Equilibrium potential is the specific voltage across a cell’s membrane at which the electrical force pulling an ion one way and the concentration force pushing it the other way exactly cancel out, so that ion has no net reason to move in or out of the cell. Every ion that can cross the membrane has its own equilibrium potential, and the value depends on how unevenly that ion is distributed between the inside and outside of the cell. It is calculated using the Nernst equation, which converts a concentration ratio into a voltage. The concept is fundamental to understanding how nerve impulses fire, how muscles contract, and how cells throughout the body manage their electrical state.
Two Opposing Forces That Balance at One Voltage
Cells maintain strikingly different concentrations of ions on either side of their membranes. Potassium is far more concentrated inside the cell, while sodium and calcium are far more concentrated outside. If you opened a channel that allowed potassium to flow freely, potassium ions would initially rush out of the cell, carried by the concentration gradient. But each potassium ion that leaves carries a positive charge with it, making the inside of the cell progressively more negative. That growing negative charge starts pulling potassium back in. At some precise voltage, the electrical pull inward matches the concentration push outward, and the net flow drops to zero. That voltage is the equilibrium potential for potassium.
The same logic applies to every permeable ion, just with different numbers and sometimes reversed directions. For sodium, the concentration gradient pushes ions into the cell, and the equilibrium voltage at which that push is perfectly balanced by the electrical repulsion is a positive value rather than a negative one. The equilibrium potential is sometimes called the reversal potential because it is the voltage at which the direction of net ion flow reverses: above it, the ion moves one way; below it, the ion moves the other way.
How the Nernst Equation Works
The Nernst equation predicts the equilibrium potential for a single ion type, and it does so by relating the ratio of that ion’s concentration outside the cell to its concentration inside the cell. The core insight is that the relationship between concentration ratios and voltage is logarithmic, not linear. Doubling the concentration ratio does not double the voltage; the effect tapers off in a way captured by a logarithm.1Advances in Physiology Education. The critical role of logarithmic transformation in Nernstian equilibrium potential calculations This matters because ion gradients across membranes span very different ranges depending on the ion, and the logarithmic relationship explains why a tenfold concentration difference translates to a fixed step in voltage rather than an ever-growing one.
In plain terms, the equation takes three inputs: the temperature (because warmer molecules move faster), the charge on the ion (a calcium ion carries twice the charge of a potassium ion), and the ratio of outside-to-inside concentrations. It outputs a single number in millivolts. You do not need to memorize the formula to understand its logic. The bigger the concentration imbalance, the larger the equilibrium potential. And for ions with a double charge, the voltage needed to counterbalance a given concentration difference is halved, because each ion crossing the membrane moves twice as much charge.
Julius Bernstein first proposed in 1902 that electrical potentials in biological cells arise from the unequal distribution of ions across a selectively permeable membrane. His membrane theory was the first plausible physical model of bioelectric events, and its core ideas remain valid today.2PubMed. Julius Bernstein (1839-1917): pioneer neurobiologist and biophysicist The Nernst equation, developed by the chemist Walther Nernst around the same period, gave Bernstein’s conceptual framework a quantitative backbone.
Equilibrium Potentials of the Major Ions
Each ion that matters for cell signaling has a characteristic equilibrium potential, and knowing these values gives you a map of the electrical forces at play in a living cell.
- Potassium (K⁺): About −90 mV. Potassium is roughly 30 to 40 times more concentrated inside the cell than outside, so its equilibrium potential is strongly negative. This is the closest value to the typical resting membrane potential of neurons, which hovers around −70 mV, because the resting membrane is most permeable to potassium.
- Sodium (Na⁺): About +60 mV. Sodium is roughly 10 times more concentrated outside the cell, so its equilibrium potential is strongly positive. When sodium channels open during a nerve impulse, the membrane potential swings toward this value.
- Calcium (Ca²⁺): About +120 to +130 mV. Cells maintain an enormous calcium gradient. Free calcium inside a resting cell sits at roughly 100 nanomolar, while extracellular calcium is in the millimolar range, a difference of about 20,000-fold.3Cell. Calcium Signaling Dynamics Because calcium also carries a double positive charge, the Nernst equation yields an extremely positive equilibrium potential, making calcium entry an intensely powerful electrical and chemical signal.
- Chloride (Cl⁻): About −70 to −85 mV in most mature neurons. Chloride is more concentrated outside the cell, and because it carries a negative charge, its equilibrium potential is negative. Tight regulation of intracellular chloride is crucial for synaptic inhibition, and disruptions in chloride balance have been linked to neurological and psychiatric disorders.4Neuron. Chloride Regulation: A Dynamic Equilibrium Crucial for Synaptic Inhibition
These numbers are not universal constants carved in stone. They shift with changes in diet, hydration, kidney function, temperature, and disease. A rise in extracellular potassium concentration, for example, shrinks the potassium gradient and makes the potassium equilibrium potential less negative. That seemingly small shift has real consequences for heart rhythm, as discussed below.
