Gibbs Free Energy Calculator — Delta G Equation: ΔG = ΔH − T × ΔS

Gibbs Free Energy Calculator

This Gibbs Free Energy Calculator lets you solve for any of the four variables in the delta G equation — ΔG (Gibbs free energy), ΔH (enthalpy), ΔS (entropy), or T (temperature) — given the remaining three. Simply select what you want to calculate, enter the known values with your preferred units, and get an instant result.

What Is Gibbs Free Energy?

Gibbs free energy (G) is a thermodynamic potential that determines whether a chemical reaction can occur spontaneously at constant temperature and pressure. The sign of ΔG tells you everything:

• ΔG < 0 — Reaction is spontaneous: it proceeds without external energy input.
• ΔG > 0 — Reaction is non-spontaneous: external energy is required to drive it forward.
• ΔG = 0 — System is at chemical equilibrium: forward and reverse rates are equal.

The Delta G Equation

The Gibbs free energy equation relates enthalpy and entropy through temperature:

ΔG = ΔH − T × ΔS

Where:

• ΔG — Change in Gibbs free energy (J, kJ, cal, kcal, or BTU)
• ΔH — Change in enthalpy (same energy unit)
• ΔS — Change in entropy (J/K, kJ/K, cal/K, or BTU/°R)
• T — Absolute temperature in Kelvin (converted automatically from °C or °F)

This calculator also supports the rearranged forms:

• ΔH = ΔG + T × ΔS
• ΔS = (ΔH − ΔG) / T
• T = (ΔH − ΔG) / ΔS

Enthalpy vs Entropy

Enthalpy (ΔH) measures the heat absorbed or released during a reaction. A negative ΔH means heat is released (exothermic); a positive ΔH means heat is absorbed (endothermic).

Entropy (ΔS) measures the change in molecular disorder or randomness. A positive ΔS means increased disorder (e.g., solids dissolving into ions); a negative ΔS means decreased disorder (e.g., gases combining into solids).

The system naturally tends toward minimum enthalpy and maximum entropy. Gibbs free energy captures this balance: a reaction is spontaneous when the enthalpic and entropic contributions together drive ΔG below zero.

Worked Example

Consider the Haber process: N₂ + 3H₂ → 2NH₃

• ΔH = −92.22 kJ (exothermic)
• ΔS = −198.75 J/K = −0.19875 kJ/K (entropy decreases — gases form a denser product)
• T = 20 °C = 293.15 K

Applying the delta G formula:

ΔG = −92.22 − 293.15 × (−0.19875) = −92.22 + 58.26 = −33.96 kJ

Since ΔG < 0, the reaction is spontaneous at 20 °C. At higher temperatures, however, the −T × ΔS term becomes more positive, and at some point ΔG may cross zero — this is the crossover temperature (also solvable with this tool by selecting "Solve for T").

Supported Units

FAQs

Why must temperature be in Kelvin?
The formula requires an absolute temperature scale so that T is always positive. The calculator converts °C and °F to Kelvin automatically.

Can ΔH and ΔS have different units?
Yes. The calculator handles mixed units internally. For example, you can enter ΔH in kJ and ΔS in J/K simultaneously.

What does ΔG = 0 mean in practice?
At equilibrium, the forward and reverse reactions proceed at equal rates. The temperature at which ΔG = 0 can be found by setting the equation to zero: T = ΔH / ΔS.

Does a negative ΔG guarantee a fast reaction?
No. Thermodynamics tells you whether a reaction is energetically possible, not how quickly it occurs. Kinetics (activation energy, catalysts) govern reaction rate. Use our Activation Energy Calculator for kinetics.