Dictionary:Archie’s formulas

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(ar’ chēz) Empirical relationships between the formation factor F (sometimes FR), porosity φ, water saturation Sw, and resistivities R. In clean granular rocks,

FIG. A-17. Archie’s formula for different lithologies. [1]


  • a = proportionality constant varying from 0.6 to 1.5,
  • m = cementation factor that varies between 1.3 and 3,
  • n = saturation exponent, often assumed to be 2,
  • Ro = resistivity of the formation when 100% saturated with formation water,
  • Rw = resistivity of the formation water,
  • Rt = true resistivity of the formation.

Archie’s law assumes that m=2 and a=1.
The Humble formula assumes that m=2.15 and a=0.65.
Values of a and m for different lithologies are shown in Figure A-17.
Named for Gus E. Archie, American engineer and geologist.



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  1. Keller, G. R., 1987, Rock and mineral properties: in Nabighian, M. N., Ed., Electromagnetic methods in applied geophysics—Theory, 1: Soc. Expl. Geophys., 13–52. http://dx.doi.org/10.1190/1.9781560802631.ch2
  2. Whaley, J., 2017, Oil in the Heart of South America, https://www.geoexpro.com/articles/2017/10/oil-in-the-heart-of-south-america], accessed November 15, 2021.
  3. Wiens, F., 1995, Phanerozoic Tectonics and Sedimentation of The Chaco Basin, Paraguay. Its Hydrocarbon Potential: Geoconsultores, 2-27, accessed November 15, 2021; https://www.researchgate.net/publication/281348744_Phanerozoic_tectonics_and_sedimentation_in_the_Chaco_Basin_of_Paraguay_with_comments_on_hydrocarbon_potential
  4. Alfredo, Carlos, and Clebsch Kuhn. “The Geological Evolution of the Paraguayan Chaco.” TTU DSpace Home. Texas Tech University, August 1, 1991. https://ttu-ir.tdl.org/handle/2346/9214?show=full.