nernst potential calculator

What Is the Nernst Potential?

The Nernst potential is the membrane voltage at which a specific ion is at electrochemical equilibrium. At that voltage, the electrical force and the concentration gradient for that ion exactly balance each other, so there is no net movement of that ion across the membrane.

In physiology, this is often called the equilibrium potential or reversal potential for a single ion. It is central to neuroscience, cardiology, renal physiology, and cell biology.

The Nernst Equation (and What Each Symbol Means)

• E: equilibrium potential (volts)
• R: gas constant (8.314 J/mol·K)
• T: absolute temperature (Kelvin)
• z: ion valence (e.g., +1, +2, -1)
• F: Faraday constant (96485 C/mol)
• C_out and C_in: outside and inside ion concentrations

This calculator reports values in mV to match common electrophysiology conventions.

How to Use This Calculator

Step-by-step

• Enter the ion valence (z): for K+ and Na+, use +1; for Ca2+, use +2; for Cl-, use -1.
• Enter outside and inside concentrations using the same unit.
• Enter temperature in Celsius.
• Click Calculate to get the equilibrium potential.

If concentrations are equal inside and outside, the Nernst potential is 0 mV regardless of the ion type.

Worked Example: Potassium in a Typical Neuron

A common textbook example uses:

• [K+]_outside = 5 mM
• [K+]_inside = 140 mM
• T = 37°C
• z = +1

This gives an equilibrium potential near -89 mV. That is why potassium strongly contributes to the negative resting membrane potential in many cells.

Why Valence Changes the Result

Valence appears in the denominator of the equation, so ions with larger charge magnitude have a smaller voltage change per concentration ratio.

• Monovalent ions (Na+, K+, Cl-) have z = ±1.
• Divalent ions (Ca2+, Mg2+) have z = +2.

For the same concentration ratio and temperature, a divalent ion’s equilibrium potential magnitude is roughly half that of a monovalent ion.

Temperature Matters More Than Many People Expect

The factor (R×T/F) increases with temperature, so equilibrium potentials shift slightly with temperature. At body temperature (37°C), the per-decade factor for monovalent ions is about 61.5 mV. At room temperature (25°C), it is about 59.2 mV.

If you are comparing patch-clamp data from room temperature and physiological temperature, this difference is often important.

Nernst vs. Goldman: When to Use Which

Use Nernst when:

• You need equilibrium potential for one ion.
• You are interpreting reversal potential of a mostly single-ion conductance.

Use Goldman-Hodgkin-Katz when:

• Multiple ions contribute simultaneously to membrane voltage.
• Relative membrane permeabilities are important.

The Nernst equation is still the foundation; Goldman extends the concept to multi-ion systems.

Typical Biological Use Cases

• Neuroscience: Comparing membrane potential to E_K, E_Na, and E_Cl to infer ion flux direction.
• Cardiac electrophysiology: Understanding action potential phases driven by different ion currents.
• Renal physiology: Modeling ion transport and tubular gradients.
• Cell signaling: Estimating calcium driving force in excitable and non-excitable cells.

Common Input Mistakes

• Using z = 1 for chloride instead of z = -1.
• Mixing concentration units (e.g., mM outside and µM inside).
• Using Celsius directly in the equation without converting to Kelvin.
• Entering zero or negative concentrations.

This page validates major input issues and provides an error message if a value is not physically meaningful.

Quick FAQ

Is this calculator for membrane potential or equilibrium potential?

It calculates equilibrium potential for one ion. Actual membrane potential may differ because multiple ions and conductances are involved.

Can I use this for chloride?

Yes. Just make sure valence is -1 and concentrations are entered correctly for outside/inside.

Does it assume ideal behavior?

Yes. Like most introductory Nernst tools, it assumes ideal dilute solutions and activity approximated by concentration.