Electrochemical Gradient Calculator

Calculator inputs

Choose a mode, confirm the sign convention, and enter values for the membrane system.

Calculation mode

Ion preset

Ion name

Ion charge, z

Inside concentration

Inside concentration unit

Outside concentration

Outside concentration unit

Membrane potential

Vm is inside minus outside.

Voltage unit

Inside activity coefficient

Outside activity coefficient

Use activity coefficients instead of ideal concentrations

Internal pH

External pH

Proton direction

Goldman–Hodgkin–Katz inputs

Potassium permeability

K⁺ inside

K⁺ outside

Sodium permeability

Na⁺ inside

Na⁺ outside

Chloride permeability

Cl⁻ inside

Cl⁻ outside

Custom cation permeability

Custom cation inside

Custom cation outside

Custom anion permeability

Custom anion inside

Custom anion outside

Use one concentration unit consistently across all GHK entries. Relative permeability values are acceptable.

Scientific options

Temperature

Temperature unit

Gas constant R

J·mol⁻¹·K⁻¹

Faraday constant F

C·mol⁻¹

Energy result unit

Decimal precision

Equilibrium tolerance

mV difference from equilibrium

Use scientific notation

Formula used

Electrochemical potential for movement from inside to outside:

Δμ̃ = RT ln(a_out/a_in) + zF(V_out − V_in)

Nernst potential with Vm = inside − outside:

E_ion = (RT/zF) ln(a_out/a_in)

Ionic driving force: Vm − E_ion

GHK voltage: Vm = (RT/F) ln[(P_KK_out + P_NaNa_out + P_ClCl_in)/(P_KK_in + P_NaNa_in + P_ClCl_out)]

The calculator uses natural logarithms internally. It converts supported units before applying each equation.

How to use this calculator

Select a single-ion, proton, equilibrium, or GHK calculation mode.
Choose an ion preset or enter a custom ion charge.
Enter membrane concentrations, potential, temperature, and optional activity coefficients.
Confirm that membrane potential means inside minus outside.
Select result units, precision, and equilibrium tolerance.
Calculate, review the direction interpretation, then export or print the results.

Example data

Example	Inside	Outside	Charge	Vm	Temperature
Potassium in a neuron	140 mmol/L	5 mmol/L	+1	−70 mV	37°C
Sodium in a neuron	15 mmol/L	145 mmol/L	+1	−70 mV	37°C
Chloride in a cell	10 mmol/L	120 mmol/L	−1	−65 mV	37°C
Calcium gradient	0.0001 mmol/L	2 mmol/L	+2	−60 mV	37°C
Mitochondrial proton example	pH 7.8	pH 7.0	+1	−150 mV	37°C

Understanding electrochemical gradients

An electrochemical gradient combines concentration differences with voltage differences across a membrane. The chemical term depends on the activity ratio between two sides. The electrical term also depends on ionic charge.

A positive ion responds differently from a negative ion. This is why chloride requires careful sign handling during interpretation. The calculator preserves charge direction throughout every supported equation.

The Nernst potential identifies the voltage that balances one ion. At that voltage, its net passive driving force approaches zero. Real membranes may still carry flux through coupled processes.

Activity coefficients improve estimates when solutions are not ideally dilute. They adjust effective concentration without changing the entered concentration itself. Strong electrolytes may require experimentally measured activity values.

The Goldman equation estimates voltage when several permeant ions contribute. Relative permeability controls how strongly each ion affects the result. Anions appear in reversed concentration positions within that equation.

Proton gradients are often expressed through proton motive force. This combines membrane voltage with the pH difference across membranes. It helps describe energy available for transport and synthesis.

Calculated direction describes thermodynamic preference rather than guaranteed biological flux. Channels, pumps, transporters, and membrane permeability determine actual movement rates. Use measured system values whenever precise conclusions are required.

Very large ratios can magnify errors in concentration measurements. Temperature and sign conventions also change the reported equilibrium voltage. Always document assumptions before comparing results across different sources.

Frequently asked questions

What does a positive electrochemical potential mean?

For the selected inside-to-outside direction, a positive value means that movement is thermodynamically unfavorable without added energy.

Why is membrane voltage defined as inside minus outside?

This convention is common in membrane physiology and keeps the Nernst comparison consistent across the calculator.

Can I calculate an anion such as chloride?

Yes. Enter a negative charge, such as −1, and the electrical contribution will reverse correctly.

When should activity coefficients be used?

Use them when nonideal solution behavior is important or when measured activities are available.

What is the difference between Nernst and GHK calculations?

The Nernst equation treats one ion, while the GHK equation combines several permeant ions.

Can mEq/L be used for divalent ions?

Yes. The calculator divides equivalents by the absolute ionic charge to obtain molar concentration.

What does proton motive force represent?

It represents the combined electrical and pH components available to drive proton-linked processes.

Why can the predicted direction differ from observed flux?

Observed flux also depends on permeability, transport proteins, coupling, kinetics, and regulatory mechanisms.

Is this calculator suitable for clinical decisions?

No. It is an educational and research aid, not a substitute for validated clinical methods.