Nernst Equation Calculator

For calculating equilibrium potential across a biological membrane.

Please check your inputs. Valence cannot be zero and concentrations must be positive numbers.

Potential vs. Concentration Ratio

This chart illustrates how the equilibrium potential changes as the ratio of extracellular to intracellular ion concentration varies.

What is Calculating Equilibrium Potential Using the Nernst Equation?

Calculating the equilibrium potential using the Nernst equation is a fundamental process in biophysics and physiology. It determines the specific membrane voltage at which the electrical force acting on an ion is equal and opposite to the chemical force produced by its concentration gradient across a cell membrane. At this equilibrium, there is no net movement of the ion across the membrane. This calculation is crucial for understanding neuronal signaling, muscle contraction, and cellular homeostasis. It’s used by neuroscientists, physiologists, and students to predict the behavior of ions like sodium (Na⁺), potassium (K⁺), calcium (Ca²⁺), and chloride (Cl⁻).

A common misunderstanding is that the Nernst potential is the same as the cell’s resting membrane potential. The resting potential is determined by the combined contributions of *all* permeable ions, weighted by their permeability, as described by the Goldman-Hodgkin-Katz (GHK) equation. The Nernst potential, by contrast, applies to only a single ion species at a time.

The Nernst Equation Formula and Explanation

The Nernst equation provides the theoretical equilibrium potential for a single ion. The formula is:

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

Here, the result E_ion is given in Volts, which our calculator converts to millivolts (mV) for convenience, as is standard in electrophysiology.

Variables in the Nernst Equation

Variable	Meaning	Unit	Typical Range
Eion	Equilibrium Potential	Volts (V) or Millivolts (mV)	-100 mV to +100 mV
R	Ideal Gas Constant	Joules / (Kelvin · mole)	8.314 J/(K·mol)
T	Absolute Temperature	Kelvin (K)	~293 K (Room temp) to ~310 K (Body temp)
z	Valence of the ion	Unitless (integer)	-2, -1, +1, +2
F	Faraday Constant	Coulombs / mole	96485 C/mol
[Ion]out/in	Ion Concentration	Millimolar (mM)	1 mM to 150 mM

Practical Examples

Example 1: Potassium (K⁺) Equilibrium Potential

Let’s calculate the Nernst potential for potassium in a typical neuron at body temperature (37°C).

• Inputs:
• Temperature (T): 37 °C
• Valence (z): +1
• [K⁺]_out: 5 mM
• [K⁺]_in: 140 mM
• Result: The calculated equilibrium potential for K⁺ is approximately -89.8 mV. This negative value indicates that the inside of the cell must be negative to counteract the strong outward-pushing concentration gradient of potassium. For more on this, see our article on {related_keywords}.

Example 2: Chloride (Cl⁻) Equilibrium Potential

Now, let’s calculate the potential for chloride, a negative ion, at the same temperature.

• Inputs:
• Temperature (T): 37 °C
• Valence (z): -1
• [Cl⁻]_out: 110 mM
• [Cl⁻]_in: 10 mM
• Result: The calculated equilibrium potential for Cl⁻ is approximately -64.2 mV. This shows that even though the concentration gradient pushes Cl⁻ inward, its negative charge means the inside of the cell must also be negative to reach equilibrium. Understanding ion channels is crucial here, as explained in our guide to {related_keywords}.

How to Use This Nernst Equation Calculator

Follow these steps to accurately determine an ion’s equilibrium potential.

1. Enter Temperature: Input the temperature of the system. You can use Celsius or Kelvin; the calculator converts automatically. The standard for biological systems is 37°C.
2. Set Ion Valence: Provide the charge of the ion (e.g., +1 for Na⁺, -1 for Cl⁻). This is a critical factor in the electrical component of the equation.
3. Input Concentrations: Enter the extracellular ([Ion] Outside) and intracellular ([Ion] Inside) concentrations. Ensure they are in the same unit, typically millimolar (mM).
4. Interpret the Results: The primary result is the equilibrium potential in millivolts (mV). This is the voltage needed to prevent any net flow of the ion. The intermediate values show the constants used in the calculation. You can learn more about cell potentials on our blog.

Key Factors That Affect Equilibrium Potential

• Concentration Gradient: The ratio of [Ion]out to [Ion]in is the most powerful factor. A larger gradient results in a larger (more positive or more negative) equilibrium potential.
• Ion Valence (z): The charge of the ion determines the sign and magnitude of the electrical force. A divalent ion like Ca²⁺ (z=+2) will have an equilibrium potential half as large as a monovalent ion like Na⁺ (z=+1) for the same gradient.
• Temperature (T): Higher temperatures increase the kinetic energy of ions, thus increasing the magnitude of the equilibrium potential. The effect is typically minor in biological systems where temperature is stable.
• Membrane Permeability: While not part of the Nernst equation itself, an ion can only influence the membrane potential if the membrane is permeable to it. Without open ion channels, the Nernst potential is purely theoretical. Our article on {related_keywords} delves deeper into this.
• Presence of Other Ions: The Nernst equation assumes a membrane permeable to only one ion. In reality, multiple ions are permeable, and the actual membrane potential is a weighted average, calculated by the GHK equation.
• Activity vs. Concentration: This calculator, like most simplified models, uses concentrations. In reality, ionic interactions mean the effective concentration, or “activity,” is slightly lower. For most biological purposes, concentration is a sufficient approximation. Explore the concept of {related_keywords} for more details.

Frequently Asked Questions (FAQ)

1. What does a positive equilibrium potential mean?

A positive equilibrium potential (e.g., for Na⁺) means the inside of the cell must be positive relative to the outside to stop the ion from flowing in along its concentration gradient.

2. What does a negative equilibrium potential mean?

A negative equilibrium potential (e.g., for K⁺) means the inside of the cell must be negative to counteract the ion’s tendency to flow out along its concentration gradient.

3. Why is the valence (z) important?

Valence determines both the direction of the electrical force (a negative ion is pushed by a negative field) and its strength. A charge of +2 requires twice the electrical force to balance compared to a charge of +1.

4. Can I use different units for concentration?

Yes, as long as the units for intracellular and extracellular concentration are the same. The equation relies on the *ratio* of the concentrations, so the specific unit (mM, µM, etc.) cancels out.

5. What happens if the valence is 0?

An uncharged molecule (like glucose) has a valence of zero and is not directly affected by membrane voltage. The Nernst equation is not applicable as it would involve division by zero. Transport depends on concentration gradients and transporters only.

6. Why does my result say “NaN” or “Error”?

This typically occurs if you enter a valence of 0, or non-positive values for concentrations. The logarithm of a non-positive number is undefined.

7. How does this differ from the Goldman-Hodgkin-Katz (GHK) equation?

The Nernst equation calculates the potential for a single ion. The GHK equation calculates the overall membrane potential by considering the concentrations *and* relative permeabilities of multiple ions (like K⁺, Na⁺, and Cl⁻) simultaneously.

8. What temperature should I use?

For mammalian cells, 37°C (310.15 K) is standard. For experiments at room temperature, use around 20-22°C (293-295 K).