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Gibbs Free Energy Calculator

Ready to calculate
ΔG = ΔH − T·ΔS.
4 Energy + 4 Entropy Units.
Crossover T + Mechanism.
100% Free.
No Data Stored.

How it Works

01Enter ΔH (Enthalpy)

Heat absorbed (+) or released (−) by the reaction. Supports J, kJ, cal, kcal

02Enter ΔS (Entropy)

Change in disorder. Positive = more disorder (gas, dissolution); negative = more order

03Enter Temperature

Reaction temperature in K, °C, or °F — auto-converted to kelvin (must be > 0 K)

04ΔG = ΔH − T·ΔS

Get Gibbs free energy plus spontaneity verdict, driving mechanism, and crossover temperature

What is a Gibbs Free Energy Calculator?

Gibbs free energy (ΔG) is the single most important number in chemical thermodynamics — the criterion that decides, with one sign, whether a reaction will proceed spontaneously, has reached equilibrium, or requires external energy to drive it. The equation ΔG = ΔH − T·ΔS was published by Josiah Willard Gibbs in his 1873-1878 series "On the Equilibrium of Heterogeneous Substances" — work so influential that James Clerk Maxwell taught it directly to his Cambridge students and built clay models illustrating Gibbs's surfaces. Our Gibbs Free Energy Calculator implements this equation with full unit flexibility: four energy units for ΔH (J, kJ, cal, kcal), four entropy units for ΔS (J/K, kJ/K, cal/K, kcal/K), and three temperature units for T (K, °C, °F). Output includes ΔG, a spontaneity verdict (spontaneous / equilibrium / non-spontaneous), the driving mechanism analysis, the crossover temperature where ΔG flips sign, and a reference table of textbook reactions.

Just enter your three inputs: the enthalpy change ΔH (negative for exothermic, positive for endothermic), the entropy change ΔS (positive when disorder increases — e.g., gas formation, dissolution; negative when disorder decreases — e.g., condensation, polymerization), and the temperature T at which you want to evaluate spontaneity. The calculator converts everything to SI (J, J/K, K), computes T·ΔS, and subtracts: ΔG = ΔH − T·ΔS. The sign decides spontaneity: ΔG < 0 means the forward reaction is spontaneous (proceeds without input), ΔG > 0 means non-spontaneous (the reverse is spontaneous), and ΔG ≈ 0 means equilibrium. The "driving mechanism" panel diagnoses whether your reaction is enthalpy-driven (low T regime), entropy-driven (high T regime), favored at all temperatures, or opposed at all temperatures.

Designed for general chemistry students learning thermodynamics, biochemistry students working with metabolic energetics (ATP hydrolysis, photosynthesis, glycolysis), materials scientists evaluating phase transitions, chemical engineers designing process conditions, and physical chemistry students preparing for the GRE Chemistry or qualifying exams, the tool runs entirely in your browser — no data is stored or transmitted.

Pro Tip: Pair this with our Equilibrium Constant Calculator to convert ΔG° to K_eq via ΔG° = −RT·ln(K), or our Nernst Equation Calculator to relate ΔG to electrochemical cell potential (ΔG = −nFE).

How to Use the Gibbs Free Energy Calculator?

Enter Enthalpy Change (ΔH): The heat absorbed (positive ΔH = endothermic) or released (negative ΔH = exothermic) by the reaction. Most thermodynamic tables report ΔH° in kJ/mol at 298.15 K. Supports J, kJ, cal, kcal — common values: methane combustion ΔH ≈ −890 kJ/mol; ATP hydrolysis ≈ −20 kJ/mol; water boiling ≈ +40.7 kJ/mol.
Enter Entropy Change (ΔS): The change in disorder of the system. Positive when disorder increases (forming gas from solid/liquid, dissolution, large molecules → small molecules); negative when disorder decreases (condensation, polymerization, gas → liquid). Common values: 100-300 J/(mol·K) for phase transitions involving gases. Supports J/K, kJ/K, cal/K, kcal/K.
Enter Temperature (T): The temperature at which spontaneity is evaluated. Standard reference: 298.15 K = 25 °C = 77 °F (room temperature). Must be greater than 0 K (absolute zero). Auto-converts °C and °F to K using T_K = °C + 273.15 and T_K = (°F − 32) × 5/9 + 273.15.
Press Calculate: The calculator normalizes inputs to SI (J, J/K, K), computes T·ΔS, and applies ΔG = ΔH − T·ΔS. The sign of ΔG immediately classifies spontaneity.
Read the Results: ΔG headline in kJ; spontaneity verdict (Spontaneous / Equilibrium / Non-Spontaneous); driving mechanism (enthalpy vs entropy regime); crossover temperature where ΔG = 0 (when ΔH and ΔS share signs); full calculation breakdown; and a reference table of 9 textbook reactions for context.

