Nernst Potential Calculator

Find the equilibrium electrochemical potential E for a single ion species across a cell membrane using the Nernst equation.

⚡ Nernst Potential Calculator
Ion valence (z)
Concentration outside cell [ion]out
mM
Concentration inside cell [ion]in
mM
Temperature
°C
Nernst equilibrium potential (E)
—
Absolute temperature (T)
—
Step-by-step working

⚡ What is the Nernst Potential Calculator?

The Nernst potential calculator finds the equilibrium electrochemical potential E for a single ion species across a cell membrane, the voltage at which the electrical force on that ion exactly balances the chemical force from its concentration gradient, so there is no net flow of the ion across the membrane. It uses the Nernst equation, E=(RT/zF)ln([ion]out/[ion]in), a foundational formula in cell physiology and neuroscience.

This calculator is used across several real-world contexts. Neuroscience students use it to compute the individual equilibrium potentials for potassium, sodium, and chloride that combine to set a neuron's resting membrane potential and drive the action potential. Physiology courses use it to explain why the resting potential sits close to the potassium equilibrium potential, since most resting cell membranes are far more permeable to K+ than to other ions. Pharmacology and cardiac electrophysiology use related equilibrium-potential calculations to understand how ion channel drugs shift excitability.

A common misconception is that the Nernst potential is the same thing as the resting membrane potential of a real cell. It is not, the Nernst potential describes the equilibrium for one ion species considered in isolation, while the actual resting potential depends on the permeabilities and gradients of multiple ions at once, captured by the more complex Goldman-Hodgkin-Katz equation. Another common point of confusion is the sign for anions: because the valence z appears in the denominator, a negative z (as for Cl-) flips the sign of the result compared to what the raw concentration ratio alone would suggest.

This calculator is useful because it removes the arithmetic error risk in a formula that mixes physical constants, a logarithm, and a sign-sensitive valence, letting students and researchers focus on interpreting the result rather than computing it by hand.

📐 Formula

E  =  (RT / zF) × ln([ion]out / [ion]in)
R = gas constant = 8.314 J/(mol·K)
T = absolute temperature in Kelvin (°C + 273.15); this calculator defaults to 37°C (310.15 K), human body temperature
z = ion valence (a nonzero integer; positive for cations, negative for anions)
F = Faraday's constant = 96,485 C/mol
[ion]out, [ion]in = ion concentration outside and inside the cell, in the same units
The result of RT/zF × ln(...) is in volts; this calculator multiplies by 1000 to display E in millivolts (mV), the conventional unit for membrane potentials.
Example: K+ at 37°C with [K+]out=5 mM, [K+]in=140 mM gives E ≈ −89.05 mV.

📖 How to Use This Calculator

Steps

1
Enter the ion valence. Type the ion's charge z, positive for cations like K+ or Na+, negative for anions like Cl-.
2
Enter the concentrations. Type the ion concentration outside the cell and inside the cell, in millimolar (mM).
3
Enter the temperature and read the result. Enter the temperature in degrees Celsius (defaults to 37°C body temperature) and read the Nernst equilibrium potential in millivolts.

💡 Example Calculations

Example 1 — Potassium (K+) in a Mammalian Neuron

Typical resting neuron concentrations: [K+]out=5 mM, [K+]in=140 mM, T=37°C

1
T = 37°C + 273.15 = 310.15 K
2
E = (8.314 × 310.15 / (1 × 96485)) × ln(5 / 140)
3
E = −89.05 mV, close to the textbook potassium equilibrium potential, which is why K+ dominates a resting neuron's membrane potential
E = −89.05 mV
Try this example →

Example 2 — Sodium (Na+) in a Mammalian Neuron

Typical resting neuron concentrations: [Na+]out=145 mM, [Na+]in=12 mM, T=37°C

1
T = 37°C + 273.15 = 310.15 K
2
E = (8.314 × 310.15 / (1 × 96485)) × ln(145 / 12)
3
E = +66.59 mV, strongly positive, consistent with the textbook sodium equilibrium potential that drives the rapid depolarization phase of an action potential
E = +66.59 mV
Try this example →

