Equilibrium Potential

Human Physiology • Cell Physiology and Membrane Transport

Written by STEM Calculators Team Published March 21, 2026 Updated March 21, 2026

Equilibrium Potential (Nernst Equation)

Compute a single ion’s equilibrium potential (E_ion) using the Nernst equation, then (optionally) compare it to membrane potential (V_m) to interpret driving force and ion movement direction.

Ion preset

Use “Fill example” to autofill typical classroom concentrations.

Ion charge z

Use negative for anions (e.g., Cl⁻).

[ion]_in (mM)

[ion]_out (mM)

Temperature (°C)

Nernst form shown in steps

Computation uses full precision; steps follow your selection.

Use simplified 37°C constant (61.5/z · log₁₀)

Compare with membrane potential V_m (mV)

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Equilibrium potential

Equilibrium potential is the membrane voltage at which one ion has no net tendency to move because its chemical gradient and electrical gradient exactly balance. An equilibrium potential calculator is useful for estimating the voltage associated with a specific ion such as K⁺, Na⁺, Cl⁻, or Ca²⁺, and for separating a single-ion balance from the whole membrane potential.

The main result is the ion’s equilibrium potential in millivolts, often written as E_ion. The value can also be compared with an actual membrane potential to show whether a driving force remains and whether the ion would tend to move inward or outward.

Core formulas

\[ E_{\text{ion}}=\frac{R \cdot T}{z \cdot F}\ln\!\left(\frac{C_{\text{out}}}{C_{\text{in}}}\right)\cdot 1000 \]

\[ E_{\text{ion}} \approx \frac{61.5}{z}\log_{10}\!\left(\frac{C_{\text{out}}}{C_{\text{in}}}\right) \quad \text{at } 37^\circ\text{C} \]

\[ \text{Driving force}=V_m-E_{\text{ion}} \]

Here, R is the gas constant, T is absolute temperature in kelvin, z is the ion charge, F is Faraday’s constant, and C_out and C_in are the extracellular and intracellular concentrations. The sign of z matters greatly: cations have positive charge, while Cl⁻ has negative charge, so its equilibrium potential changes sign relative to the same concentration ratio.

How to interpret the result

A more negative equilibrium potential means the inside of the cell would need to be more negative to exactly balance that ion’s concentration gradient. A more positive equilibrium potential means the inside would need to be more positive. Results are usually reported in mV, while concentrations are often entered in mM.

When a membrane potential is also known, comparing V_m with E_ion reveals whether the ion is already at balance or still has a remaining driving force. A zero driving force means no net movement for that ion. For cations, a negative driving force tends to favor inward movement and a positive driving force tends to favor outward movement; for anions, the interpretation reverses.

Common pitfalls

Confusing equilibrium potential for one ion with the total membrane potential.
Using the wrong sign for ion charge, especially for Cl⁻.
Mixing concentration units or entering inside and outside values in reverse order.
Using the 37 °C shortcut when temperature is not close to body temperature.

Micro example: if K⁺ is 140 mM inside and 5 mM outside at 37 °C, then the equilibrium potential is about \(-89\ \text{mV}\). If the membrane potential is \(-70\ \text{mV}\), a K⁺ driving force still remains.

This tool is appropriate for single-ion electrical balance, Nernst equation practice, and quick comparison of E_ion with V_m. It is not a full membrane-potential model; when several ions and permeability must be combined, the next step is a membrane potential or Goldman equation analysis.

Frequently Asked Questions

What is an equilibrium potential?

An equilibrium potential is the membrane voltage at which the electrical and chemical forces on one ion exactly balance. At that voltage, the ion has no net movement across the membrane.

How is equilibrium potential different from membrane potential?

Equilibrium potential applies to one ion only, while membrane potential reflects the combined influence of multiple ions and their permeabilities. They can be equal for one ion without describing the full cell voltage.

Why does chloride use a negative charge in the Nernst equation?

Chloride is an anion, so its charge z is negative. That negative charge changes the sign of the equilibrium-potential result relative to a cation with the same concentration ratio.

How do I tell whether an ion will move inward or outward?

Compare the membrane potential with the ion's equilibrium potential using the driving force Vm - Eion. The direction depends on both the sign of that driving force and whether the ion is a cation or an anion.

When should I use the 37 C classroom form instead of the full Nernst equation?

Use the 37 C shortcut when the temperature is close to body temperature and a fast classroom estimate is enough. Use the full Nernst equation when temperature changes matter or when a more exact calculation is needed.

Equilibrium Potential

Equilibrium Potential (Nernst Equation)

Calculation steps

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Frequently Asked Questions

Equilibrium Potential (Nernst Equation)

Calculation steps

Copy / export

Rate this calculator

Frequently Asked Questions

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