How is Gibbs free energy calculated?

The Gibbs free energy equation distills the entire second law of thermodynamics into one line: balance the system's enthalpy preference (heat) against the universe's entropy preference (disorder), with temperature as the scaling factor between them. Here's the complete derivation:

Gibbs's insight in 1873 was that for a process at constant T and P (typical lab conditions), the universe's total entropy change reduces to a system-only quantity: G = H − T·S. Minimizing G of the system corresponds to maximizing entropy of the universe.

Definition of Gibbs Free Energy

Gibbs free energy is defined as the state function:

G = H − T·S

where H is enthalpy, T is absolute temperature, and S is entropy.

Change in Gibbs Free Energy at Constant T

For a process at constant temperature:

ΔG = ΔH − T·ΔS

This is the equation our calculator uses. Note that T must be in kelvin (absolute temperature) — using °C or °F gives the wrong answer because they don't scale linearly from zero.

Spontaneity Criterion

  • ΔG < 0: Reaction is spontaneous (exergonic). Proceeds in the forward direction. Maximum work the system can do = |ΔG|.
  • ΔG = 0: System is at equilibrium. No net change. Forward and reverse rates are equal.
  • ΔG > 0: Reaction is non-spontaneous (endergonic). The reverse reaction is spontaneous. To drive the forward reaction, you must couple it to another exergonic process (e.g., ATP hydrolysis, photochemistry, electrolysis).

The Four Spontaneity Cases

The signs of ΔH and ΔS produce four behaviors:

  • ΔH < 0, ΔS > 0: Both terms favor reaction. Spontaneous at all temperatures. Examples: methane combustion (ΔH = −890, ΔS = +43 J/(mol·K)), explosions.
  • ΔH > 0, ΔS < 0: Both terms oppose reaction. Non-spontaneous at all temperatures. Examples: photosynthesis (driven by sunlight), endergonic biosynthesis.
  • ΔH < 0, ΔS < 0: Enthalpy-driven; spontaneous below crossover T. Heat release wins at low T but entropy loss eventually dominates at high T. Example: water freezing (spontaneous below 273.15 K).
  • ΔH > 0, ΔS > 0: Entropy-driven; spontaneous above crossover T. Heat cost is paid by entropy gain at high T. Example: water boiling (spontaneous above 373.15 K).

Crossover Temperature (When ΔG = 0)

When ΔH and ΔS share signs, there's a temperature where ΔG flips. Setting ΔG = 0:

T_crossover = ΔH / ΔS

This is the temperature at which the reaction is at equilibrium (poised to switch direction). For ice ↔ water: T = 6010/22.0 = 273.2 K = 0 °C — exactly the melting point. The calculator reports this temperature whenever it exists and is positive.

Standard ΔG° vs Non-Standard ΔG

The calculator gives ΔG for the conditions you input. For non-standard concentrations or activities, use:

ΔG = ΔG° + R·T·ln(Q)

where R = 8.314 J/(mol·K) is the gas constant, T is in K, and Q is the reaction quotient. At equilibrium Q = K and ΔG = 0, giving the crucial relation ΔG° = −R·T·ln(K) — bridging thermodynamics and equilibrium chemistry.