Why the Resting Membrane Potential Is Not the Same as Any Single Equilibrium Potential
A common point of confusion is expecting the cell’s actual membrane voltage to sit right at the equilibrium potential of potassium, since the resting membrane is most permeable to that ion. In reality, the resting membrane is also slightly permeable to sodium and chloride. Because sodium’s equilibrium potential is positive and potassium’s is negative, even a small leak of sodium pulls the resting voltage away from potassium’s equilibrium potential and toward something a bit less negative, typically around −70 mV rather than −90 mV.
To account for the contributions of multiple ions simultaneously, researchers use the Goldman-Hodgkin-Katz equation. Where the Nernst equation handles one ion at a time, the Goldman equation weights each ion’s contribution by how permeable the membrane is to that ion at a given moment. When permeability to potassium dominates, the membrane voltage stays close to potassium’s equilibrium potential. When sodium permeability surges, as it does during the rising phase of a nerve impulse, the membrane voltage races toward sodium’s equilibrium potential. At the peak of an action potential, the membrane has become so permeable to sodium that its voltage approaches the sodium equilibrium potential. During the afterhyperpolarization phase, potassium permeability temporarily exceeds even its resting level, and the voltage dips below the normal resting potential, briefly overshooting toward the potassium equilibrium potential.5PubMed. A classic experiment revisited: membrane permeability changes during the action potential
The key principle is straightforward: the membrane potential at any instant approaches the equilibrium potential of whichever ion the membrane is most permeable to at that instant. Equilibrium potentials set the boundaries, and permeability determines where between those boundaries the actual voltage lands.
Driving Force and Why It Matters
Once you know the equilibrium potential for a given ion and the actual membrane potential, the difference between the two tells you the driving force on that ion. If the membrane potential is −70 mV and potassium’s equilibrium potential is −90 mV, there is a 20 mV driving force pushing potassium out of the cell. If sodium’s equilibrium potential is +60 mV, the driving force on sodium at −70 mV is a hefty 130 mV pulling sodium inward.
Driving force is what determines how much current flows through an open channel. A channel can be wide open, but if the membrane voltage happens to sit exactly at that ion’s equilibrium potential, no net current flows through it. Conversely, even a modest number of open channels can carry a large current when the driving force is big. This is why calcium, with its equilibrium potential far above any voltage the cell normally reaches, creates such a dramatic signal when calcium channels open. The driving force on calcium is almost always enormous.
Researchers measuring the activity of ion channels often identify the reversal potential experimentally by finding the voltage at which the current through a channel flips direction. Early single-channel recordings at the frog neuromuscular junction showed that the reversal potential shifted in a predictable, roughly linear way with the logarithm of external sodium concentration, just as the Nernst equation would predict.6PubMed Central. Ion-concentration dependence of the reversal potential and the single channel conductance of ion channels at the frog neuromuscular junction That result was a powerful confirmation that the equilibrium-potential framework accurately describes real biological channels, not just theoretical ones.
A Common Misconception About Ion Movement During Action Potentials
It is easy to imagine that each nerve impulse dramatically reshuffles the ions across the membrane, flooding the cell with sodium and draining its potassium. In fact, the number of ions that cross during a single action potential is tiny relative to the total pools inside and outside the cell. The movement of charge is enough to produce a large, brief swing in voltage, but it does not meaningfully change the overall concentration gradients. A neuron can fire thousands of action potentials before the gradients would degrade to any noticeable degree, and even then, the sodium-potassium pump steadily works in the background to restore whatever small losses accumulate.
This means that the equilibrium potentials for sodium and potassium remain essentially constant from one action potential to the next. The Nernst equation inputs barely change during normal signaling. What changes rapidly is the membrane’s permeability, as channels open and close on a millisecond timescale, swinging the membrane potential between the fixed goalposts set by the equilibrium potentials.
When Equilibrium Potentials Shift in Disease
Although equilibrium potentials are stable during moment-to-moment signaling, they can change under pathological conditions that alter ion concentrations in the blood or in tissue fluids. The most clinically significant example involves potassium. When blood potassium rises, a condition called hyperkalemia, the concentration gradient for potassium across heart muscle cells shrinks. The potassium equilibrium potential becomes less negative, and as a result, the resting membrane potential of cardiac cells also becomes less negative. That may sound like a minor technical detail, but it changes the excitability of the heart in dangerous ways, potentially triggering arrhythmias.
