Resting membrane potential
The resting membrane potential is the voltage difference across the membrane of a cell when it is not actively firing an action potential. In neurons, this value is usually negative because ion concentrations differ across the membrane and the membrane is much more permeable to K+ than to Na+ at rest.
Core idea and main equations
A useful first approximation is the K+ equilibrium potential, because resting membranes often behave as though K+ has the strongest influence. A more complete estimate uses the Goldman-Hodgkin-Katz relation, which combines concentration gradients with relative permeabilities for K+, Na+, and Cl−.
\[
\begin{aligned}
E_{ion} &= \frac{R \cdot T}{z \cdot F}\ln\!\left(\frac{[ion]_{out}}{[ion]_{in}}\right)\cdot 1000
\end{aligned}
\]
\[
\begin{aligned}
V_m &= \frac{R \cdot T}{F}\ln\!\left(
\frac{P_K[K^+]_{out} + P_{Na}[Na^+]_{out} + P_{Cl}[Cl^-]_{in}}
{P_K[K^+]_{in} + P_{Na}[Na^+]_{in} + P_{Cl}[Cl^-]_{out}}
\right)\cdot 1000
\end{aligned}
\]
Symbols: \(R\) is the gas constant, \(T\) is absolute temperature in kelvin, \(F\) is Faraday’s constant, \(z\) is ion charge, and \(P\) represents relative permeability. The Cl− terms appear reversed in the GHK expression because chloride is an anion.
How to interpret the result
A more negative value means the inside of the cell is electrically more negative relative to the outside. If the estimate sits close to \(E_K\), the membrane is behaving in a strongly K+-dominated way. If the result becomes less negative, either Na+ influence is larger, the K+ gradient is weaker, or the selected permeabilities reduce K+ dominance.
Results are usually reported in millivolts. The calculator also compares \(V_m\) with \(E_K\), \(E_{Na}\), and \(E_{Cl}\), which helps show whether the resting voltage is most strongly pulled toward the K+, Na+, or Cl− equilibrium level.
- Using °C directly instead of converting temperature to kelvin.
- Swapping inside and outside concentrations in the logarithm.
- Forgetting that Cl− is an anion, so its sign treatment differs.
- Interpreting permeability ratios as concentrations instead of weighting factors.
Micro example: if \([K^+]_{in} = 140\) mM and \([K^+]_{out} = 5\) mM at body temperature, the K+ equilibrium potential is strongly negative. That is why a neuron at rest often ends up near a negative voltage, commonly around the neighborhood of \(-70\) mV rather than near zero.
This tool is useful for resting-state voltage exploration, especially when one concentration or one permeability is changed and the voltage shift is observed immediately. It is not a full action-potential simulator; for that, the next step is studying conductance changes over time, voltage-gated channels, and dynamic membrane models.