes. Programmers use De Morgan's laws to simplify complex logical conditions in `if` statements, making code cleaner to read and more efficient to execute by compilers.