⚡ Gibbs Free Energy Calculator

ΔG = ΔH − TΔS — Determine reaction spontaneity.

ΔH (kJ/mol)

ΔS (J/mol·K)

Temperature (K)

—kJ/mol

ΔG

Spontaneous?—

TΔS contribution—

How to Use This Calculator

Enter the enthalpy change ΔH in kJ/mol, the entropy change ΔS in J/(mol·K), and the temperature in Kelvin. The calculator applies ΔG = ΔH − TΔS with the correct unit conversion (ΔS is divided by 1000 to convert J to kJ) and tells you whether the reaction is spontaneous at that temperature.

Enter ΔH in kJ/mol. This value is negative for exothermic reactions (releases heat) and positive for endothermic ones. For the combustion of methane, ΔH = -890.3 kJ/mol.

Enter ΔS in J/(mol·K). Note the units are joules, not kilojoules. Reactions that increase disorder (gas produced, solid dissolves) have positive ΔS. Typical values range from -200 to +300 J/(mol·K).

Enter the temperature in Kelvin. Convert Celsius to Kelvin by adding 273.15. Room temperature (25 °C) is 298 K. High-temperature industrial reactions might run at 800 K or more.

Click Calculate ΔG. The result shows ΔG in kJ/mol, whether the reaction is spontaneous, and the TΔS contribution so you can see the relative sizes of the enthalpy and entropy terms.

The Gibbs Free Energy Equation

ΔG = ΔH − TΔS ΔG < 0: Spontaneous in forward direction ΔG = 0: System is at equilibrium ΔG > 0: Non-spontaneous (reverse direction is spontaneous)

T is the absolute temperature in Kelvin. ΔH and ΔS must use consistent energy units (both kJ or both J) before calculating. A common mistake is forgetting to convert ΔS from J/(mol·K) to kJ/(mol·K), which gives ΔG values that are off by a factor of 1000.

Spontaneity at Different Temperatures

ΔH negative, ΔS positiveSpontaneous at all temperatures (ΔG always negative)

ΔH positive, ΔS negativeNever spontaneous at any temperature (ΔG always positive)

ΔH negative, ΔS negativeSpontaneous only at low T (enthalpy term dominates)

ΔH positive, ΔS positiveSpontaneous only at high T (entropy term dominates)

Where This Calculation Comes Up

The crossover temperature (where ΔG = 0 and T = ΔH/ΔS) is one of the most useful numbers in thermochemistry. For the decomposition of calcium carbonate CaCO₃ → CaO + CO₂, ΔH = +178 kJ/mol and ΔS = +161 J/(mol·K). The crossover temperature is 178,000/161 = 1106 K (833 °C). Below that temperature the reaction is not spontaneous; above it, calcination proceeds. This is exactly why cement kilns operate above 900 °C. You can calculate the same threshold for any reversible reaction to find at what temperature product formation becomes favoured.

In biochemistry, ΔG° relates to the equilibrium constant through ΔG° = -RT ln K. At 298 K with R = 8.314 J/(mol·K), a ΔG° of -5.7 kJ/mol corresponds to K = 10, and -11.4 kJ/mol corresponds to K = 100. Cells couple reactions with large negative ΔG (like ATP hydrolysis, ΔG° = -30.5 kJ/mol) to reactions with positive ΔG that would otherwise not occur. Calculating ΔG under cellular conditions (not standard conditions) requires the full expression ΔG = ΔG° + RT ln Q, but this calculator gives you the standard value to start from.

Frequently Asked Questions

What is Gibbs free energy?

ΔG = ΔH − TΔS. It predicts spontaneity: ΔG < 0 means spontaneous, ΔG > 0 non-spontaneous, ΔG = 0 at equilibrium.

What units are used?

ΔH in kJ/mol, ΔS in J/(mol·K), T in Kelvin. Note: ΔS must be converted to kJ by dividing by 1000.

When is a reaction always spontaneous?

When ΔH < 0 and ΔS > 0 (exothermic and entropy increasing). ΔG is negative at all temperatures.

When is a reaction never spontaneous?

When ΔH > 0 and ΔS < 0 (endothermic and entropy decreasing). ΔG is always positive.

What is the relationship between ΔG and equilibrium?

ΔG° = −RT ln K, where K is the equilibrium constant. More negative ΔG° means K > 1 and products are favoured.