Goldman Equation Calculator

The Goldman Equation Calculator predicts the resting membrane potential of a cell based on how permeable its membrane is to different ions — a core concept in neuroscience and cell biology. Enter the intracellular and extracellular concentrations of potassium (K+), sodium (Na+), and chloride (Cl-), along with each ion's relative permeability and the temperature, to calculate the Membrane Potential (Vm). Secondary outputs include the individual equilibrium potentials for each ion — EK, ENa, and ECl.

K

Temperature in Kelvin (310K = 37°C body temperature)

mM

Extracellular potassium concentration

mM

Intracellular potassium concentration

Relative permeability to potassium

mM

Extracellular sodium concentration

mM

Intracellular sodium concentration

Relative permeability to sodium

mM

Extracellular chloride concentration

mM

Intracellular chloride concentration

Relative permeability to chloride

Results

Membrane Potential (Vm)

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K+ Equilibrium Potential (EK)

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Na+ Equilibrium Potential (ENa)

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Cl- Equilibrium Potential (ECl)

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Frequently Asked Questions

What is the Goldman-Hodgkin-Katz equation?

The Goldman-Hodgkin-Katz (GHK) equation calculates the membrane potential when multiple ions contribute to it. Unlike the Nernst equation which considers only one ion, the GHK equation accounts for the permeabilities and concentrations of multiple ions simultaneously.

How does the GHK equation differ from the Nernst equation?

The Nernst equation calculates the equilibrium potential for a single ion, while the GHK equation considers multiple ions and their relative permeabilities. The GHK equation is more realistic for biological membranes where several ions contribute to the membrane potential.

What do the permeability values represent?

Permeability values (PK, PNa, PCl) represent how easily each ion can cross the membrane. Higher permeability means the ion has more influence on the membrane potential. These values are typically expressed relative to each other.

Why is temperature important in the calculation?

Temperature affects the kinetic energy of ions and influences their movement across membranes. The GHK equation includes temperature in the RT/F term, where higher temperatures generally lead to more positive potentials due to increased ion mobility.

What are typical ion concentration values for mammalian cells?

Typical concentrations are: K+ (5mM outside, 140mM inside), Na+ (145mM outside, 15mM inside), and Cl- (110mM outside, 10mM inside). These gradients are maintained by active transport mechanisms like the Na+/K+ pump.

How does membrane permeability affect the resting potential?

The ion with the highest permeability has the greatest influence on membrane potential. In resting neurons, K+ typically has the highest permeability, making the membrane potential closer to the K+ equilibrium potential (-90mV).

What causes the membrane potential to be different from individual equilibrium potentials?

When multiple ion channels are open, each ion tries to drive the membrane toward its own equilibrium potential. The actual membrane potential is a weighted average based on each ion's permeability and concentration gradient.