Real-World Example

Gibbs Free Energy Calculator – Worked Examples

Consider the Haber process for ammonia synthesis: N₂(g) + 3 H₂(g) → 2 NH₃(g), the foundation of synthetic fertilizer that feeds nearly half the world's population. Standard values: ΔH° = −92.4 kJ/mol, ΔS° = −198.7 J/(mol·K). Find ΔG° at 25 °C (298.15 K) and at 500 °C (773.15 K).
  • At 298.15 K: T·ΔS = 298.15 × (−198.7) = −59,232 J/mol = −59.23 kJ/mol.
  • ΔG° = ΔH° − T·ΔS = −92.4 − (−59.23) = −92.4 + 59.23 = −33.17 kJ/mol.
  • Verdict: Spontaneous at room temperature. Why isn't the world flooded with ammonia then? Because the activation energy is enormous — N≡N triple bond is the second-strongest bond in nature (945 kJ/mol). Without an iron catalyst, the reaction is kinetically frozen.
  • At 773.15 K (500 °C, typical Haber-Bosch conditions): T·ΔS = 773.15 × (−198.7) = −153,624 J/mol = −153.6 kJ/mol.
  • ΔG° = −92.4 − (−153.6) = +61.2 kJ/mol → Non-spontaneous.
  • The high-T paradox: Higher temperature speeds the reaction (kinetics) but reduces the equilibrium yield (thermodynamics — entropy term −T·ΔS becomes very negative). Industry compromises at 400-500 °C with high pressure (200-300 atm) to push equilibrium back to products via Le Chatelier.
  • Crossover T: ΔG = 0 when T = ΔH/ΔS = (−92,400)/(−198.7) = 465 K = 192 °C. Above 192 °C, the Haber reaction is thermodynamically unfavorable in the forward direction at standard conditions.

Now consider water boiling: H₂O(l) → H₂O(g) at 1 atm. ΔH = +40.7 kJ/mol (vaporization), ΔS = +109 J/(mol·K). Find ΔG at 25 °C and at 100 °C.

  • At 298.15 K (room T): ΔG = 40.7 − (298.15 × 0.109) = 40.7 − 32.50 = +8.20 kJ/mol. Non-spontaneous — water doesn't boil at room temperature (well, it evaporates slowly because we're not at equilibrium with pure water vapor).
  • At 373.15 K (100 °C): ΔG = 40.7 − (373.15 × 0.109) = 40.7 − 40.67 = +0.03 kJ/mol ≈ 0. Equilibrium — exactly the boiling point at 1 atm. ✓
  • Crossover T: T = 40,700 / 109 = 373.4 K = 100.3 °C. The slight 0.3 K offset comes from the approximate values; thermodynamic tables give exactly 373.15 K.

Finally, the universal energy currency: ATP hydrolysis, ATP + H₂O → ADP + P_i. ΔH ≈ −20 kJ/mol, ΔS ≈ +90 J/(mol·K) at body temperature 310.15 K (37 °C). ΔG = −20 − (310.15 × 0.090) = −20 − 27.91 = −47.9 kJ/mol (under cellular conditions ΔG is closer to −30.5 kJ/mol because real concentrations differ from standard 1 M). This very negative ΔG is what drives 100% of muscle contraction, active transport, biosynthesis, and signal transduction in every living cell.

Who Should Use the Gibbs Free Energy Calculator?

1
General Chemistry Students: Solve thermodynamics homework on reaction spontaneity, predict whether a reaction proceeds, find crossover temperatures, and connect ΔG° to equilibrium constants.
2
Biochemistry Students: Understand cellular metabolism — why ATP hydrolysis (ΔG = −30.5 kJ/mol) drives biosynthesis, why photosynthesis (ΔG = +2865 kJ/mol) requires sunlight, why glycolysis is exergonic.
3
Chemical Engineers: Design industrial process conditions — pick T to optimize yield (Haber, methanol synthesis, water-gas shift), evaluate which side reactions are thermodynamically possible.
4
Materials Scientists: Predict phase stability — which polymorph is stable at a given T (graphite vs diamond, calcite vs aragonite), where solid-solid phase transitions occur.
5
Pharmaceutical Scientists: Evaluate drug-target binding (ΔG_binding determines K_d), polymorph stability of crystalline APIs, drug-excipient compatibility.
6
Environmental Chemists: Assess whether environmental reactions occur — corrosion, mineral weathering, atmospheric chemistry, biogeochemical cycles.

Technical Reference

Gibbs's Original Work: J. W. Gibbs, "On the Equilibrium of Heterogeneous Substances," Trans. Connecticut Acad. III, 108-248 (1873) and 343-524 (1878). 350+ pages of dense mathematics that founded chemical thermodynamics. Maxwell built clay surfaces of Gibbs's free-energy landscapes for water and showed them at the Royal Institution. The unit "joule per mole" used worldwide to report ΔG° comes directly from this work.