The relationship between potassium levels and cardiac risk runs in both directions. In low-potassium states, or hypokalemia, certain potassium channels in heart cells undergo a surprising transformation. Under normal conditions, a type of potassium channel called TWIK1 is strongly selective for potassium and plays an inhibitory role, helping to keep the cell’s resting potential negative. But in low extracellular potassium, TWIK1 can become permeable to sodium as well, shifting from an inhibitory channel to an excitatory one. This paradoxical depolarization of heart cells in hypokalemia may contribute to cardiac arrhythmias.7PubMed Central. Altered and dynamic ion selectivity of K+ channels in cell development and excitability The finding challenged a long-held assumption that the ion selectivity of potassium channels was fixed and could only be altered by genetic mutations.
Chloride equilibrium potential shifts also have medical significance. During early brain development, neurons have higher intracellular chloride concentrations than adult neurons do, so the chloride equilibrium potential is less negative. Activation of chloride channels in immature neurons can actually be excitatory rather than inhibitory, the opposite of what happens in adult brains. Conditions that push intracellular chloride in adult neurons back toward immature levels, including certain types of brain injury and epilepsy, can impair the brain’s inhibitory signaling and contribute to seizure activity.4Neuron. Chloride Regulation: A Dynamic Equilibrium Crucial for Synaptic Inhibition
Equilibrium Potentials Beyond Neurons
The concept of equilibrium potential is most often taught in the context of nerve and muscle cells, but it governs ion movement in every cell type. Epithelial cells lining the airways, for instance, manage the thin layer of fluid on their surface partly through ion transport, and the equilibrium potentials for sodium, chloride, and potassium across both the airway-facing and blood-facing membranes determine which direction those ions flow. Biophysical models of human bronchial epithelium calculate the reversal potential for each ionic species over time to predict fluid secretion and absorption, treating the membrane potential as instantly adjusting to whatever steady state the current ion concentrations dictate.8Biophysical Journal. A Dynamical Biophysical Model of the Human Bronchial Epithelium Integrating Ion, Water, and pH Regulation Cystic fibrosis, a disease that disrupts chloride channels in epithelial cells, is at its core a disorder of altered chloride equilibrium and driving force at the cell surface.
Kidney cells use similar principles when deciding how much sodium to reclaim from the fluid that will become urine. The equilibrium potential for sodium across the kidney tubule membrane determines whether sodium will enter the cell passively or needs to be actively pumped. Pancreatic beta cells rely on potassium channel closure to depolarize toward the calcium equilibrium potential, which triggers insulin release. Even in plant cells, where the relevant ions include hydrogen and potassium, the Nernst equation predicts the resting voltage of the cell and helps explain how roots absorb nutrients from soil.
The universality of equilibrium potentials reflects something basic about cell life. Any membrane that is selectively permeable to an ion and maintains a concentration difference for that ion will develop a voltage. Whether that voltage governs a thought, a heartbeat, the secretion of mucus, or the release of a hormone, the physics is the same.
Why Calcium’s Equilibrium Potential Is in a League of Its Own
Calcium stands out from the other major biological ions in two respects that amplify its signaling power. First, the concentration gradient is staggering. Cells keep their free internal calcium at roughly 100 nanomolar while bathing in extracellular fluid at millimolar concentrations, a roughly 20,000-fold difference.3Cell. Calcium Signaling Dynamics No other common biological ion is maintained at such extreme asymmetry. Second, calcium’s double charge means that for any given concentration ratio, the Nernst equation yields half the millivoltage it would for a singly charged ion. But because the concentration ratio is so immense, the equilibrium potential still ends up far more positive than sodium’s. The combined effect is a massive electrochemical driving force inward at virtually all physiological membrane potentials.
This is why cells use calcium as a trigger signal rather than a sustained carrier of information. Even a brief opening of a few calcium channels lets a significant amount of charge and chemical signal flood in. The cell then rapidly clears the calcium, either pumping it back outside or sequestering it inside internal compartments like the endoplasmic reticulum, resetting the system for the next signal. The enormous equilibrium potential ensures that the “on” switch is powerful, and the aggressive removal machinery ensures the “off” switch is fast.
Temperature, the Quiet Variable
Temperature appears in the Nernst equation and affects the calculated equilibrium potential, though in warm-blooded animals the effect is modest because body temperature stays within a narrow range. In cold-blooded animals or in isolated tissue experiments conducted at varying temperatures, the impact is more visible. Raising the temperature increases the kinetic energy of ions and slightly increases the voltage needed to counterbalance a given concentration gradient. At human body temperature, a tenfold concentration difference for a singly charged ion translates to about 61.5 millivolts of equilibrium potential. At room temperature, that same ratio gives roughly 58 millivolts. The difference is small but can matter in precise electrophysiological recordings, which is why researchers carefully report and control the temperature of their experimental solutions.
Fever, hypothermia, or therapeutic cooling of the brain after cardiac arrest all change the temperature of tissue and therefore nudge every equilibrium potential slightly. In practice these shifts are usually overshadowed by the far larger effects of altered blood chemistry, but they serve as a reminder that equilibrium potential is a dynamic quantity determined by real physical conditions, not a fixed label attached to each ion.