Gibbs Free Energy Calculator
Solve ΔG = ΔH − TΔS for any of the four quantities, and see whether a reaction is spontaneous. Static 3D diagrams and charts show the spontaneous vs non-spontaneous energy picture and the temperature where ΔG changes sign.
Reviewed by the ToolNestr Editorial Team — July 2026
Enter any three of the four values; the fourth solves live. ΔH in kJ/mol, ΔS in J/(mol·K), T in Kelvin, ΔG in kJ/mol.
Two ideas that trip students up
1. Spontaneous: ΔG < 0
The product platform sits below the reactant platform in free energy — the reaction rolls downhill on its own.
2. Non-spontaneous: ΔG > 0
Here the product platform sits above the reactant platform — the forward reaction must be driven by an external energy input.
Gibbs free energy graphs
How it works
The core idea in one line: spontaneity is a tug-of-war between the heat a reaction releases (ΔH) and the disorder it creates (ΔS), and temperature decides which one wins.
ΔG = ΔH − TΔS
ΔH in kJ/mol, ΔS in J/(mol·K)/1000, T in K, ΔG in kJ/mol
Tcrossover = ΔH / ΔS
temperature where ΔG changes sign (ΔS in kJ/mol·K)
ΔG < 0 → spontaneous
ΔG > 0 → non-spontaneous; ΔG = 0 → equilibrium
Because ΔG = ΔH − TΔS, whenever ΔH and ΔS share the same sign, there is a crossover temperature T = ΔH/ΔS where ΔG switches sign — below it one direction is favored, above it the other is. When ΔH and ΔS have opposite signs, ΔG keeps the same sign at every temperature, so the reaction is either always spontaneous or never spontaneous.
Worked example 1 — ammonia synthesis-like reaction at 298 K
Given: ΔH = −92.4 kJ/mol, ΔS = −198.7 J/(mol·K), T = 298 K. Find ΔG and classify spontaneity.
ΔG ≈ −33.19 kJ/mol < 0, so the reaction is spontaneous at 298 K — even though entropy decreases, the large negative ΔH dominates at this temperature.
Worked example 2 — finding the crossover temperature
Given: A reaction has ΔH = +40.0 kJ/mol and ΔS = +100.0 J/(mol·K) (both positive). Find the temperature at which ΔG = 0.
Below 400 K, ΔG is positive (non-spontaneous); above 400 K, ΔG becomes negative (spontaneous) — because both ΔH and ΔS are positive, higher temperature favors spontaneity.
The four ΔH/ΔS sign combinations and their spontaneity behavior
ΔG = ΔH − TΔS — how temperature affects spontaneity depends entirely on the signs of ΔH and ΔS.
| ΔH | ΔS | Spontaneity |
|---|---|---|
| Negative (exothermic) | Positive (more disorder) | Spontaneous at all temperatures |
| Positive (endothermic) | Negative (less disorder) | Non-spontaneous at all temperatures |
| Negative (exothermic) | Negative (less disorder) | Spontaneous only at low T |
| Positive (endothermic) | Positive (more disorder) | Spontaneous only at high T |
The last two rows have a crossover temperature T = ΔH/ΔS where ΔG changes sign — the worked examples above are the third and fourth cases.
Where Gibbs free energy actually matters
🧊 Ice melting and phase transitions
Ice melting has ΔH > 0 (absorbs heat) and ΔS > 0 (liquid is more disordered than solid), so it is spontaneous only above 0°C — exactly the crossover-temperature behavior ΔG = ΔH − TΔS predicts.
🏭 Industrial reaction feasibility
Chemical engineers use ΔG to decide whether a proposed reaction will proceed on its own at a given operating temperature, or whether the process needs to be driven by coupling it to another reaction or supplying continuous energy.
🧬 Protein folding and biochemistry
Proteins fold into their functional shapes because the folded state has lower Gibbs free energy than the unfolded state at body temperature — ΔG governs which molecular conformations are thermodynamically favored in living cells.