Why T must be in Kelvin. The equation ΔG = ΔH − T·ΔS multiplies T by ΔS. ΔS has units of J/K — it counts entropy per kelvin of temperature. Using °C instead of K shifts T by 273.15 and gives a wildly wrong T·ΔS. Always convert: T_K = T_°C + 273.15 = (T_°F − 32) × 5/9 + 273.15. The calculator does this automatically.

Standard State (°). Thermodynamic tables report ΔH° and ΔS° at standard conditions: 1 bar pressure, 1 M concentration for solutes, pure solid/liquid for those phases. The standard state is denoted with a superscript ° (or ⊖). Calculator output is ΔG (whatever your conditions) — for non-standard concentrations apply the correction ΔG = ΔG° + R·T·ln(Q).

Standard Reference Values (NIST/CRC Handbook, 298.15 K):

  • Combustion of CH₄: ΔH° = −890.4 kJ/mol, ΔS° = −242 J/(mol·K), ΔG° = −818 kJ/mol
  • Combustion of C₈H₁₈ (octane): ΔH° = −5470 kJ/mol, ΔG° = −5298 kJ/mol
  • Photosynthesis (per glucose): ΔG° = +2865 kJ/mol — driven by 8 photons per O₂
  • Glucose → 2 Lactate (anaerobic glycolysis): ΔG° = −196 kJ/mol
  • Glucose → 6 CO₂ (aerobic respiration): ΔG° = −2870 kJ/mol
  • ATP + H₂O → ADP + P_i (cellular): ΔG° = −30.5 kJ/mol; ΔG (in cell) ≈ −50 kJ/mol
  • Water vaporization (1 atm): ΔH = +40.7, ΔS = +109; equilibrium at 373.15 K
  • Water freezing (1 atm): ΔH = −6.01, ΔS = −22.0; equilibrium at 273.15 K
  • NaCl(s) → Na⁺(aq) + Cl⁻(aq): ΔH = +3.88, ΔS = +43.4, ΔG = −9.06 kJ/mol

Connection to Equilibrium Constant. At equilibrium ΔG = 0, so ΔG° = −R·T·ln(K_eq). At 298.15 K this gives a useful conversion: ΔG° = −5.71 × log₁₀(K) kJ/mol. So ΔG° = −5.71 kJ/mol → K = 10; ΔG° = −57.1 → K = 10¹⁰. A factor of ~5.7 kJ/mol per decade of K.

Connection to Cell Potential. For electrochemical reactions, ΔG = −n·F·E, where n is moles of electrons transferred, F = 96,485 C/mol is Faraday's constant, E is cell potential in volts. Spontaneous redox: E > 0, ΔG < 0. The Nernst equation E = E° − (RT/nF)·ln(Q) follows directly.

Limits of the Equation. ΔG = ΔH − T·ΔS assumes ΔH and ΔS are temperature-independent. In reality both shift with T (heat capacity Cp matters): ΔH(T₂) = ΔH(T₁) + ΔCp·(T₂ − T₁), ΔS(T₂) = ΔS(T₁) + ΔCp·ln(T₂/T₁). For modest T windows (within ±100 K), the approximation is good to ~5%. For broader ranges use the Van't Hoff equation directly or full Gibbs-Helmholtz integration.

Key Takeaways

Gibbs free energy ΔG = ΔH − T·ΔS is the universal spontaneity criterion in chemistry: ΔG < 0 = spontaneous, ΔG = 0 = equilibrium, ΔG > 0 = non-spontaneous. The four sign combinations of ΔH and ΔS produce four behaviors — both-favor (always spontaneous), both-oppose (never), enthalpy-driven (spontaneous below T_crossover), entropy-driven (spontaneous above T_crossover). The crossover temperature T = ΔH/ΔS marks where ΔG flips sign and is the thermodynamic phase transition or equilibrium temperature. Use the ToolsACE Gibbs Free Energy Calculator to evaluate any reaction's spontaneity, identify the driving mechanism, find crossover temperatures, and compare against 9 reference reactions including methane combustion, photosynthesis, water phase changes, ATP hydrolysis, and the Haber process. Bookmark it for chemistry coursework, biochemistry metabolism analysis, materials phase stability, and any time you need to know whether a reaction will go.

