Nernst Potential Calculator

Easily calculate the equilibrium potential for any ion across a membrane using our Nernst Potential Calculator.

Calculate Nernst Potential

Typical Nernst Potentials at 37°C

Ion	Valence (z)	[Ion]out (mM)	[Ion]in (mM)	Nernst Potential (mV)
K+	1	5	150	-90.1
Na+	1	145	15	+60.8
Cl-	-1	110	10	-64.0
Ca2+	2	1.8	0.0001	+130.6

Approximate Nernst potentials for common ions in a typical mammalian neuron at 37°C.

What is a Nernst Potential Calculator?

A Nernst Potential Calculator is a tool used to determine the equilibrium potential (also known as the Nernst potential or reversal potential) for a specific ion across a cell membrane. This potential is the membrane voltage at which there is no net flow of that particular ion across the membrane, assuming the membrane is permeable only to that ion. The Nernst Potential Calculator uses the Nernst equation, which relates the equilibrium potential to the ion’s valence, the temperature, and the concentrations of the ion inside and outside the cell.

Biologists, neuroscientists, physiologists, and students use a Nernst Potential Calculator to understand how ion concentration gradients contribute to the membrane potential of cells, particularly nerve and muscle cells. It’s fundamental for understanding phenomena like resting membrane potential and the generation of action potentials. The Nernst Potential Calculator helps predict the direction an ion will move across the membrane at a given membrane potential.

Common misconceptions include thinking the Nernst potential is the actual membrane potential (it’s the equilibrium for *one* ion, while the actual membrane potential, like the resting potential, is influenced by multiple ions and their permeabilities – see the Goldman-Hodgkin-Katz equation), or that it requires active transport (it describes the equilibrium based on existing gradients, though active transport maintains those gradients long-term). Our Nernst Potential Calculator simplifies these calculations.

Nernst Potential Calculator Formula and Mathematical Explanation

The Nernst equation is used by the Nernst Potential Calculator to find the equilibrium potential (E_ion) for a specific ion:

E_ion = (RT / zF) * ln([Ion]_out / [Ion]_in)

Where:

• E_ion is the Nernst potential for the ion (in Volts).
• R is the ideal gas constant (8.314 J·mol^-1·K^-1).
• T is the absolute temperature (in Kelvin).
• z is the valence (charge) of the ion (e.g., +1 for K⁺, +2 for Ca²⁺, -1 for Cl^–).
• F is Faraday’s constant (96485 C·mol^-1).
• ln is the natural logarithm.
• [Ion]_out is the concentration of the ion outside the cell.
• [Ion]_in is the concentration of the ion inside the cell.

To get the result in millivolts (mV), we multiply by 1000. Also, it’s common to use logarithm base 10, so the equation becomes:

E_ion (mV) = (2.303 * RT / zF) * log₁₀([Ion]_out / [Ion]_in) * 1000

At a typical body temperature of 37°C (310.15 K), the term (2.303 * RT / F) * 1000 is approximately 61.54 mV. So, at 37°C:

E_ion (mV) ≈ (61.54 / z) * log₁₀([Ion]_out / [Ion]_in)

Our Nernst Potential Calculator performs these calculations precisely based on the temperature you input.

Variables in the Nernst Equation

Variable	Meaning	Unit	Typical Value/Range
Eion	Nernst Potential	Volts (V) or Millivolts (mV)	-100 to +150 mV
R	Ideal Gas Constant	J·mol^-1·K^-1	8.314
T	Absolute Temperature	Kelvin (K)	273.15 to 313.15 K (0 to 40°C)
z	Valence of the ion	Dimensionless	+1, +2, -1, -2
F	Faraday’s Constant	C·mol^-1	96485
[Ion]out	External ion concentration	mM (millimolar)	0.0001 to 200 mM
[Ion]in	Internal ion concentration	mM (millimolar)	0.0001 to 200 mM

Practical Examples (Real-World Use Cases)

Let’s see how the Nernst Potential Calculator works with typical physiological values.

Example 1: Potassium (K+) in a Neuron

• Temperature: 37°C (310.15 K)
• Valence (z): +1
• [K+]_out: 5 mM
• [K+]_in: 150 mM

Using the Nernst Potential Calculator or the formula at 37°C: E_K ≈ (61.54 / 1) * log₁₀(5 / 150) ≈ 61.54 * log₁₀(0.0333) ≈ 61.54 * (-1.477) ≈ -90.9 mV. The calculator above gives a more precise value based on the exact temperature and constants.

Interpretation: If the membrane were only permeable to K+, the membrane potential would be around -90.9 mV. At the typical resting membrane potential (around -70 mV), K+ ions have a net tendency to move out of the cell, down their electrochemical gradient.

Example 2: Sodium (Na+) in a Neuron

• Temperature: 37°C (310.15 K)
• Valence (z): +1
• [Na+]_out: 145 mM
• [Na+]_in: 15 mM

Using the Nernst Potential Calculator: E_Na ≈ (61.54 / 1) * log₁₀(145 / 15) ≈ 61.54 * log₁₀(9.667) ≈ 61.54 * (0.985) ≈ +60.6 mV.

