Membrane potential calculator: Nernst potentials and the Goldman-Hodgkin-Katz (GHK) equation with I-V curves

What it does

A nerve cell is negative inside because its membrane lets some ions through more easily than others, and those ions are at different concentrations inside and out. This calculator works out:

• the Nernst (equilibrium) potential of each ion: the voltage at which that ion would stop flowing, E = (RT/zF) ln(outside/inside);
• the membrane potential from the Goldman-Hodgkin-Katz (GHK) voltage equation, which weighs K⁺, Na⁺ and Cl⁻ by how permeable the membrane is to each;
• the driving force on each ion (membrane potential minus its Nernst potential) and its GHK current;
• GHK current-voltage curves for each ion and their total.

For electrodes and batteries, use the Nernst and cell potential calculator instead; this page is about cells and ion gradients. For study and teaching, not for clinical use.

How to use it

1. Concentrations: type each ion’s concentration outside and inside the cell, in mmol/L.
2. Permeability: relative to K⁺. The “Permeabilities” list fills in a resting membrane (K⁺ : Na⁺ : Cl⁻ = 1 : 0.05 : 0.45) or the peak of an action potential (1 : 20 : 0.45), which shows how opening Na⁺ channels swings the voltage.
3. Temperature changes RT/F: about 26.7 mV at 37 °C and 25.3 mV at 20 °C.
4. P of K⁺ in cm/s only sets the size of the currents.
5. Give Ca²⁺ a permeability to include it: the classic GHK voltage equation only handles ions of one charge, so the tool then also finds the potential where all four GHK currents add to zero.

Worked example

The illustrative example neuron at 37 °C: K⁺ 5 mM outside and 140 inside, Na⁺ 145 and 12, Cl⁻ 110 and 10, with resting permeabilities 1 : 0.05 : 0.45.

• E_K = −89.1 mV, E_Na = +66.6 mV, E_Cl = −64.1 mV, E_Ca = +132.3 mV.
• Membrane potential (GHK) = −64.9 mV.
• K⁺ has a driving force of +24.1 mV (it leaks out), Na⁺ −131.5 mV (it leaks in), and Cl⁻ is almost at equilibrium.
• Choosing “Spike peak” gives +51.1 mV.

Tips

• The membrane potential always lies between the Nernst potentials of the permeant ions, closest to the most permeant one.
• Raising outside K⁺ depolarises the cell strongly; raising outside Na⁺ at rest hardly does.
• The GHK curves rectify: K⁺ carries outward current more easily than inward because there is more K⁺ inside.

FAQ

Why does the sum of currents not include the Na⁺/K⁺ pump? The GHK equation describes passive leak only; the pump’s small electrogenic current is left out.

Does anything leave my device? No. Everything is worked out in your browser.

Last updated 2026-11-09.