Gibbs Free Energy Calculator

Calculate for any variable—Gibbs free energy of reaction ΔG, reaction enthalpy ΔH, reaction entropy ΔS, or temperature T—using the Gibbs-Helmholtz equation ΔG = ΔH − T·ΔS. Simply leave the variable you are looking for blank. The calculator automatically converts between units (J/kJ, K/°C, etc.) and can be switched to molar standard values (kJ/mol, J/(mol·K)), which are common in reference tables. Additionally, it directly displays whether a reaction occurs spontaneously under the given conditions.

Enter Values

Do you have ΔG° and want to know how far the reaction proceeds towards equilibrium? Use our Equilibrium Constant Calculator.

Displays units as kJ/mol or J/(mol·K) – for standard values like ΔH°, ΔS° from reference tables. The calculation itself does not change, as 'per mol' cancels out in the formula.
Gibbs free energy of reaction. (usually standard molar values, e.g., ΔH°, ΔS° from reference tables)
Reaction enthalpy. (usually standard molar values, e.g., ΔH°, ΔS° from reference tables)
Reaction entropy. (usually standard molar values, e.g., ΔH°, ΔS° from reference tables)
Absolute temperature at which the reaction occurs.

Explanation: Gibbs Free Energy

What is Gibbs Free Energy?

Gibbs free energy (also known as free enthalpy) tells you whether a chemical reaction occurs spontaneously (voluntarily) at constant pressure and temperature.

It combines two opposing effects: the energy gain or loss of a reaction (enthalpy ΔH) and the change in disorder of the system (entropy ΔS), weighted by the temperature T.

Overview of the Four Variables

Gibbs Free Energy of Reaction (ΔG)

ΔG describes whether a reaction occurs spontaneously. If ΔG is negative, the reaction is spontaneous; if ΔG is positive, energy must be supplied.

Reaction Enthalpy (ΔH)

ΔH indicates whether heat is released during the reaction (exothermic, ΔH < 0) or absorbed (endothermic, ΔH > 0).

Reaction Entropy (ΔS)

ΔS describes the change in disorder. If disorder increases (e.g., gas formation), ΔS is positive.

Temperature (T)

T is the absolute temperature in Kelvin at which the reaction occurs. It determines how heavily the entropy term is weighted.

The Formula ΔG = ΔH − T·ΔS

The Gibbs-Helmholtz equation links all four variables in a single formula.

Basic Formula

ΔG = ΔH − T·ΔS

If ΔH is negative and ΔS is positive, ΔG is negative at any temperature – the reaction always occurs spontaneously. In all other cases, the temperature plays a deciding role.

Solving the Formula for Each Variable

Depending on which variable is being solved for, the formula is rearranged as follows:

Solving for ΔH

ΔH = ΔG + T·ΔS
Used when ΔG, T, and ΔS are known.

Solving for ΔS

ΔS = (ΔH − ΔG) / T
Used when ΔG, ΔH, and T are known. Note: T cannot be 0.

Solving for T

T = (ΔH − ΔG) / ΔS
Used when ΔG, ΔH, and ΔS are known. Note: ΔS cannot be 0.

Pay Attention to the Units!

ΔG and ΔH are usually given in kJ, whereas ΔS is given in J/K – which is a 1000-times smaller unit. Before plugging them into the formula, all variables must be converted to the same base unit (J or K). The calculator handles this automatically.

When Does a Reaction Occur Spontaneously?

ΔG < 0: The reaction occurs spontaneously. ΔG > 0: The reaction does not occur spontaneously, energy must be supplied. ΔG = 0: The system is in equilibrium.

Total Values or Molar Values – The Calculator Adapts

In reference tables, ΔH° and ΔS° are usually listed as molar quantities, meaning per mole of reaction turnover (e.g., kJ/mol, J/(mol·K)). Mathematically, this does not change ΔG = ΔH − T·ΔS, as 'per mol' cancels out on both sides – so you can enter molar values in exactly the same way as total values. With the 'Molar values' toggle switch above, the calculator displays the matching units (kJ/mol instead of kJ) so you don't have to convert them yourself.