Frequently Asked Questions

What is the Gibbs Free Energy Calculator?
It computes the Gibbs free energy change ΔG = ΔH − T·ΔS from the enthalpy change ΔH, the entropy change ΔS, and the temperature T — the universal spontaneity criterion in chemistry. Output: ΔG headline (kJ), spontaneity verdict (Spontaneous / Equilibrium / Non-Spontaneous), driving mechanism analysis (enthalpy-driven, entropy-driven, both-favor, both-oppose), crossover temperature where ΔG = 0 (when ΔH and ΔS share signs), full calculation breakdown, and a reference table of 9 textbook reactions.

Supports four energy units (J, kJ, cal, kcal), four entropy units (J/K, kJ/K, cal/K, kcal/K), and three temperature units (K, °C, °F) with automatic conversion. Designed for general chemistry students, biochemistry students working with metabolic energetics, materials scientists, chemical engineers, and pharmaceutical scientists. Runs entirely in your browser — no data stored or transmitted.

Pro Tip: Use our Equilibrium Constant Calculator to convert ΔG° to K_eq via ΔG° = −RT·ln(K).

What's the formula for Gibbs free energy?
ΔG = ΔH − T·ΔS, where ΔH is the enthalpy change (heat absorbed/released), T is the absolute temperature in kelvin, and ΔS is the entropy change (change in disorder). The full state function is G = H − T·S; at constant temperature, the change is ΔG = ΔH − T·ΔS. Units must be consistent — convert ΔH and ΔS to compatible energy units (J and J/K, or kJ and kJ/K) before computing T·ΔS.
Why must temperature be in Kelvin?
Because the equation multiplies T by ΔS (which has units of J/K — joules per kelvin of temperature). Kelvin starts at absolute zero, so it scales linearly with thermal energy. Celsius and Fahrenheit don't — they have arbitrary zero points (water freezing for °C, brine freezing for °F). Using 25 °C instead of 298.15 K in T·ΔS would give a result 273.15 K too low. The calculator auto-converts, but if you compute by hand always use kelvin.
What does negative ΔG mean?
ΔG < 0 means the reaction is spontaneous in the forward direction at that temperature — it will proceed without external energy input. The system can do work (up to magnitude |ΔG|) on the surroundings. Examples: combustion of fuels, ATP hydrolysis, electrochemical batteries discharging, dissolution of NaCl in water. Note: 'spontaneous' means thermodynamically possible — the reaction can still be slow if the activation energy is high (diamond → graphite is spontaneous but takes geologic time).
What's the crossover temperature?
When ΔH and ΔS have the same sign, there's a temperature T_crossover = ΔH/ΔS where ΔG = 0. Below T_crossover the reaction is spontaneous in one direction; above it, in the other. For water boiling (ΔH = +40.7, ΔS = +109): T_crossover = 40,700/109 ≈ 373 K = 100 °C — exactly the boiling point at 1 atm. For water freezing (ΔH = −6.01, ΔS = −22.0): T_crossover = 273 K = 0 °C. Phase-transition temperatures ARE crossover temperatures.
What's the difference between ΔG and ΔG°?
ΔG° is the standard Gibbs free energy change — at 1 bar, 1 M concentrations, pure phases. Tabulated in thermodynamic handbooks. ΔG is the actual Gibbs energy change at whatever conditions you're at. Convert: ΔG = ΔG° + R·T·ln(Q), where Q is the reaction quotient (concentrations or partial pressures of products over reactants, raised to stoichiometric coefficients). At equilibrium Q = K and ΔG = 0, giving ΔG° = −R·T·ln(K).
Why isn't the Haber process spontaneous at high temperature?
ΔH° = −92.4 kJ/mol and ΔS° = −198.7 J/(mol·K). At high T, the −T·ΔS term becomes very large and positive (since ΔS < 0). At T_crossover = 92,400/198.7 = 465 K = 192 °C, ΔG° flips from negative to positive. So the reaction is thermodynamically favored only below 192 °C — but at low T the kinetics are too slow (the N≡N triple bond is the second-strongest bond in nature). Industry runs Haber-Bosch at 400-500 °C with iron catalyst and 200-300 atm pressure: high T for kinetics, high P to push equilibrium back to products via Le Chatelier (4 mol gas → 2 mol gas).
How does ΔG relate to the equilibrium constant K?
ΔG° = −R·T·ln(K) at equilibrium. Useful conversion at 298.15 K: ΔG° = −5.71 × log₁₀(K) kJ/mol. So ΔG° = −5.71 kJ/mol → K = 10; ΔG° = −34.2 → K = 10⁶ (strongly favored); ΔG° = +5.71 → K = 0.1 (mostly reactants); ΔG° = +57.1 → K = 10⁻¹⁰ (essentially no reaction). A factor of ~5.7 kJ/mol per decade of K.
How does ΔG relate to cell potential E?
ΔG = −n·F·E, where n is the moles of electrons transferred per mole of reaction, F = 96,485 C/mol is Faraday's constant, and E is the cell potential in volts. Spontaneous electrochemical reactions have E > 0, hence ΔG < 0. For a 1.5 V battery delivering 1 mol e⁻: ΔG = −1 × 96,485 × 1.5 = −145 kJ. The Nernst equation E = E° − (RT/nF)·ln(Q) is just the rearrangement of ΔG = ΔG° + RT·ln(Q) for electrochemical systems.
Can a non-spontaneous reaction be made spontaneous?
Yes — by coupling it to a spontaneous reaction with a more negative ΔG. This is how cells drive endergonic processes: ATP hydrolysis (ΔG = −30.5 kJ/mol) is coupled to glucose-6-phosphate synthesis (ΔG = +13.8 kJ/mol). Net: glucose + ATP → glucose-6-P + ADP, ΔG = −16.7 kJ/mol — spontaneous. Industrial examples: electrolysis (electrical energy drives non-spontaneous reactions like H₂O → H₂ + ½O₂); photosynthesis (light energy drives CO₂ → glucose).
What does "spontaneous but slow" mean?
Spontaneity is about thermodynamics (whether a reaction CAN go), not kinetics (how FAST it goes). The classic example: diamond → graphite has ΔG° = −2.9 kJ/mol (spontaneous) but the activation energy is so high (~370 kJ/mol) that the half-life of diamond at room temperature is longer than the age of the universe. Similarly, gasoline + air is wildly spontaneous (ΔG ≈ −5300 kJ/mol per mole of octane) but doesn't ignite without a spark to overcome the activation barrier. ΔG predicts what reactions can happen; activation energy and catalysts determine whether they will happen on a useful timescale.

