Goldman–Hodgkin–Katz Equation Calculator

How it works

V_m = (RT/F) · ln[(P_K[K]ₒ + P_Na[Na]ₒ + P_Cl[Cl]ᵢ) ÷ (P_K[K]ᵢ + P_Na[Na]ᵢ + P_Cl[Cl]ₒ)]

The Nernst equation gives the equilibrium potential of one ion; the Goldman–Hodgkin–Katz equation weights every permeant ion by how easily it crosses the membrane. At rest potassium channels dominate, so the membrane sits near E_K but is pulled positive by the small sodium leak. During an action potential P_Na rises hundreds of fold and the potential swings toward E_Na — the last row shows that shift. Chloride enters with inside and outside swapped because it is an anion.

Worked example

Typical mammalian neuron (K 5/140, Na 145/15, Cl 110/10 mM; P 1 : 0.04 : 0.45) at 37 °C: V_m = −70 mV, between E_K (−89) and E_Na (+61).

Frequently asked questions