Family relationship

The family relationship between two individuals a and b, where G_a and G_b respectively are the number of generations between each individual and their nearest common ancestor, can be calculated by the following:

x = min (G_a,G_b)

y = |G_a-G_b|

• If x=0 and y=0 then they are the same person.
• If x=0 and y=1 then they are parent and child.
• If x=0 and y=2 then they are grandparent and grandchild.
• If x=0 and y>2 then they are great ... great-grandparent and great ... great-grandchild, with y−2 greats.

• If x=1 and y=0 then they are siblings (brothers or sisters).
• If x=1 and y=1 then they are uncle/aunt and nephew/niece.
• If x=1 and y>1 then they are great ... great uncle/aunt and great ... great nephew/niece, with y−1 greats.

• If x>1 and y=0 then they are x−1^th cousins.
• If x>1 and y>0 then they are x−1^th cousins y times removed.

So two people sharing a pair of grandparents have x=2 and y=0 and are described as being first cousins.

If x>0 and they only share one nearest common ancestor rather than two, then the word "half" is sometimes added at the beginning of the relationship.