Author Spotlight

The ToolsACE Team - ToolsACE.io Team

The ToolsACE Team

Our chemistry tools team implements Josiah Willard Gibbs's 1873 free-energy equation ΔG = ΔH − T·ΔS — the single most important criterion for predicting reaction spontaneity in chemistry, biochemistry, materials science, and chemical engineering. The calculator handles four energy units (J, kJ, cal, kcal) for ΔH, four entropy units (J/K, kJ/K, cal/K, kcal/K) for ΔS, and three temperature units (K, °C, °F) for T, with full SI normalization for the calculation. Output includes ΔG with spontaneity verdict (spontaneous/equilibrium/non-spontaneous), the driving mechanism analysis (enthalpy-driven, entropy-driven, both-favor, both-oppose), the crossover temperature where ΔG = 0 (when ΔH and ΔS share signs), a complete calculation breakdown, and a reference table of ΔH/ΔS/ΔG values for 9 textbook reactions including methane combustion, photosynthesis, water phase changes, ATP hydrolysis, the Haber process, and diamond → graphite.

Chemical ThermodynamicsReaction Spontaneity & EquilibriumSoftware Engineering Team

Disclaimer

Calculations assume ΔH and ΔS are temperature-independent over the working range — accurate within ~5% across moderate T windows but not across phase transitions or very wide T spans (use Kirchhoff equations or full Gibbs-Helmholtz integration for those). Output is for the standard convention: ΔG = ΔH − T·ΔS. For non-standard concentrations, apply ΔG = ΔG° + R·T·ln(Q). Spontaneity is thermodynamic, not kinetic — a thermodynamically spontaneous reaction can still be slow if activation energy is high.