Gibbs Free Energy Calculator

Free Gibbs Free Energy Calculator

This tool solves the Gibbs free energy equation, ΔG = ΔH − TΔS, for whichever piece you're missing — ΔG, ΔH, ΔS, or temperature — and tells you straight away whether a process will happen on its own. Type in the values you already know, pick your units, and it handles every conversion behind the scenes, shows the full working, and points out the exact temperature where a reaction would switch from spontaneous to non-spontaneous (or the other way around).

There's also an Advanced Tools tab for the parts of thermodynamics that go beyond the basic equation: flipping between standard free energy (ΔG°) and the equilibrium constant K, adjusting for real (non-standard) conditions using the reaction quotient Q, and converting a free energy value into the standard cell potential E° for electrochemistry problems. Everything is free, works instantly in your browser, and needs no sign-up.

What Is Gibbs Free Energy?

Gibbs free energy, named after the American scientist Josiah Willard Gibbs, is a single number that tells you whether a chemical or physical process can happen by itself, without any outside push. It does this by combining two things that usually pull in opposite directions: enthalpy (ΔH), which is the heat a process gives off or takes in, and entropy (ΔS), which is a measure of how much disorder or spread-out-ness increases.

Think of ΔG as the process's 'willingness' to happen on its own. A reaction can release a lot of heat but still refuse to happen if it makes things too ordered; another reaction might absorb heat but still run happily if it creates enough disorder to make up for it. Gibbs free energy is what lets you weigh both effects together and get one clear answer.

The Gibbs Free Energy Formula

The equation is ΔG = ΔH − TΔS. ΔH is the change in enthalpy, usually given in kJ/mol or kcal/mol. ΔS is the change in entropy, almost always given in much smaller units — J/(mol·K) rather than kJ/(mol·K). T is the absolute temperature, and it must be in kelvin; using Celsius or Fahrenheit directly in this formula gives a wrong answer.

The biggest everyday mistake with this formula isn't the algebra — it's the units. ΔH usually comes in kilojoules and ΔS in plain joules, so if you don't convert one of them first, your answer can be off by a factor of a thousand. This calculator converts everything to a common basis automatically, so you can enter values in whatever unit your textbook or lab data happens to use.

How to Use This Calculator

Start on the Standard Solver tab and choose what you want to find — ΔG, ΔH, ΔS, or T — from the dropdown. The three boxes for the values you already know will appear automatically, and the one you're solving for gets a simple unit selector instead, so you can still choose how the answer is displayed.

Type in your numbers with the correct sign — negative for heat released or for a decrease in disorder, positive for heat absorbed or an increase in disorder — pick the matching units, and the result, spontaneity verdict, and full step-by-step solution update instantly. No need to press a calculate button.

Reading the Sign: What Negative or Positive ΔG Means

The sign of ΔG is the whole story. A negative ΔG means the process is spontaneous (chemists also call this exergonic) — it can proceed on its own and, in principle, could be harnessed to do useful work. A positive ΔG means the process is non-spontaneous (endergonic) — it needs a continuous input of energy to keep going, and left alone it will run backward instead.

A ΔG of exactly zero means the system is sitting at equilibrium. Forward and reverse processes are happening at exactly matched rates, so there's no further net change — this is the same idea as a see-saw perfectly balanced in the middle.

The Four Sign Combinations of ΔH and ΔS

Because ΔG depends on both ΔH and ΔS, and temperature sits right in the middle of the equation, there are exactly four possible situations, and it's worth knowing all of them by heart. If ΔH is negative and ΔS is positive, the reaction is spontaneous at every temperature — both terms are pushing in the same helpful direction. If ΔH is positive and ΔS is negative, the reaction is never spontaneous, at any temperature — both terms work against it.

The two mixed cases are the interesting ones. If ΔH is negative and ΔS is also negative, the reaction is spontaneous only at low temperature, because a large TΔS term at high temperature eventually overwhelms the favorable ΔH. If ΔH is positive and ΔS is positive, the opposite happens — the reaction only becomes spontaneous once the temperature is high enough for TΔS to outweigh the unfavorable ΔH.

Crossover Temperature: Where a Reaction Changes Its Mind

For the two mixed cases above, there's a precise temperature where the reaction flips from spontaneous to non-spontaneous, or the reverse. That's the point where ΔG equals exactly zero, which happens at T = ΔH / ΔS. This calculator works out that crossover temperature automatically from whatever ΔH and ΔS values end up in the result.

A simple, familiar example is ice melting. At exactly 0°C (273.15 K), solid and liquid water sit in perfect balance — ΔG for melting is zero. Below that temperature, freezing is spontaneous; above it, melting is spontaneous. That single crossover temperature is the melting point itself, and it comes from exactly this same T = ΔH/ΔS relationship.

