Gibbs Free Energy Calculator
Use this fast, accurate Gibbs free energy calculator to find any one of the four variables in the famous relation ΔG = ΔH − TΔS. Enter three values in your preferred units. We convert behind the scenes and give you clear results with spontaneity guidance, examples, and best-practice notes.
What is Gibbs free energy?
Gibbs free energy, usually written as G, measures the maximum useful non-expansion work a system can deliver at constant temperature and pressure. The change in Gibbs free energy ΔG tells you whether a reaction or process moves forward on its own or needs help. A negative ΔG signals spontaneity. A positive ΔG says the process is non-spontaneous under the stated conditions.
Formal definitions come from thermodynamics and statistical mechanics. If you want the deep dive, see the IUPAC Gold Book entry on Gibbs energy and the summary article on Gibbs free energy.
How the ΔG equation works
The workhorse relation you use in everyday chemistry is:
ΔG = ΔH − TΔS
Each symbol carries weight:
- ΔH — enthalpy change. Heat released or absorbed at constant pressure.
- T — absolute temperature in kelvins.
- ΔS — entropy change. Disorder gained or lost by the system.
Enthalpy pushes reactions that give off heat. Entropy pushes reactions that spread energy and matter. Temperature scales the entropy term, so the same reaction can flip behavior at different temperatures.
Spontaneity rules at a glance
Use this quick matrix to predict direction. It assumes ΔH and ΔS don’t change sign over the temperature range of interest.
| ΔH | ΔS | Low T | High T |
|---|---|---|---|
| − (exothermic) | + (entropy increases) | Spontaneous | Spontaneous |
| − | − | Spontaneous | Non-spontaneous |
| + | + | Non-spontaneous | Spontaneous |
| + | − | Non-spontaneous | Non-spontaneous |
How to use the calculator
- Select the quantity you want to solve for: ΔG, ΔH, ΔS, or T.
- Enter the other three values. Pick units that match your data. We normalize internally.
- Press calculate. You’ll see the result, the full set of values in standard units, and a spontaneity label like “Spontaneous (ΔG < 0)”.
You can mix units. For example, use kilojoules for ΔH, joules per kelvin for ΔS, and kelvins for T. The engine converts to a consistent base system before computing.
Units, constants, and conversions
Keep temperature in kelvins for thermodynamic work. Use the conversion T(K) = T(°C) + 273.15.
- ΔH: J, kJ, cal, or kcal. We follow SI by reporting in kJ.
- ΔS: J/K or kJ/K. We match the energy unit scaling so ΔH and TΔS align.
- ΔG: J or kJ. We show kJ by default.
If you move into equilibrium work you also meet the gas constant R. The value used most often is R = 8.314462618 J·mol⁻¹·K⁻¹, as listed by NIST CODATA.
Worked examples
Example 1 — Will the reaction go on its own?
Suppose ΔH = −125 kJ, ΔS = +285 J/K, and T = 298 K. Convert entropy to kJ/K: 0.285 kJ/K. Compute:
ΔG = ΔH − TΔS = −125 − 298×0.285 = −125 − 84.93 = −209.93 kJ
ΔG is negative. The process is spontaneous at room temperature.
Example 2 — Find ΔH from ΔG, ΔS, and T
Let ΔG = +12 kJ, ΔS = −40 J/K (−0.040 kJ/K), T = 350 K.
ΔH = ΔG + TΔS = 12 + 350×(−0.040) = 12 − 14 = −2 kJ
The enthalpy term is slightly exothermic. Entropy is unfavorable here so the overall ΔG rises above zero at this temperature.
Example 3 — From equilibrium constant to ΔG°
At equilibrium we relate standard Gibbs energy to the equilibrium constant with:
ΔG° = −RT ln K
Imagine K = 4.2×10³ at 298 K. Using R = 8.314462618 J·mol⁻¹·K⁻¹:
ΔG° = −8.314462618 × 298 × ln(4.2×10³) = −8.314462618 × 298 × 8.341 = −20680 J·mol⁻¹ ≈ −20.68 kJ·mol⁻¹.
A strongly negative ΔG° pairs with a large K as expected. Background reading: ΔG and K relationship.
Energy–temperature diagram
The graphic below shows how the entropy term changes the outcome. The slope equals −ΔS while the intercept equals ΔH. Where the line crosses zero you have the threshold temperature for spontaneity.
ΔG°, equilibrium, and cell potential
Chemists often switch between energy language and equilibrium language. The bridge is:
ΔG° = −RT ln K
Large K values produce negative ΔG°. Small K values produce positive ΔG°. At K = 1, ΔG° equals zero.
Electrochemistry uses a second bridge. Standard Gibbs energy links to the standard cell potential:
ΔG° = −nF E°
Here n equals moles of electrons transferred and F equals the Faraday constant. See the succinct overview in LibreTexts.
Common pitfalls and pro tips
- Keep temperature in kelvins. Celsius in the equation leads to the wrong answer.
- Match units. Convert ΔS to kJ/K if ΔH is in kJ. The calculator can do it, yet understanding prevents mistakes on exams and in lab notebooks.
- Mind standard vs. non-standard conditions. ΔG and ΔG° are not the same away from 1 bar and unit activities.
- Watch for temperature dependence. ΔH and ΔS can vary with temperature for big ranges. The simple linear model works best over modest spans.
- Remember coupling. A non-spontaneous step (ΔG > 0) can proceed when coupled to a strongly spontaneous step. Biochemistry thrives on this trick.
Frequently asked questions
What does a negative ΔG mean?
A negative ΔG means the process is thermodynamically favorable at the stated temperature and pressure. You still need a pathway. Kinetics can slow a favorable reaction if the activation barrier is high.
Can ΔG be zero?
Yes. ΔG equals zero at equilibrium for the conditions in question. The system shows no net change even though molecules continue to react in both directions.
How do I convert between ΔG° and K?
Use ΔG° = −RT ln K. Plug R in J·mol⁻¹·K⁻¹ and T in K. Convert the result to kJ if you prefer. When K is 1 the natural log is zero so ΔG° is zero.
Is entropy always positive?
The universe tends to higher entropy, yet a system can lose entropy in a single step. Freezing water shows ΔS < 0 for the system even though the surroundings carry away heat.
Why does temperature change spontaneity?
Temperature multiplies the entropy term. Raise T and the TΔS term grows. If ΔS is positive then high temperature pushes ΔG downward. If ΔS is negative then high temperature pushes ΔG upward.
Wrap-up
When you need a decision at the bench or on an exam, reach for the Gibbs Free Energy Calculator. Enter three values and the tool computes the fourth along with a clear spontaneity verdict. The equation ΔG = ΔH − TΔS organizes your thinking. Entropy and enthalpy tug in different directions; temperature chooses the winner. Bookmark this page for quick checks and explore the linked resources to go deeper.
Quick answers
- Formula: ΔG = ΔH − TΔS (T in kelvins).
- Spontaneous? ΔG < 0 means yes. ΔG > 0 means no. ΔG = 0 at equilibrium.
- Equilibrium link: ΔG° = −RT ln K.
- Electrochemistry link: ΔG° = −nF E°.
- Units: ΔH and ΔG in kJ, ΔS in kJ·K⁻¹, T in K.