Example Problems

Two examples demonstrate how to calculate depending on the variable you are solving for.

Example 1: Calculating ΔG

A reaction has ΔH = −92 kJ and ΔS = −198 J/K at T = 298 K. Does the reaction occur spontaneously?

Given

ΔH = −92 kJ = −92000 J, ΔS = −198 J/K, T = 298 K

Find

ΔG

Solution

ΔG = ΔH − T·ΔS

ΔG = −92000 J − 298 K · (−198 J/K) = −92000 J + 59004 J = −32996 J

ΔG ≈ −33.0 kJ → negative, the reaction occurs spontaneously.

Example 2: Finding the Transition Temperature T

At what temperature does a reaction with ΔH = 40 kJ and ΔS = 100 J/K become spontaneous (ΔG = 0)?

Given

ΔG = 0 J, ΔH = 40000 J, ΔS = 100 J/K

Find

T

Solution

T = (ΔH − ΔG) / ΔS

T = (40000 J − 0 J) / 100 J/K = 400 K

T = 400 K (≈ 126.85 °C) → from this temperature onward, the reaction occurs spontaneously.

Tips and Common Mistakes

Common Sources of Error

Units Not Aligned

ΔH and ΔG are often given in kJ, but ΔS in J/K. If both values are put into the formula unchanged, an error by a factor of 1000 occurs.

Temperature in °C instead of Kelvin

The formula always requires the absolute temperature in Kelvin, not in degrees Celsius. Do not forget to add 273.15.

Signs Swapped

A negative ΔH means an exothermic reaction, a negative ΔG means spontaneity. Check both signs independently of each other.

Best Approach

First write down all given variables with their units, convert them to J, J/K, and K, and only then insert them into the appropriately rearranged formula.

Where is Gibbs Free Energy Used?

Gibbs free energy is key to predicting whether chemical and biochemical processes will occur:

  • Predicting the spontaneity of chemical reactions
  • Calculating equilibrium constants (ΔG = −RT·lnK)
  • Evaluating metabolic reactions in biochemistry (e.g., ATP hydrolysis)

Frequently Asked Questions about Gibbs Free Energy

ΔG determines whether a reaction occurs spontaneously at constant pressure and temperature. If ΔG is negative, the reaction proceeds spontaneously; if ΔG is positive, energy must be supplied for it to occur; at ΔG = 0, the system is in equilibrium.

Yes. In $ \Delta G = \Delta H - T \cdot \Delta S $, a positive ΔH can be overcompensated at high temperature by a sufficiently large gain in entropy (ΔS > 0), making ΔG negative anyway. A well-known example is the spontaneous dissolution of salts like ammonium nitrate in water, where the solution cools down (endothermic), but the reaction still occurs spontaneously.

gibbs_faq_a3

This so-called transition temperature marks the point at which a reaction changes from non-spontaneous to spontaneous (or vice versa) – provided ΔH and ΔS have the same sign. It can be calculated directly from T = ΔH/ΔS (for the case where ΔG = 0). Below or above this temperature, the sign of ΔG flips.

In reference tables, ΔH° and ΔS° are usually listed as standard molar values, i.e., relative to 1 mol of reaction turnover (e.g., kJ/mol, J/(mol·K)). Mathematically, this does not change the formula ΔG = ΔH − T·ΔS, since "per mole" cancels out on both sides. The toggle simply adjusts the displayed unit so you can enter table values directly without manual conversion.

Through the relationship ΔG° = −R·T·ln(K), the equilibrium constant K can be calculated from the standard Gibbs free energy of reaction (and vice versa). A strongly negative ΔG° corresponds to a large K, meaning the equilibrium lies far on the product side. While this conversion is not part of this calculator, it is a direct application of Gibbs free energy in chemical thermodynamics.