Action Potential & Membrane Potential Calculator

Calculate action potential threshold, resting membrane potential, and Nernst equation for ions.

Calculate

Ion concentration inside [X]i (mM) (mM)

Ion concentration outside [X]o (mM) (mM)

Ion valence z

K+=+1, Na+=+1, Cl-=-1, Ca2+=+2

Temperature T (°C) (°C)

Please check your inputs and try again.

Nernst Versus Goldman

The Nernst equation gives the equilibrium potential for one ion — the voltage at which its electrical and chemical gradients balance exactly. Real membranes are permeable to several ions at once, so resting potential requires the Goldman equation.

E_ion = (RT/zF) ln([X]_out/[X]_in) = (61.5/z) log₁₀([X]_out/[X]_in) mV at 37°C

Ion	Inside	Outside	E at 37°C
K⁺	140 mM	5 mM	−89 mV
Na⁺	15 mM	145 mM	+61 mV
Cl⁻	10 mM	110 mM	−64 mV
Ca²⁺	0.0001 mM	2 mM	+132 mV

Resting potential sits near −70 mV, close to E_K but not at it, because the membrane is mostly but not exclusively potassium-permeable. The small sodium leak pulls it a few millivolts positive of E_K.

Why the Action Potential Has Its Shape

An action potential is the membrane's permeability shifting from potassium-dominated to sodium-dominated and back. The peak approaches E_Na without reaching it, because potassium channels are already opening as sodium channels inactivate.

Phase	Dominant permeability	Membrane potential moves toward
Rest	K⁺	E_K = −89 mV
Upstroke	Na⁺	E_Na = +61 mV
Repolarisation	K⁺	E_K
Afterhyperpolarisation	K⁺ (still elevated)	Briefly closer to E_K than rest

Note the calcium figure: because intracellular calcium is held around 10⁻⁷ M, its equilibrium potential is over +130 mV. This enormous driving force is why small calcium currents produce large signalling effects, and why calcium is used as a second messenger rather than a charge carrier.

Very few ions actually cross during an action potential — concentrations change immeasurably. The Na⁺/K⁺ ATPase maintains gradients over time but is not what repolarises the membrane.

Worked Examples

Example 1: K+ Nernst: [K+]i=140mM, [K+]o=5mM

E=(RT/F)×ln(5/140) at 37°C

Result: E=-89.1mV — close to resting potential

K+ equilibrium potential near resting V_m

Example 2: Na+ Nernst: [Na+]i=15mM, [Na+]o=145mM

E=(RT/F)×ln(145/15) at 37°C

Result: E=+60.6mV — positive, drives depolarization

Na+ influx during action potential upstroke

Example 3: Why calcium signalling is so effective

E_Ca above +130 mV

Result: Enormous driving force

Intracellular calcium is held near 10⁻⁷ M, so opening a few channels produces a large relative concentration change — ideal for signalling.

Example 4: Why resting potential is not E_K

Membrane mostly K⁺-permeable, small Na⁺ leak

Result: −70 mV rather than −89 mV

The sodium leak pulls the potential positive of the potassium equilibrium. Goldman weighting by relative permeability gives the observed value.

Common Mistakes

⚠️

Using Nernst to calculate resting potential

Nernst applies to a single ion at equilibrium. Resting potential involves several permeabilities and requires the Goldman equation.

⚠️

Expecting the action potential peak to reach E_Na

Potassium channels open as sodium channels inactivate, so the peak falls short of the sodium equilibrium potential.

⚠️

Thinking the sodium pump repolarises the membrane

Repolarisation is driven by potassium efflux through voltage-gated channels. The pump restores gradients over a much longer timescale.

⚠️

Forgetting valence for divalent ions

Calcium carries z = 2, halving the Nernst slope. Using z = 1 doubles the calculated equilibrium potential.

Frequently Asked Questions

Hodgkin-Huxley model?

V_m changes caused by voltage-gated Na+ and K+ channels. Depolarization → Na+ channels open (fast) → AP upstroke. Na+ inactivation + K+ channels open → repolarization. K+ channel slow closing → hyperpolarization. Used to model all excitable cells.

Resting vs action potential?

Resting: V_m≈-70mV, high K+ permeability (leak channels). Action potential: V_m rises to +40mV (Na+ influx) then falls back (-70mV, K+ efflux). Speed: 0.5 m/s (unmyelinated) to 100 m/s (myelinated, saltatory conduction).

What does the Nernst equation give?

The equilibrium potential for a single ion — the membrane voltage at which its electrical and chemical gradients exactly balance.

Why is resting potential not equal to E_K?

Because the membrane has a small sodium permeability that pulls the potential positive of the potassium equilibrium. Goldman accounts for multiple ions.

Why doesn't the action potential reach E_Na?

Potassium channels open while sodium channels inactivate, so the two permeabilities overlap and the peak falls short.

Why is the calcium equilibrium potential so high?

Because intracellular calcium is held extremely low, around 10⁻⁷ M. The steep gradient gives an equilibrium potential above +130 mV.