Membrane Potential Calculator
Calculate resting membrane potential using the Nernst equation and Goldman-Hodgkin-Katz equation. Find reversal potential for ion channels and action potential thresholds.
🧬 Cell Biology📐 E = (RT/zF) × ln([X]out/[X]in)🧬 Biology
Ion concentration outside (mM)
Ion concentration inside (mM)
Ion valence z
Temperature T (K)
Please enter valid values.
Formula & Reference
| Variable | Symbol | Formula | Units |
|---|---|---|---|
| Membrane Potential Calculator | — | E = (RT/zF) × ln([X]out/[X]in) | mV |
Step-by-Step Examples
Example 1
Na⁺ Equilibrium Potential
[Na⁺]out = 145 mM, [Na⁺]in = 15 mM, z = +1, T = 310 K.
- E(Na) = (8.314x310/(1x96485)) x ln(145/15) x 1000
- = 0.02671 x ln(9.67) x 1000
- = 0.02671 x 2.269 x 1000 = +60.6 mV
✓ E(Na⁺) = +61 mV (Na⁺ wants to flow in)
Example 2
K⁺ Equilibrium Potential
[K⁺]out = 5 mM, [K⁺]in = 150 mM, z = +1.
- E(K) = (0.02671) x ln(5/150) x 1000
- = 0.02671 x (-3.401) x 1000 = -90.8 mV
✓ E(K⁺) = -91 mV (resting potential ~-70 mV is close to K⁺ equilibrium)
Example 3
Cl⁻ Equilibrium Potential
[Cl⁻]out = 110 mM, [Cl⁻]in = 10 mM, z = -1.
- E(Cl) = (0.02671/(-1)) x ln(110/10) x 1000
- = -0.02671 x 2.398 x 1000 = -63.8 mV
✓ E(Cl⁻) = -64 mV
Real-World Applications
Neuroscience
Action potentials depend on voltage-gated Na⁺ and K⁺ channels. Nernst equation predicts their driving forces.
Cardiac Physiology
Cardiac action potential shaped by Na⁺, K⁺, Ca²⁺, and Cl⁻ equilibrium potentials.
Cell Biology
Mitochondrial membrane potential (~-180 mV inside negative) drives ATP synthesis by ATP synthase.
Pharmacology
Local anesthetics (lidocaine) block Na⁺ channels. Antiarrhythmics target cardiac ion channels.
Common Mistakes to Avoid
⚠️
Sign matters: cation vs anion
For cations (z>0): higher outside than inside gives positive E. For anions (z<0): higher outside gives negative E.
⚠️
Nernst vs Goldman equation
Nernst: equilibrium potential for ONE ion. Goldman: weighted average considering permeability of all ions. Goldman gives the resting membrane potential.
⚠️
Temperature affects potential
At 37 C (310 K): RT/F = 26.7 mV. At 25 C (298 K): 25.7 mV. At 37 C with z=1: change 10-fold in ratio = 61.5 mV (Nernst).
Frequently Asked Questions
What is the Nernst equation? ▾
E = (RT/zF) ln([X]out/[X]in). Gives the equilibrium potential for one ionic species -- the voltage at which there is no net driving force for that ion.
What is the resting membrane potential? ▾
Typically -70 mV in neurons (inside negative). Maintained by: high K⁺ permeability at rest (K⁺ equilibrium near -90 mV), Na⁺/K⁺ ATPase pumping, lower Na⁺ and Cl⁻ permeability.
What is an action potential? ▾
A rapid, transient reversal of membrane potential from -70 mV to about +40 mV. Triggered by depolarization above threshold. Na⁺ channels open (fast, inward current), then K⁺ channels open (repolarization).
What is the Goldman equation? ▾
Considers multiple ions simultaneously, weighted by permeability: Em = (RT/F) ln((PK[K]o + PNa[Na]o + PCl[Cl]i)/(PK[K]i + PNa[Na]i + PCl[Cl]o)). Gives actual resting Vm.
What causes long QT syndrome? ▾
Mutations in cardiac K⁺ channel genes (HERG) reduce repolarization current. Action potential is prolonged. Risk of ventricular fibrillation. Some drugs also block HERG (drug-induced long QT).