Nernst Equation Calculator for Transport Analysis
Estimate an ion’s equilibrium potential, compare it with membrane potential, and interpret the likely direction of electrochemical transport across a membrane.
Enter intracellular concentration.
Enter extracellular concentration.
Optional interpretation aid. A typical neuron resting potential is near -70 mV.
Results will appear here
Enter concentrations, charge, and temperature, then click Calculate Transport.
The calculator uses the Nernst equation: E = (RT / zF) ln(Cout / Cin).
Equilibrium potential
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Driving force
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Understanding How the Nernst Equation Calculates Transport
The Nernst equation is one of the core quantitative tools in physiology, biophysics, electrochemistry, and membrane transport research. When people say the Nernst equation calculates transport, what they usually mean is that it calculates the equilibrium potential for a specific ion across a membrane. That equilibrium potential tells you the membrane voltage at which the electrical force exactly balances the chemical diffusion force for that ion. In practical terms, it helps you understand whether an ion such as potassium, sodium, chloride, or calcium is likely to move into the cell, out of the cell, or remain at electrochemical equilibrium.
Transport across membranes is driven by gradients. The first gradient is the concentration difference between two sides of the membrane. The second is the electrical potential difference. A positively charged ion may be pushed outward by its concentration gradient but pulled inward by a negative membrane voltage. The Nernst equation combines these competing influences into one value: the equilibrium potential. If the membrane potential equals the Nernst potential for that ion, there is no net transport of that ion across a selectively permeable membrane.
Here, Eion is the equilibrium potential, R is the gas constant, T is the absolute temperature in kelvin, z is the ionic charge, and F is the Faraday constant. For quick physiological work at 37 degrees C, many textbooks simplify this to:
What the Nernst equation actually tells you about transport
The equation does not directly calculate a transport rate such as molecules per second. Instead, it calculates the electrochemical balance point. That is incredibly useful because transport direction depends on the difference between the actual membrane potential and the equilibrium potential. This difference is commonly called the driving force:
For a cation, if the membrane potential is more positive than the equilibrium potential, the electrochemical conditions often favor outward movement of positive charge. If the membrane potential is more negative than the equilibrium potential, inward movement is often favored. For anions like chloride, interpretation flips because the ion carries a negative charge. This is why calculators that interpret Nernst transport usually ask for both ion charge and membrane potential.
Why this matters in real biology and medicine
Every excitable cell relies on electrochemical gradients. Neurons, cardiomyocytes, skeletal muscle fibers, renal tubule cells, intestinal epithelial cells, and secretory glands all depend on the controlled movement of ions. The Nernst equation helps explain why potassium tends to leave many cells at rest, why sodium tends to enter, why calcium has such a strong inward driving force, and why chloride can either enter or leave depending on tissue context.
In the nervous system, resting membrane potential sits close to the potassium equilibrium potential because resting membranes are often highly permeable to potassium. In cardiac electrophysiology, different ion equilibrium potentials shape depolarization, plateau behavior, and repolarization. In nephrology, ion gradients determine how renal epithelial cells reabsorb or secrete solutes. In laboratory membrane transport studies, the Nernst equation provides a baseline expectation before adding permeability, conductance, or transporter kinetics.
Typical mammalian ion gradients
The table below uses representative physiological values commonly discussed in human cell physiology. Actual numbers vary by tissue, species, and experimental conditions, but these examples are realistic and useful for interpretation.
| Ion | Typical intracellular concentration | Typical extracellular concentration | Approximate Nernst potential at 37 degrees C | Transport tendency at Vm = -70 mV |
|---|---|---|---|---|
| K+ | 140 mM | 4 to 5 mM | About -89 to -95 mV | Mild outward driving tendency in many resting cells |
| Na+ | 10 to 15 mM | 135 to 145 mM | About +60 to +70 mV | Strong inward driving tendency |
| Cl- | 4 to 30 mM | 100 to 110 mM | Often about -30 to -90 mV depending on cell type | Variable, tissue dependent |
| Ca2+ | About 0.0001 mM free cytosolic | About 1.2 to 2.0 mM | Often above +120 mV | Very strong inward driving tendency |
These values help explain a basic physiological pattern: sodium and calcium generally want to move inward, while potassium often tends to move outward at rest. Chloride is more context dependent because intracellular chloride varies widely among mature neurons, immature neurons, epithelial cells, and secretory tissues.
