The authors agree that the surname points back to the Latin term quadrus or quadrum, which designated a plot of land of roughly square shape, linked to the system of Roman centuriation and equivalent to about 2,500 square metres. E. Rossoni notes that the surname could have originated as a nickname identifying small owners of that type of plot, or else derive from place names containing the term "Quadro," such as Quadro di Todi, in the Perugia area, or Quadro di Riano, in the Rome area.

R. Brondolo adds two alternative etymologies: one that traces it back to advocator, in the form Avogadri, with the meaning of "lawyers"; and another that links it to aquadri, a Lombard term that designated "forest wardens."

As to the geographic distribution, Rossoni documents a presence of the surname in areas of Milan, Bergamo, Brescia, Vicenza, Bologna, Florence and Rome. The variant Quadrini is proper to central Italy, with nuclei in the Piceno and the Terni, Rome and Frosinone areas. Quadrino is concentrated in lower Lazio, especially in Fondi, Latina area. Brondolo, for his part, places the surname in Lombardy and southern Piedmont.