Gibbs Energy Calculator - ΔG from ΔH, Temperature, and ΔS

The gibbs energy calculator is a thermodynamics tool that takes the enthalpy change ΔH, the entropy change ΔS, and the absolute temperature T of a reaction and returns ΔG = ΔH − T·ΔS in kJ/mol and kcal/mol along with a spontaneity verdict. Use it to decide whether a reaction will run on its own at constant temperature and pressure without juggling units or signed numbers by hand.

• • General chemistry homework and exam problems: Solve a ΔG problem when the worksheet gives you ΔH, ΔS, and T and asks whether the reaction is spontaneous at that temperature.
• • Spontaneity screening for synthesis reactions: Compare candidate synthetic routes by computing ΔG at the planned reaction temperature before committing lab time.
• • Biochemistry and protein-folding estimates: Convert a measured enthalpy and entropy of unfolding into ΔG to compare the stability of folded and unfolded states.
• • Engineering estimates for reactor design: Use ΔG as a fast check on whether a candidate reaction is thermodynamically feasible before modelling kinetics and mass balance in detail.

Gibbs energy is the maximum non-expansion work a closed system can deliver at constant temperature and pressure. The IUPAC definition ties it to enthalpy and entropy through G = H − TS, and ΔG = ΔH − T·ΔS is the working form chemists use on a worksheet.

The sign of ΔG does the heavy lifting. Negative ΔG means the reaction releases free energy and runs spontaneously; positive ΔG means external energy has to be added; ΔG = 0 marks equilibrium where the forward and reverse rates balance.

When a reaction has a positive ΔG and needs external energy, activation energy calculator estimates the kinetic barrier the same reactants must clear before products can form.

The calculator reads your three inputs, converts ΔS into the same units as ΔH, multiplies by T, and subtracts the T·ΔS term from ΔH. The same arithmetic underpins every published derivation of ΔG, so the answer lines up with general-chemistry textbooks and IUPAC conventions.

• ΔH (enthalpyChange): Heat released or absorbed at constant pressure, in kJ/mol. Negative values mark exothermic reactions.
• ΔS (entropyChange): Change in disorder of the system, in J/(mol·K). The calculator divides by 1000 to convert to kJ/(mol·K).
• T (temperatureK): Absolute temperature in Kelvin. Add 273.15 to a Celsius value, so 25 °C is 298.15 K.
• ΔG (deltaG): Change in Gibbs free energy in kJ/mol, the primary answer.
• ΔG in kcal/mol (deltaGkcal): Same ΔG converted with the NIST thermochemical calorie (1 kcal = 4.184 kJ exactly).
• Spontaneity (spontaneity): spontaneous when ΔG < 0, non-spontaneous when ΔG > 0, equilibrium when ΔG ≈ 0.

All three inputs are independent. The calculator first converts entropy from J/(mol·K) to kJ/(mol·K) by dividing by 1000, so the T·ΔS term is in kJ/mol and can be subtracted from ΔH directly. If T is 0 K (or any value ≤ 0), the calculator refuses the input rather than silently accepting a value below absolute zero.

According to Chemistry LibreTexts, Gibbs free energy combines enthalpy and entropy through ΔG = ΔH − T·ΔS, where ΔH is the enthalpy change, T is absolute temperature, and ΔS is the entropy change.

Once ΔG tells you a reaction is favorable, Arrhenius equation calculator turns the same temperature into a forward rate constant k.

Four ideas explain every number on the result panel and every sign convention used by the calculator.

When ΔH is negative and ΔS is positive, ΔG is negative at every temperature and the reaction is always spontaneous. When ΔH is positive and ΔS is negative, ΔG is positive at every temperature and the reaction is never spontaneous. The mixed-sign cases are where a temperature change can flip the verdict.

Combustion is the cleanest worked example for the sign convention because CO₂ and H₂O are the only products, and combustion reaction calculator produces the balanced equation that supplies the ΔH and ΔS values.

Six short steps cover the standard workflow. The calculator updates every time you change a field.

