In examining the GHK equation (see below), it is clear that the relative contribution of any given ion is determined not only by its concentration gradient across the plasma membrane, but also by its relative membrane permeability. p_K, p_Na, and p_Cl are the relative membrane permeabilities for K⁺, Na⁺, and Cl^-, respectively. Permeability refers to the ease with which ions cross the membrane, and is directly proportional to the total number of open channels for a given ion in the membrane. Therefore, if many K⁺ channels are open, p_K will be high. If only a few K⁺ channels are open, p_K will be small. If all K⁺ channels are closed or if no K⁺ channels exist in the membrane, p_K will be zero. Normally, permeabilities are reported as relative permeabilities with p_K having the reference value of one (because in most cells at rest p_K is larger than p_Na and p_Cl). For a typical neuron at rest, p_K : p_Na : p_Cl = 1 : 0.05 : 0.45. In contrast, approximate relative permeability values at the peak of a typical neuronal action potential are p_K : p_Na : p_Cl = 1 : 12 : 0.45.

When two or more ions contribute to the membrane potential, it is likely that the membrane potential would not be at the equilibrium potential for any of the contributing ions. Thus, no ion would be at its equilibrium (i.e., V_eq. ≠ V_m). When an ion is not at its equilibrium, an electrochemical driving force (V_DF) acts on the ion, causing the net movement of the ion across the membrane down its electrochemical gradient. The driving force is quantified by the difference between the membrane potential and the ion equilibrium potential (V_DF = V_m − V_eq.). The sign (i.e., positive or negative) of the driving force acting on an ion along with the knowledge of the valence of the ion (i.e., cation or anion) can be used to predict the direction of ion flow across the plasma membrane (i.e., into or out of the cell). For example, for cations (positively charged ions such as Na⁺, K⁺, H⁺, and Ca²⁺), a positive driving force (i.e., V_DF > 0) predicts ion movement out of the cell (efflux) down its electrochemical gradient, and a negative driving force (i.e., V_DF < 0) predicts ion movement into the cell (influx). The situation is reversed for anions (negatively charged ions such as Cl⁻ and HCO₃⁻), where a positive driving force predicts ion movement into the cell (influx), and a negative driving force predicts ion movement out of the cell (efflux). If the membrane potential (V_m) is exactly at the equilibrium potential (V_eq.) for an ion, the driving force acting on the ion would be zero. If V_m = V_eq., it can be seen that V_DF = V_m − V_eq. = 0. In this case, there would be no net movement of the ion across the plasma membrane into or out of the cell (i.e., no net flux of ion). See the Electrochemical Driving Force Calculator, and the lecture notes on the Resting Membrane Potential for additional details.

Please note that the unit of temperature used in the Goldman-Hodgkin-Katz equation is the Kelvin. It is also important to note that although this worksheet allows you to select different concentration units, during the calculation, the numerator and denominator concentration units for K⁺, Na⁺, and Cl^- are converted so that they match. Moreover, the calculator ensures that there is consistency in the concentration units used for K⁺, Na⁺, and Cl^-. Also note that based on the constants used (R = 8.314 J.K^-1.mol^-1 and F = 96485 C.mol^-1), the unit of V_m will be in Volts. Keeping this fact in mind, this tool simplifies the calculation by allowing you to calculate directly to or from mV.

The calculated equilibrium potentials for K⁺ (V_K), Na⁺ (V_Na), and Cl^- (V_Cl), as well as the calculated electrochemical driving forces acting on K⁺ (V_{DF, K}), Na⁺ (V_{DF, Na}), and Cl^- (V_{DF, Cl}), are read-only values. The sign of the electrochemical driving force (V_DF = V_m − V_eq.) acting on any given ion allows us to determine the direction of ion flow (i.e., into or out of the cell). This information is also provided after every calculation.