Nernst Equilibrium Potential for a Membrane Ion (37 °C)

An ion sitting across a membrane feels two forces: the concentration gradient pushing it down, and the membrane voltage pushing it one way or the other. The equilibrium potential is the voltage where those exactly cancel, so no net current flows even though the concentration gradient is still there. For potassium at 4 mM outside and 140 mM inside, $61.5 \log_{10}(4/140) = -95$ mV, and that is why a resting neuron sits near −70 mV: it is potassium-dominated, pulled toward potassium's equilibrium and held short of it by a smaller sodium leak.

The 61.5 is the general Nernst constant $RT\ln 10/F$ evaluated at 37 °C, which is what separates this page from the electrochemistry version. At 20 °C the same constant is 58.2, at 25 °C it is 59.2, and textbooks that quote 61.5 for a room-temperature experiment are quietly wrong by five percent. Note also that the charge number sits in the denominator and carries its sign: calcium at $z = +2$ gets half the voltage per decade, and chloride at $z = -1$ flips the whole thing, so the extracellular-over-intracellular ratio produces a negative potential rather than a positive one.

What this equation cannot do is give you a resting membrane potential. It describes one ion in isolation, as though the membrane were permeable to nothing else. A real membrane leaks several ions at once, and the potential lands at a permeability-weighted compromise given by the Goldman-Hodgkin-Katz equation. The useful thing the Nernst potential does give you is the direction of drive: compare it to the actual membrane potential, and the difference tells you which way that ion will move if its channel opens, which is the whole basis of how an action potential works.