🔋 Battery and electrochemical cell design
The Gibbs free energy of a redox reaction relates directly to the cell voltage a battery can produce (ΔG = −nFE°cell) — a more negative ΔG means a stronger driving force and a higher cell voltage.
Common misconceptions
"A negative ΔH always means the reaction happens spontaneously."
Not necessarily — spontaneity depends on ΔG, not ΔH alone. If ΔS is very negative and T is high enough, the −TΔS term can outweigh even a negative ΔH, flipping ΔG positive. Exothermic reactions are common but not automatically spontaneous.
"ΔG tells you how fast a reaction happens."
ΔG is a thermodynamic quantity describing whether a reaction is favorable overall, not how quickly it proceeds. A reaction can have a very negative ΔG yet be kinetically extremely slow without a catalyst — spontaneity and rate are separate questions.
"Spontaneous means it happens instantly and by itself, unassisted."
"Spontaneous" in thermodynamics only means the reaction is thermodynamically favorable in the forward direction — it says nothing about how fast, and many spontaneous reactions still need an initial energy input (activation energy) to get started.
"ΔS in J and ΔH in kJ can be plugged into ΔG = ΔH − TΔS directly without converting."
They must be converted to the same energy unit first — usually by dividing ΔS (in J/mol·K) by 1000 to get kJ/(mol·K) before multiplying by T. Skipping this conversion is one of the most common arithmetic errors in this calculation.
Formula sources & further reading
The formulas here are standard, traceable to:
- • OpenStax, Chemistry 2e — Chapter 16, Thermodynamics: free energy (free, peer-reviewed). openstax.org
- • Brown, LeMay & Bursten, Chemistry: The Central Science — Chapter 19, Chemical Thermodynamics.
- • Zumdahl & Zumdahl, Chemistry — Gibbs free energy and spontaneity.
ΔG = ΔH − TΔS, with ΔH in kJ/mol, ΔS in J/(mol·K) converted to kJ/(mol·K), and T in Kelvin. Results are rounded for display.
How to use this calculator
Enter three values
Fill any three of ΔH, ΔS, T and ΔG; the fourth solves live.
Watch the classification
A label reports spontaneous, non-spontaneous, or at equilibrium.
See the crossover
The charts trace ΔG vs T to show where a reaction flips spontaneity, if it does.
Related tools
Frequently asked questions
What is Gibbs free energy?
Gibbs free energy (G) combines a reaction's enthalpy change (heat) and entropy change (disorder) into a single quantity that predicts spontaneity at constant temperature and pressure: ΔG = ΔH − TΔS. A negative ΔG means the reaction proceeds spontaneously as written.
What does the sign of ΔG mean?
ΔG < 0 means the reaction is spontaneous (favorable) in the forward direction at that temperature. ΔG > 0 means it is non-spontaneous forward (but spontaneous in reverse). ΔG = 0 means the system is at equilibrium — no net driving force either way.
What units does ΔH, ΔS and T use in this calculator?
This calculator uses the standard convention: ΔH in kJ/mol, ΔS in J/(mol·K), and T in Kelvin. Because ΔH is in kJ but ΔS is in J, the calculator divides ΔS by 1000 before multiplying by T, so the TΔS term comes out in kJ/mol to match ΔH, giving ΔG in kJ/mol.
Can a reaction be non-spontaneous at one temperature but spontaneous at another?
Yes — this happens whenever ΔH and ΔS have the same sign. Because ΔG = ΔH − TΔS, raising T makes the −TΔS term larger in magnitude. If ΔS is positive, raising T eventually makes ΔG negative (spontaneous at high T); if ΔS is negative, raising T eventually makes ΔG positive (non-spontaneous at high T). The crossover temperature is T = ΔH/ΔS.
How is ΔG related to the equilibrium constant K?
At standard conditions, ΔG° = −RT ln(K). A very negative ΔG° corresponds to a large K (equilibrium favors products); a very positive ΔG° corresponds to a small K (equilibrium favors reactants). ΔG° = 0 corresponds to K = 1.