Worked Example: Is This Reaction Spontaneous at Room Temperature?

Take the industrial synthesis of ammonia, N2 + 3H2 → 2NH3, which has ΔH ≈ −92.2 kJ/mol and ΔS ≈ −198.7 J/(mol·K) — heat is released, but gas molecules are being 'used up' to build a more ordered product, so entropy drops. At room temperature, 298 K, the TΔS term works out to 298 × (−198.7) = −59,211 J/mol, or about −59.2 kJ/mol.

Plugging into ΔG = ΔH − TΔS gives −92.2 − (−59.2) = −33.0 kJ/mol — clearly negative, so the reaction is thermodynamically spontaneous at room temperature. In real industrial practice, though, the Haber process is still run at high temperature (400–500°C) and high pressure — not because thermodynamics demands it, but because the reaction is far too slow at room temperature; the higher temperature speeds up the kinetics even though it actually makes ΔG less favorable, which is exactly the kind of trade-off this calculator can help you see by comparing results at different temperatures.

Gibbs Free Energy and the Equilibrium Constant (K)

Standard Gibbs free energy, ΔG°, connects directly to a reaction's equilibrium constant K through ΔG° = −RT ln K, where R is the gas constant, 8.314 J/(mol·K). A large negative ΔG° gives a huge K, meaning the reaction runs essentially to completion. A ΔG° close to zero gives a K close to 1, meaning a real, meaningful mixture of both reactants and products at equilibrium. A positive ΔG° gives a tiny K, meaning barely any product forms at all.

The Advanced Tools tab on this calculator lets you go either direction instantly — enter a known ΔG° to get K, or enter a known K to get ΔG° — at any temperature you choose, with the full working shown underneath.

Advanced Tools: Reaction Quotient (Q) and Real-World ΔG

Most real reactions aren't sitting neatly at the standard conditions (1 M concentrations, 1 atm pressure) that ΔG° assumes. The actual free energy at any given moment is ΔG = ΔG° + RT ln Q, where Q is the reaction quotient — the same ratio of products to reactants used for K, just calculated at whatever concentrations exist right now, not necessarily at equilibrium.

This calculator's Advanced Tools tab includes a Q input for exactly this reason. Leave it at 1 to stay at standard conditions, or enter a different value to see the real driving force at that instant. As a reaction proceeds, Q keeps shifting until ΔG eventually reaches zero — and that's the precise moment the system has settled into equilibrium.

Connecting to Electrochemistry: Cell Potential (E°)

Gibbs free energy also bridges directly into electrochemistry through ΔG° = −nFE°, where n is the number of moles of electrons transferred in the reaction and F is Faraday's constant, 96,485 coulombs per mole. This is the same relationship that connects a battery's voltage to the underlying thermodynamics of the chemical reaction happening inside it.

Enter a value for n on the Advanced Tools tab and the calculator will work out the corresponding standard cell potential, E°, in volts — useful for anyone moving between a thermodynamics course and an electrochemistry one, or checking a redox reaction's spontaneity from a cell voltage instead of a raw ΔG value.

Units This Calculator Handles

For ΔH and ΔG, you can choose kJ/mol, kcal/mol, or plain J/mol. For ΔS, you can choose J/(mol·K) or cal/(mol·K) — the two units you'll see in almost every textbook. For temperature, you can enter °C, °F, or K directly. Behind the scenes, every value is converted to joules, joules per kelvin, and kelvin before any calculation happens, and the final answer is converted back into whichever unit you asked for.

Limitations to Keep in Mind

This calculator, like most classroom and general chemistry tools, treats ΔH and ΔS as constant across the temperature range you're testing. In reality, both shift slightly with temperature because of heat capacity effects, so results far outside typical lab or classroom conditions (very high temperatures, or conditions near a phase change) should be treated as good estimates rather than lab-grade precision.

The equilibrium constant and cell potential results from the Advanced Tools tab assume standard-state reference conditions unless you adjust them with the reaction quotient Q. For serious research or engineering work, always cross-check against measured data and standard reference tables rather than relying on a single calculated value.

Quick Reference: Every Formula on This Page

ΔG = ΔH − TΔS — the core Gibbs free energy equation. T* = ΔH / ΔS — the crossover temperature where ΔG = 0. ΔG° = −RT ln K, and equivalently K = e^(−ΔG°/RT) — the link between standard free energy and the equilibrium constant. ΔG = ΔG° + RT ln Q — the correction for non-standard, real-world conditions. ΔG° = −nFE° — the bridge between thermodynamics and electrochemical cell potential.