Gibbs Free Energy Calculator

The Gibbs free energy (symbol G) is the single most important quantity in chemical thermodynamics. Its change, ΔG, tells you whether a reaction, phase transition, or electrochemical cell will proceed spontaneously under a given set of conditions — without knowing anything about the reaction mechanism or kinetics.

This calculator covers the full core toolkit:

• ΔG from ΔH and ΔS — the fundamental Gibbs equation at any temperature
• Rearranged forms — find ΔH or ΔS when the other two quantities are known
• Crossover temperature — the T at which ΔG changes sign (where ΔH = T·ΔS)
• Equilibrium constant K — convert between ΔG° and K in either direction
• Nernst equation — cell potential and ΔG for electrochemical cells under non-standard conditions

Every mode shows a full substitution line so you can follow (and check) the arithmetic.

How it works

The Gibbs equation

The master equation is:

ΔG = ΔH − T·ΔS

where ΔH is the enthalpy change (kJ/mol), T is the absolute temperature (K), and ΔS is the entropy change (J/mol·K). The calculator converts ΔS to kJ/mol·K internally so both terms share the same unit before subtraction.

The sign of ΔG determines spontaneity:

Equilibrium constant

At standard conditions the standard Gibbs energy relates to the equilibrium constant by:

ΔG° = −R·T·ln K    or equivalently    K = exp(−ΔG°/(R·T))

R = 8.314 J/mol·K (the universal gas constant). The calculator handles both directions: enter ΔG° to get K, or enter a known K to recover ΔG°.

Nernst equation

For electrochemical cells the standard potential E° is corrected to real conditions via:

E = E° − (R·T)/(n·F) · ln Q

where n is the number of electrons transferred per formula unit and F = 96 485 C/mol. The corresponding Gibbs energy of the cell is ΔG = −n·F·E.

At exactly 298.15 K the prefactor RT/F = 0.025693 V, so the equation simplifies to E = E° − (0.025693/n)·ln Q — a form you will see in many textbooks.

Worked example

Problem: is the synthesis of ammonia spontaneous at 298 K?

For N₂(g) + 3 H₂(g) → 2 NH₃(g):

• ΔH° = −92.4 kJ/mol
• ΔS° = −198.1 J/mol·K

Step 1: convert ΔS to kJ: −198.1 ÷ 1000 = −0.1981 kJ/mol·K

Step 2: apply the Gibbs equation: ΔG = −92.4 − (298.15 × (−0.1981)) = −92.4 + 59.05 = −33.35 kJ/mol

Conclusion: ΔG < 0 → spontaneous at 298 K. Enter these values in the calculator and the spontaneity badge will light up green.

Crossover temperature: T = ΔH / ΔS = (−92 400 J/mol) / (−198.1 J/mol·K) ≈ 467 K. Above 467 K the reaction becomes non-spontaneous under standard conditions.

Formula reference

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