Goldman Equation Calculator

Model resting potential with flexible permeability inputs. Switch temperature units, validate ranges, and see warnings. Download tidy tables and share calculations with colleagues easily.

Calculator Inputs

Common: 37 °C or 310.15 K.
Default uses natural logarithm.
mV is typical for physiology.

Permeabilities (relative) Use ratios; Pk often set to 1.

Ion concentrations (mM) All values must be greater than zero.

Example Data

This sample uses common physiological values. Your results may differ based on tissue and conditions.

TempPkPnaPcl K+ inK+ out Na+ inNa+ out Cl inCl out Vm (mV)
37 °C10.040.45 1405 15145 10110 −67.34

Tip: changing Pna upward typically makes Vm less negative.

Formula Used

The calculator uses the Goldman-Hodgkin-Katz voltage equation:

Vm = (R·T/F) · ln( (Pk·[K]out + Pna·[Na]out + Pcl·[Cl]in) / (Pk·[K]in + Pna·[Na]in + Pcl·[Cl]out) )

  • R is the gas constant (8.314462618 J/mol·K).
  • T is absolute temperature in Kelvin.
  • F is Faraday’s constant (96485.33212 C/mol).
  • P values are relative permeabilities.
  • Cl⁻ terms are reversed because chloride is an anion.

How to Use This Calculator

  1. Choose temperature units and enter the temperature value.
  2. Set permeabilities for K⁺, Na⁺, and Cl⁻ (relative values).
  3. Enter inside and outside concentrations in mM.
  4. Click Calculate to see Vm below the header.
  5. Use Download CSV or Download PDF for records.

Goldman Equation Guide

1. Purpose of the Goldman equation

The Goldman equation estimates membrane voltage when several ions contribute. It is widely used to model resting potentials, where K+, Na+, and Cl dominate the electrical balance across a thin membrane.

2. Why permeability matters

Concentration gradients provide the driving force, but permeability controls how strongly each ion influences voltage. Increasing Pk makes Vm more negative, while increasing Pna generally depolarizes Vm toward zero.

3. Handling chloride correctly

Chloride is an anion, so its terms appear “swapped” compared with cations. Using [Cl]in in the numerator and [Cl]out in the denominator reflects the opposite charge sign in the electrochemical balance.

4. Temperature and scaling

Vm scales with temperature through the RT/F factor. At 37 °C (310.15 K), RT/F is about 26.7 mV, so small ratio changes can shift Vm noticeably. Cold conditions typically reduce magnitude of predicted voltages.

5. Typical concentration ranges

Many mammalian cells have high intracellular K+ (≈120–150 mM) and low extracellular K+ (≈3–6 mM). Sodium is often opposite: low inside (≈5–20 mM) and high outside (≈135–155 mM). Chloride varies by cell type.

6. Interpreting the result

A negative Vm means the inside is negative relative to outside. If you observe a Vm near −60 to −80 mV with the sample ratios, the inputs are consistent with common resting conditions in excitable tissues.

7. Sensitivity checks

Adjust one parameter at a time to understand sensitivity. Raising extracellular K+ from 5 to 10 mM can markedly depolarize Vm. Similarly, increasing Pna from 0.04 to 0.1 can shift Vm upward by several millivolts.

8. Practical reporting

For lab notes, record temperature, permeability ratios, and all concentrations. The CSV export keeps a tidy parameter list, and the PDF summary is useful for attaching to reports or sharing with collaborators.

FAQs

1) What does the Goldman equation compute?

It estimates membrane voltage from ion concentrations and relative permeabilities, typically for K⁺, Na⁺, and Cl⁻ in resting conditions.

2) Why do chloride terms look reversed?

Chloride carries negative charge. The equation accounts for this by using intracellular chloride in the numerator and extracellular chloride in the denominator.

3) Do permeabilities need absolute units?

No. Relative ratios are sufficient. Many models set Pk to 1 and scale Pna and Pcl relative to potassium permeability.

4) Which temperature should I use?

Use the temperature of the preparation or environment. For human physiology, 37 °C is common; experimental setups may be lower.

5) Why is my Vm unusually large?

Large magnitude can come from extreme gradients, very small denominators, or unrealistic permeabilities. Recheck concentration units and ensure all values are positive.

6) Is this the same as the Nernst equation?

No. Nernst applies to one ion at equilibrium. Goldman combines multiple ions and permeabilities to approximate the overall membrane voltage.

7) Can I model another ion with this tool?

This calculator focuses on K⁺, Na⁺, and Cl⁻. To include additional ions, you would extend the numerator and denominator with their permeability-weighted terms.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.