1. 1 Gather ΔH, ΔS, and T: Look up ΔH and ΔS for the reaction at the planned temperature from a thermochemical table (NIST WebBook or Atkins). Convert the temperature to Kelvin with T_K = T_°C + 273.15.
2. 2 Enter the enthalpy change ΔH: Type ΔH in kJ/mol. Use a negative number for an exothermic reaction, a positive number for an endothermic one.
3. 3 Enter the entropy change ΔS: Type ΔS in J/(mol·K). The calculator divides by 1000 internally so the T·ΔS term ends up in kJ/mol like ΔH.
4. 4 Enter the absolute temperature T: Type the temperature in Kelvin. If you have °C, add 273.15 first. The calculator refuses values at or below 0 K.
5. 5 Read ΔG in kJ/mol and kcal/mol: The primary answer is ΔG in kJ/mol. The kcal/mol row is the same value divided by 4.184, which matches the NIST thermochemical calorie.
6. 6 Read the spontaneity verdict: The verdict below ΔG reads spontaneous, non-spontaneous, or at equilibrium based on the sign and magnitude of ΔG.

For the ammonia synthesis at 293.15 K, enter ΔH = −92.22 kJ/mol, ΔS = −198.75 J/(mol·K), and T = 293.15 K. The calculator returns ΔG = −33.96 kJ/mol (≈ −8.12 kcal/mol) and the verdict spontaneous, matching the standard worked example for N₂ + 3 H₂ → 2 NH₃.

After ΔG confirms a reaction will run on its own, stoichiometry reaction calculator sizes the limiting reactant so the predicted spontaneity has a real concentration to act on.

The gibbs energy calculator removes the unit-juggling and sign-checking steps so the chemistry question is the part that gets your attention.

• • Three plain numeric inputs: ΔH, ΔS, and T are typed as plain numbers with their native units; no equation parsing required.
• • Two energy units in one click: ΔG is shown in kJ/mol and kcal/mol at the same time, using the exact NIST thermochemical calorie (1 cal = 4.184 J).
• • Spontaneity verdict attached to the answer: The spontaneity row tells you whether ΔG < 0, ΔG > 0, or ΔG ≈ 0 without having to inspect the number yourself.
• • Real-time recalculation on every keystroke: Changing any field re-runs the formula immediately, so you can sweep a temperature range and watch ΔG cross zero to find the equilibrium temperature.
• • Pairs with the rest of the chemistry toolset: Hand ΔH, ΔS, and the verdict to a stoichiometry or equilibrium-constant calculator to size the next step.
• • Useful on a phone in lab: The form layout stays single-column on small screens, so you can recheck a ΔG while standing at the bench.

Once the sign of ΔG is known, the same data can be turned into an equilibrium constant via ΔG° = −RT ln K, the bridge between thermodynamics and equilibrium concentrations.

For reactions that include elements beyond C, H, and O, chemical equation balancer calculator produces the balanced equation so ΔH and ΔS can be read off a thermochemical table.

The arithmetic is exact, but the choices you make for the inputs change what ΔG actually tells you about the reaction.

• • The calculator covers the constant-pressure, constant-temperature regime. It does not adjust ΔH or ΔS for temperature-dependent heat capacities, so very large temperature swings need a separate Kirchhoff-law correction.
• • For non-standard concentrations or partial pressures, the simple ΔG = ΔH − T·ΔS form gives ΔG°. Use ΔG = ΔG° + RT ln Q when conditions differ from 1 bar or 1 M.

Two extra forms extend the same data. The standard-state equilibrium constant K connects to ΔG° by ΔG° = −RT ln K, and the non-standard free energy change is ΔG = ΔG° + RT ln Q, where Q is the reaction quotient. The CODATA value of R = 8.314 J/(mol·K) goes into both forms.

According to IUPAC Gold Book, Gibbs energy G = H − TS, and ΔG at constant temperature and pressure indicates the maximum non-expansion work obtainable from a closed system.

Temperature dependence of ΔG shows up in thermal treatment design too, and annealing temperature calculator applies the same idea to pick a hold temperature for materials needing a specific free-energy state.