Catherine, Duchess of Cambridge is your 10th cousin thrice removed.
your father → Rufus Samuel Nichols
his father → Tressie (King) Nichols
his mother → Michael O. King
her father → Margaret (Wright) King
his mother → James GRANT Wright
her father → William Wright
his father → John Wright Jr
his father → Dorothy Wright
his mother → Dorothy Awbrey
her mother → Thomas Meador, the "Orphan"
her father → Thomas Meadors "The Elder"
his father → Ambrose Meador
his father → Rev. John Meadows
his brother → Philip Meadows
his son → Sarah Martineau
his daughter → Thomas Martineau
her son → Elizabeth Greenhow
his daughter → Frances Elizabeth Lupton
her daughter → Francis Martineau Lupton
her son → Olive Christiana Middleton
his daughter → Peter Francis Middleton
her son → Michael Middleton
his son → Catherine, Duchess of Cambridge