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Membrane Potential Calculator

Calculate membrane potential using Nernst or Goldman-Hodgkin-Katz equations

Typical Values

Resting potential: -70 to -90 mV (neurons)

Action potential peak: +30 to +40 mV

At rest, the membrane is most permeable to K+, so Vm is close to EK.

What Is Membrane Potential?

Membrane potential is the electrical voltage difference across a biological membrane, typically ranging from −90 mV to +40 mV in living cells. It arises from the unequal distribution of ions (primarily K⁺, Na⁺, and Cl⁻) across the cell membrane and the selective permeability of the membrane to different ion species. This voltage difference is fundamental to the function of neurons, muscle cells, and virtually all living cells.

The membrane potential plays a critical role in nerve impulse transmission, muscle contraction, and cellular signaling. In neurons, rapid changes in membrane potential form action potentials — the electrical signals that carry information through the nervous system. At rest, most neurons maintain a membrane potential of approximately −70 mV, established primarily by potassium ion diffusion through leak channels.

This calculator supports two calculation methods: the Nernst equation for finding the equilibrium potential of a single ion species, and the Goldman-Hodgkin-Katz (GHK) equation for estimating the overall membrane potential considering multiple ions and their relative permeabilities. Both methods are essential tools in electrophysiology and cellular biophysics.

The Nernst and GHK Equations

The Nernst equation calculates the equilibrium potential for a single ion species — the voltage at which the electrical force exactly balances the concentration gradient for that ion. The GHK equation extends this to multiple ions, weighting each by its membrane permeability.

Nernst and Goldman-Hodgkin-Katz Equations

E = (RT/zF) × ln([ion]out/[ion]in); Vm = (RT/F) × ln[(PK[K]o + PNa[Na]o + PCl[Cl]i) / (PK[K]i + PNa[Na]i + PCl[Cl]o)]

Where:

  • R= Universal gas constant (8.314 J/(mol·K))
  • T= Absolute temperature in Kelvin
  • z= Ion charge (valence)
  • F= Faraday constant (96,485 C/mol)
  • [ion]out/[ion]in= Extracellular and intracellular ion concentrations
  • PK, PNa, PCl= Relative permeabilities of K⁺, Na⁺, and Cl⁻

How to Use This Calculator

This calculator offers two modes for different analysis needs:

  1. Select Calculation Method: Choose "Nernst Equation" for single-ion equilibrium potentials or "Goldman-Hodgkin-Katz" for the combined membrane potential.
  2. Set Temperature: Enter the temperature in Kelvin (default 310 K, which is body temperature of 37°C).
  3. For Nernst Mode: Select the ion type (K⁺, Na⁺, Ca²⁺, Cl⁻, or H⁺), then enter the intracellular and extracellular concentrations in mM.
  4. For GHK Mode: Enter the relative permeabilities for K⁺, Na⁺, and Cl⁻, along with the intracellular and extracellular concentrations for all three ions in mM.
  5. View Results: The membrane potential is displayed in mV, with additional details including individual equilibrium potentials (in GHK mode) and the Nernst factor.

Interpreting the Results

A negative membrane potential means the inside of the cell is negative relative to the outside — this is the normal resting state for most cells. A positive potential means the inside is positive, which occurs during the peak of an action potential.

Individual equilibrium potentials: In GHK mode, the calculator shows EK, ENa, and ECl separately. The overall membrane potential sits between these values, weighted by permeability. Since resting cells are most permeable to K⁺ (PK ≫ PNa), the resting potential is closest to EK (approximately −90 mV).

Typical values: Resting neurons: −60 to −80 mV. Action potential peak: +30 to +40 mV. Skeletal muscle: −90 mV. Cardiac muscle: −85 mV. During an action potential, Na⁺ permeability increases dramatically, shifting the membrane potential toward ENa (+60 mV), before K⁺ channels restore the resting potential.

Real-World Applications

Membrane potential calculations are central to neuroscience, where they explain how neurons generate and propagate action potentials. Understanding the Nernst and GHK equations is essential for interpreting electroencephalograms (EEG), electromyograms (EMG), and other clinical electrophysiology recordings.

In cardiology, membrane potential dynamics explain heart rhythm generation and the mechanism of anti-arrhythmic drugs. The cardiac action potential has a distinctive plateau phase caused by calcium channel activity, which can be understood through GHK predictions.

In pharmacology, many drugs work by blocking specific ion channels, altering membrane permeabilities and thus changing the membrane potential. Local anesthetics block Na⁺ channels, while potassium-sparing diuretics affect K⁺ channels. Understanding the GHK equation helps predict how these drugs alter cellular excitability.

In plant biology, membrane potentials drive nutrient uptake, guard cell regulation for stomatal opening, and signal transmission in response to stimuli. The same fundamental equations apply across all kingdoms of life.