Example 3 — Chloride (Cl-) with a Negative Valence

Typical concentrations: [Cl-]out=110 mM, [Cl-]in=4 mM, T=37°C, z=−1

1
T = 37°C + 273.15 = 310.15 K
2
ln(110 / 4) = +3.314, a positive number since [Cl-]out > [Cl-]in
3
Dividing by the negative valence z=−1 flips the sign: E = (8.314 × 310.15 / (−1 × 96485)) × 3.314 = −88.57 mV, a physiologically sensible chloride equilibrium potential, even though the concentration ratio alone was positive
E = −88.57 mV
Try this example →

❓ Frequently Asked Questions

What is the Nernst potential?+
The Nernst potential (or equilibrium potential) is the membrane voltage at which the electrical force on an ion exactly balances its concentration gradient, so there is no net flow of that ion across the membrane. It is calculated with E=(RT/zF)ln([ion]out/[ion]in).
What is the Nernst equation formula?+
E = (RT/zF) x ln([ion]out/[ion]in), where R is the gas constant (8.314 J/(mol*K)), T is absolute temperature in Kelvin, z is the ion's valence, F is Faraday's constant (96485 C/mol), and [ion]out and [ion]in are the extracellular and intracellular concentrations.
What is the resting potassium (K+) Nernst potential in a neuron?+
Using typical mammalian neuron concentrations ([K+]out=5 mM, [K+]in=140 mM) at 37°C, the Nernst potential for K+ is about -89 mV, strongly negative, which is why potassium dominates the resting membrane potential of most neurons.
What is the sodium (Na+) Nernst potential in a neuron?+
Using typical mammalian neuron concentrations ([Na+]out=145 mM, [Na+]in=12 mM) at 37°C, the Nernst potential for Na+ is about +67 mV, strongly positive, which is why an action potential's rapid depolarization phase drives the membrane voltage toward positive values as Na+ channels open.
Why is the chloride (Cl-) Nernst potential negative even though ln(out/in) is positive?+
Because chloride's valence z=-1 is negative, dividing by a negative z flips the sign of the whole expression. With [Cl-]out=110 mM and [Cl-]in=4 mM, ln(110/4) is a positive number, but dividing by z=-1 makes the final Nernst potential negative, around -89 mV, this sign flip for anions is the single most common point of confusion when first learning the equation.
Why does this calculator default to 37°C instead of 25°C?+
37°C (310.15 K) is human body temperature and the physiologically relevant value for mammalian cell membrane potentials. Some introductory textbooks use 25°C room temperature instead for simplicity, which changes the RT/zF prefactor and therefore the final millivolt value, always match the temperature to your source data.
Can the ion valence z be negative?+
Yes, z is negative for anions. Chloride (Cl-) uses z=-1, and other monovalent anions like bicarbonate (HCO3-) also use z=-1. Divalent anions would use z=-2. This calculator validates that z is a nonzero whole number, since z=0 would divide by zero.
What units should I use for the ion concentrations?+
Millimolar (mM) is the standard unit in physiology and is used in the worked examples on this page, but the formula only depends on the ratio [ion]out/[ion]in, so any consistent concentration unit (M, mM, or µM) works as long as both values use the same unit.
Is the Nernst potential the same as the resting membrane potential?+
No. The Nernst potential is the equilibrium potential for a single ion species considered alone. The actual resting membrane potential of a real cell depends on the permeabilities and Nernst potentials of multiple ions simultaneously (typically K+, Na+, and Cl-), and is calculated with the Goldman-Hodgkin-Katz equation, not the single-ion Nernst equation.
What happens to the Nernst potential if the concentrations on both sides are equal?+
If [ion]out equals [ion]in, the ratio inside the logarithm is 1, and ln(1)=0, so the Nernst potential is exactly 0 mV. With no concentration gradient, there is no driving force for net ion movement at any membrane voltage.
Tags: Nernst Potential Calculator Nernst Equation Calculator Equilibrium Potential Calculator Membrane Potential Electrochemical Gradient Calculator Formula Free Online

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What is the Nernst potential?