Interpretation: The equilibrium potential for Na+ is about +60.6 mV. At resting potential (-70 mV), there’s a strong electrochemical driving force for Na+ to enter the cell if ion channels permeable to Na+ open.

How to Use This Nernst Potential Calculator

1. Select Ion (Optional): Choose a common ion from the dropdown (K+, Na+, Cl-, Ca2+). This will pre-fill typical valence and concentration values, which you can then adjust. Select “Custom” to enter all values manually.
2. Enter Temperature: Input the temperature in Celsius. The calculator converts it to Kelvin for the calculation.
3. Enter Valence (z): Specify the charge of the ion (e.g., 1 for K+, -1 for Cl-, 2 for Ca2+). This is auto-filled if you select an ion.
4. Enter Concentrations: Input the ion concentration outside ([Ion]out) and inside ([Ion]in) the cell, both in mM. Ensure these are positive values.
5. Calculate: Click the “Calculate” button or see results update as you type if inputs are valid.
6. Read Results: The primary result is the Nernst Potential in mV. Intermediate values like RT/F, the concentration ratio, and the logarithm of the ratio are also shown for clarity.
7. Use Reset: Click “Reset” to return to default values (K+ at 37°C with typical concentrations).
8. Copy Results: Click “Copy Results” to copy the main result and key parameters to your clipboard.

The Nernst Potential Calculator helps you understand the driving force on an ion at different membrane potentials. If the actual membrane potential is different from the Nernst potential for an ion, there will be a net movement of that ion across the membrane if it is permeable to it, contributing to the overall electrochemical gradient.

Key Factors That Affect Nernst Potential Calculator Results

1. Temperature (T): The Nernst potential is directly proportional to the absolute temperature (in Kelvin). Higher temperatures result in a larger magnitude of the Nernst potential (for a given ratio and valence), meaning a steeper electrical gradient is needed to balance the concentration gradient.
2. Valence of the Ion (z): The valence appears in the denominator, so ions with higher valences (like Ca²⁺, z=2) will have a smaller Nernst potential for the same concentration ratio compared to monovalent ions (like K⁺, z=1). The sign of the valence also determines the sign of the potential relative to the concentration ratio.
3. Concentration Gradient ([Ion]_out / [Ion]_in): This is the most significant factor. The Nernst potential is proportional to the logarithm of the ratio of the external to internal ion concentrations. A larger concentration difference leads to a larger magnitude Nernst potential.
4. Gas Constant (R) and Faraday’s Constant (F): These are physical constants, so they don’t vary under normal biological conditions, but they are crucial components of the equation used by the Nernst Potential Calculator.
5. Logarithm Base: Whether natural logarithm (ln) or base-10 logarithm (log₁₀) is used affects the constant factor (RT/F vs. 2.303*RT/F). Our Nernst Potential Calculator uses the natural log internally but can be expressed with log10 for the ~61.54 mV/z factor at 37°C.
6. Permeability (Indirect): While not directly in the Nernst equation, the permeability of the membrane to the ion is crucial. The Nernst potential only becomes relevant to the *actual* membrane potential if the membrane is permeable to that ion. The resting membrane potential is determined by the Nernst potentials and relative permeabilities of multiple ions.

Frequently Asked Questions (FAQ)

What is the Nernst potential?

The Nernst potential (or equilibrium potential) is the membrane voltage at which the electrical force on an ion is equal and opposite to the chemical force due to its concentration gradient, resulting in no net movement of the ion across the membrane (if it were permeable only to that ion).

How does the Nernst Potential Calculator work?

It uses the Nernst equation, inputting temperature, ion valence, and concentrations inside and outside the cell to calculate the equilibrium potential for that ion.

Why is temperature important in the Nernst equation?

Temperature influences the kinetic energy of ions and thus the magnitude of the electrical potential required to balance a given concentration gradient. The Nernst potential is directly proportional to the absolute temperature.

What does the valence ‘z’ represent?

‘z’ is the charge of the ion. For example, z=+1 for K⁺ and Na⁺, z=+2 for Ca²⁺, and z=-1 for Cl^–.

Can the Nernst potential be measured directly?

The Nernst potential is a theoretical value calculated for a single ion. The actual membrane potential can be measured and is influenced by the Nernst potentials and permeabilities of multiple ions, as described by the Goldman-Hodgkin-Katz equation. Our Goldman-Hodgkin-Katz calculator can help with that.

What if the concentrations are equal inside and outside?

If [Ion]_out = [Ion]_in, the ratio is 1, and log(1) = 0, so the Nernst potential is 0 mV, regardless of temperature or valence. There’s no concentration gradient to balance.

What units are used in the Nernst Potential Calculator?

Temperature is in Celsius (converted to Kelvin), concentrations are in mM, and the resulting Nernst potential is given in millivolts (mV).

How does the Nernst potential relate to the resting membrane potential?

The resting membrane potential of a cell is close to the Nernst potential of the ion to which the membrane is most permeable at rest (usually K+), but it’s also influenced by other ions like Na+ and Cl- according to their relative permeabilities. It’s a weighted average, as seen in the GHK equation. Explore more about cell physiology basics.