Worked Examples

Nernst Equation for Potassium

Problem:

Calculate the equilibrium potential for K⁺ at 37°C (310 K) with [K⁺]in = 140 mM and [K⁺]out = 4 mM.

Solution Steps:

  1. 1E = (RT/zF) × ln([out]/[in])
  2. 2R = 8.314, T = 310 K, z = +1, F = 96485 C/mol
  3. 3E = (8.314 × 310 / (1 × 96485)) × ln(4/140)
  4. 4E = 0.02669 × ln(0.02857) = 0.02669 × (−3.555) = −0.0949 V = −94.9 mV

Result:

EK = −94.9 mV (close to typical resting potential of −90 mV for K⁺ equilibrium)

GHK Equation for Resting Neuron

Problem:

Calculate the membrane potential for a neuron with PK=1, PNa=0.04, PCl=0.45, and standard concentrations at 37°C.

Solution Steps:

  1. 1Numerator = PK[K]o + PNa[Na]o + PCl[Cl]i = 1×4 + 0.04×145 + 0.45×4 = 4 + 5.8 + 1.8 = 11.6
  2. 2Denominator = PK[K]i + PNa[Na]i + PCl[Cl]o = 1×140 + 0.04×12 + 0.45×120 = 140 + 0.48 + 54 = 194.48
  3. 3Vm = (RT/F) × ln(11.6/194.48) = 0.02669 × ln(0.05964) = 0.02669 × (−2.820)
  4. 4Vm = −0.0753 V = −75.3 mV

Result:

Vm = −75.3 mV (typical resting membrane potential for a neuron)

Nernst Equation for Sodium

Problem:

Find the equilibrium potential for Na⁺ at 37°C with [Na⁺]in = 12 mM and [Na⁺]out = 145 mM.

Solution Steps:

  1. 1E = (RT/zF) × ln([out]/[in])
  2. 2E = (8.314 × 310 / (1 × 96485)) × ln(145/12)
  3. 3E = 0.02669 × ln(12.083) = 0.02669 × 2.492
  4. 4E = 0.06652 V = +66.5 mV

Result:

ENa = +66.5 mV (sodium equilibrium potential — why depolarization drives Na⁺ inward)

Tips & Best Practices

  • ✓At body temperature (37°C or 310 K), the Nernst factor RT/F ≈ 26.7 mV, giving E ≈ 61.5/z × log₁₀([out]/[in]) mV.
  • ✓A 10-fold change in concentration ratio changes the equilibrium potential by about 61.5/z mV at 37°C.
  • ✓The resting membrane potential is closest to EK because K⁺ permeability dominates at rest.
  • ✓During an action potential peak, the membrane potential approaches ENa because Na⁺ permeability becomes dominant.
  • ✓Use the GHK equation when considering the combined effect of multiple ions on membrane potential.
  • ✓Default concentrations in the calculator represent typical mammalian neuron values.

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Frequently Asked Questions

The resting membrane potential is negative because cells are most permeable to potassium ions at rest, and the K⁺ equilibrium potential is around −90 mV. The Na⁺/K⁺-ATPase pump also contributes by pumping 3 Na⁺ out for every 2 K⁺ in, creating a net negative charge inside. The resting potential settles between the K⁺ and Na⁺ equilibrium potentials, weighted by their permeabilities.
During an action potential, voltage-gated Na⁺ channels open rapidly, increasing Na⁺ permeability and depolarizing the membrane toward ENa (+60 mV). At the peak, Na⁺ channels inactivate and K⁺ channels open, repolarizing the membrane back toward EK. The Na⁺/K⁺-ATPase then restores ion gradients. This entire process takes about 1-2 milliseconds in neurons.
Temperature affects the Nernst factor (RT/F), which scales the logarithmic term. At higher temperatures, the same concentration gradient produces a slightly larger absolute potential. The factor RT/F at 25°C is 25.69 mV, while at 37°C it is 26.73 mV. Temperature also affects ion channel kinetics and membrane permeability, which have indirect effects on the actual membrane potential.
The Goldman (GHK) equation extends the Nernst equation to account for multiple ion species simultaneously, each with its own permeability. It predicts the actual membrane potential based on the relative permeabilities and concentrations of K⁺, Na⁺, and Cl⁻. This is more realistic than the Nernst equation alone because biological membranes are permeable to several ions at once.
Yes, membrane potential can be measured using intracellular microelectrodes, patch-clamp techniques, or fluorescent voltage-sensitive dyes. Microelectrodes pierce the cell membrane and measure the voltage relative to an external reference. Patch-clamp provides higher resolution and can measure single ion channel currents. These techniques are fundamental tools in electrophysiology research.

Sources & References

Last updated: 2026-06-06

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Editorial Note

MyCalcBuddy Editorial Team

This page is maintained as an educational calculator reference.

Source

Formula Source: Chemistry: The Central Science

by Brown, LeMay, Bursten

UpdatedLast reviewed: May 2026
CheckedFormula checks are based on standard references and internal QA review.