The Nernst potential (or equilibrium potential) is the membrane voltage at which the electrical force on an ion exactly balances its concentration gradient, so there is no net flow of that ion across the membrane. It is calculated with E=(RT/zF)ln([ion]out/[ion]in).

What is the Nernst equation formula?

E = (RT/zF) x ln([ion]out/[ion]in), where R is the gas constant (8.314 J/(mol*K)), T is absolute temperature in Kelvin, z is the ion's valence, F is Faraday's constant (96485 C/mol), and [ion]out and [ion]in are the extracellular and intracellular concentrations.

What is the resting potassium (K+) Nernst potential in a neuron?

Using typical mammalian neuron concentrations ([K+]out=5 mM, [K+]in=140 mM) at 37°C, the Nernst potential for K+ is about -89 mV, strongly negative, which is why potassium dominates the resting membrane potential of most neurons.

What is the sodium (Na+) Nernst potential in a neuron?

Using typical mammalian neuron concentrations ([Na+]out=145 mM, [Na+]in=12 mM) at 37°C, the Nernst potential for Na+ is about +67 mV, strongly positive, which is why an action potential's rapid depolarization phase drives the membrane voltage toward positive values as Na+ channels open.

Why is the chloride (Cl-) Nernst potential negative even though ln(out/in) is positive?

Because chloride's valence z=-1 is negative, dividing by a negative z flips the sign of the whole expression. With [Cl-]out=110 mM and [Cl-]in=4 mM, ln(110/4) is a positive number, but dividing by z=-1 makes the final Nernst potential negative, around -89 mV, this sign flip for anions is the single most common point of confusion when first learning the equation.

Why does this calculator default to 37°C instead of 25°C?

37°C (310.15 K) is human body temperature and the physiologically relevant value for mammalian cell membrane potentials. Some introductory textbooks use 25°C room temperature instead for simplicity, which changes the RT/zF prefactor and therefore the final millivolt value, always match the temperature to your source data.

Can the ion valence z be negative?

Yes, z is negative for anions. Chloride (Cl-) uses z=-1, and other monovalent anions like bicarbonate (HCO3-) also use z=-1. Divalent anions would use z=-2. This calculator validates that z is a nonzero whole number, since z=0 would divide by zero.

What units should I use for the ion concentrations?

Millimolar (mM) is the standard unit in physiology and is used in the worked examples on this page, but the formula only depends on the ratio [ion]out/[ion]in, so any consistent concentration unit (M, mM, or µM) works as long as both values use the same unit.

Is the Nernst potential the same as the resting membrane potential?

No. The Nernst potential is the equilibrium potential for a single ion species considered alone. The actual resting membrane potential of a real cell depends on the permeabilities and Nernst potentials of multiple ions simultaneously (typically K+, Na+, and Cl-), and is calculated with the Goldman-Hodgkin-Katz equation, not the single-ion Nernst equation.

What happens to the Nernst potential if the concentrations on both sides are equal?

If [ion]out equals [ion]in, the ratio inside the logarithm is 1, and ln(1)=0, so the Nernst potential is exactly 0 mV. With no concentration gradient, there is no driving force for net ion movement at any membrane voltage.

📌 Quick Tips

💡The default temperature is 37°C (310.15 K), human body temperature, since that is the physiologically relevant value for neurons and other mammalian cells. Some textbooks instead use 25°C room temperature for the Nernst equation, which gives a noticeably different result, always check which temperature a reference value assumes.
💡The sign of the ion valence z matters. Cations (K+, Na+, Ca2+) use a positive z, while anions (Cl-, HCO3-) use a negative z, which flips the sign of the final result compared to using the raw concentration ratio alone.
💡A concentration gradient alone does not tell you the sign of E, the valence does. The same concentration ratio produces opposite-sign potentials for a cation versus an anion.
💡The resting membrane potential of a real neuron (around -70 mV) is not equal to any single ion's Nernst potential, it is a weighted average of several ions' Nernst potentials set mainly by the Goldman-Hodgkin-Katz equation, dominated by whichever ion the membrane is most permeable to at rest (usually K+).
💡Since the formula uses a concentration ratio, any consistent concentration unit works (mM is standard in physiology), the units cancel inside the logarithm.