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Permeability has dimensions of area: square meters, square centimeters or square feet.
Permeability can also be measured in darcy. One darcy (or 1 D) is equivalent to the permeability of a medium, through which flow velocity is equal 1 cm/s with a pressure difference of 1 atm over 1 cm and a liquid viscosity equal to 1 centipoise (cP).
Tab "Permeability" of the dialog window "Unit converter (part 1)"
Conversion table

m2 
cm2 
μm2 
ft2 
darcy 
millidarcy 
m2 
1 
104 
1012 
10.764 
1.013.1012 
1.013.1015 
cm2 
104 
1 
108 
1.076.103 
1.013.108 
1.013.1011 
μm2 
1012 
108 
1 
1.076.1011 
1.013 
1013.25 
ft2 
9.29.102 
9.29.102 
9.29.1010 
1 
9.41.1010 
9.41.1013 
darcy 
9.87.1013 
9.87.109 
0.987 
1.06.1011 
1 
1000 
millidarcy 
9.87.1016 
9.87.1012 
9.87.104 
1.06.1014 
0.001 
1 