Nernst equation versus Goldman equation
Students and practitioners often confuse the Nernst equation with the Goldman-Hodgkin-Katz equation. The difference is important. The Nernst equation applies to one ion at a time. It tells you the equilibrium potential for that ion if the membrane were permeable only to that ion. The Goldman equation, by contrast, estimates the membrane potential produced by multiple ions at once when relative permeabilities are known.
| Feature | Nernst equation | Goldman-Hodgkin-Katz equation |
|---|---|---|
| Main purpose | Find equilibrium potential for one ion | Estimate membrane potential from multiple ions |
| Best use case | Ion specific transport interpretation | Whole membrane voltage modeling |
| Inputs | Inside concentration, outside concentration, temperature, charge | Concentrations plus relative membrane permeabilities |
| Transport insight | Shows equilibrium point and driving force for one ion | Shows combined membrane behavior |
How to interpret the calculator results
- Enter the ion concentration inside the cell. This is the intracellular concentration, sometimes written as Cin.
- Enter the concentration outside the cell. This is the extracellular concentration, often written as Cout.
- Select the ionic charge. Potassium and sodium are +1, calcium is +2, chloride is -1.
- Enter temperature. Physiological calculations are often done at 37 degrees C, but the exact temperature matters.
- Enter membrane potential if you want transport interpretation. The difference between Vm and Eion indicates net electrochemical direction.
If the equilibrium potential is close to the membrane potential, then the ion is near electrochemical equilibrium and there will be little net movement even if channels are open. If the equilibrium potential is far from membrane potential, there is a stronger driving force. However, do not forget that driving force alone does not guarantee large flux. The membrane must also be permeable to that ion. A strong driving force with almost zero permeability will produce minimal transport.
Worked example with potassium
Suppose intracellular potassium is 140 mM and extracellular potassium is 5 mM at 37 degrees C. For K+, z = +1. Using the simplified physiological form:
EK = 61.5 log10(5 / 140) = about -89 mV
If the membrane potential is -70 mV, then the membrane is more positive than EK. Under many standard sign conventions, potassium experiences an outward electrochemical tendency. This is one reason potassium efflux contributes to repolarization and stabilization of negative resting membrane potential in many cells.
Worked example with sodium
Now consider sodium with intracellular sodium of 12 mM and extracellular sodium of 145 mM. For Na+, z = +1:
ENa = 61.5 log10(145 / 12) = about +66 mV
If the membrane potential is -70 mV, the membrane is far more negative than ENa, so sodium has a strong inward electrochemical tendency. That explains why opening sodium channels drives rapid depolarization in neurons and muscle cells.
Factors that change the result
- Temperature: Higher temperature slightly increases the magnitude of the calculated equilibrium potential for a given concentration ratio.
- Charge number: Divalent ions such as Ca2+ and Mg2+ have z = +2, which changes the scaling factor.
- Measurement accuracy: Small errors in low concentrations, especially for calcium, can greatly influence interpretation.
- Activity versus concentration: The most rigorous thermodynamic treatment uses ion activity, not just concentration.
- Compartment definition: Intracellular and extracellular concentrations can differ among microdomains, organelles, and local membrane surfaces.
Limitations of using the Nernst equation alone
Although the Nernst equation is foundational, it is not a complete transport model. It assumes a selective membrane and equilibrium conditions for one ion. It does not account for ion channel gating kinetics, transporter saturation, membrane resistance, convection, solvent drag, paracellular leak, or coupled transport. A sodium glucose cotransporter, for example, depends on both sodium and glucose gradients and requires a different thermodynamic framework. Likewise, current amplitude through an ion channel depends on channel number, open probability, conductance, and membrane surface area, not just on equilibrium potential.
For advanced work, researchers often combine Nernst analysis with current voltage relationships, patch clamp measurements, or flux assays. In epithelial transport, one may combine Nernst predictions with transepithelial resistance, short circuit current, and transporter expression data. In computational neuroscience, the Nernst equation is typically paired with Goldman-based membrane equations or Hodgkin-Huxley style channel kinetics.
Authoritative references for deeper study
If you want to validate transport calculations against expert educational or government sources, review the following:
- NCBI Bookshelf for physiology and membrane biophysics texts hosted by the U.S. National Library of Medicine.
- National Institute of Neurological Disorders and Stroke for neuroscience context related to ion channels and membrane signaling.
- OpenStax for university level educational material on cell membranes, electrochemical gradients, and transport.
Practical summary
When people say the Nernst equation calculates transport, the most precise interpretation is this: it calculates the equilibrium potential for a single ion, and that value helps you infer the likely direction and strength of electrochemical transport when compared with the actual membrane potential. The equation is fundamental because it links chemistry and electricity in one compact expression. For clinicians, students, and researchers, it provides immediate intuition about why ions move the way they do in cells and tissues.
Use the calculator above whenever you need to estimate whether an ion is likely to move inward or outward under a defined set of conditions. For a fast membrane transport interpretation, focus on four questions: What is the ion concentration inside? What is it outside? What charge does the ion carry? And how does the resulting equilibrium potential compare with membrane potential? Those four data points often reveal the dominant direction of passive electrochemical movement.