Gibbs free energy calculator
With ΔH of −100 kJ/mol, ΔS of −0.2 kJ/(mol·K) and 298.15 K, ΔG is −40.37 kJ/mol, so the reaction is spontaneous. Enter the three values to see ΔG, the TΔS term of −59.63 and the verdict. Free in your browser.
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Worked example
- Delta h
- -100
- Delta s
- -0.2
- Temperature k
- 298.15
- T delta s
- -59.63
- Delta g
- -40.37
- Spontaneity
- spontaneous
Gibbs free energy tells you whether a chemical or physical process can proceed spontaneously at constant temperature and pressure. The defining isothermal relation is Delta G equals Delta H minus T times Delta S: the enthalpy change is the heat-like driving term, the product of absolute temperature and entropy change is the disorder term, and their difference is the free energy available for non-expansion work. When Delta G is negative the forward process is spontaneous under those conditions; when it is positive the reverse is favored; when it is zero the system sits at equilibrium for that temperature. This calculator takes three finite numbers—enthalpy change, entropy change, and temperature in kelvin—returns Delta G together with the intermediate T Delta S product and a clear spontaneity label, and rejects physically invalid negative kelvin temperatures instead of inventing a meaningless result. Keep energy units consistent between Delta H and Delta S (for example both in kilojoules per mole, or both in joules per mole with matching entropy units).
How Gibbs free energy is computed from ΔH, ΔS and T
Start from the classical thermodynamic identity for the change in Gibbs free energy at constant temperature: Delta G equals Delta H minus T times Delta S. Here Delta H is the enthalpy change of the process, Delta S is the entropy change of the system, and T is the absolute temperature on the kelvin scale.
The product T Delta S has the same energy units as Delta H once you keep Delta S expressed as energy per kelvin in the matching unit family, so their difference is a well-defined free-energy change. Physically, enthalpy captures heat exchanged at constant pressure while the T Delta S term accounts for the portion of energy tied up in entropy production or consumption; free energy is what remains available for useful work beyond expansion work.
Sign conventions follow standard chemistry textbooks: negative Delta H is exothermic, positive Delta S increases disorder, and the combination can make Delta G negative even for endothermic processes if temperature and entropy cooperate. Absolute temperature must not be negative; kelvin values below zero are rejected because they lie outside the thermodynamic temperature scale used in this formula. Zero kelvin is accepted as a mathematical edge case and yields Delta G equal to Delta H.
Missing fields, non-numeric strings, NaN, and Infinity fail validation before any arithmetic runs.
Where Gibbs free energy calculations show up in real work
General chemistry and physical chemistry courses assign endless Delta G sign tables, temperature thresholds where spontaneity flips, and comparisons of enthalpy-driven versus entropy-driven reactions; a single trusted oracle that returns both the number and the spontaneity class speeds grading and demo setup. Process engineers screening reaction conditions at fixed pressure estimate whether a candidate path is thermodynamically favorable before investing in kinetics or catalyst studies. Materials and battery researchers compare free-energy changes of competing solid-state transformations at operating temperature.
Environmental and geochemistry models evaluate mineral dissolution or precipitation affinity using the same isothermal relation once tabulated Delta H and Delta S are in hand. If you later need only entropy change from heat over temperature, heat capacity integrals, van't Hoff equilibrium constants, or tabulated formation free energies from databases, treat those as separate search intents and landings rather than overloading this isothermal Gibbs calculator page.
What you can do with it
Homework and exam answer keys
Compute ΔG and spontaneity class from textbook ΔH, ΔS, and T sets so teachers and auto-graders share one ground truth.
Reaction favorability at process temperature
Screen whether a reaction is thermodynamically spontaneous at a chosen kelvin temperature before kinetic or scale-up work.
Entropy-driven versus enthalpy-driven cases
Compare high-T and low-T outcomes when ΔH and ΔS have opposing signs and the TΔS term can reverse the sign of ΔG.
FAQ
What formula does this Gibbs free energy calculator use?
The isothermal relation ΔG = ΔH − TΔS.
What happens if temperature is negative?
Absolute temperature in kelvin cannot be negative; negative kelvin is physically invalid for this formula.
What units should I use for ΔH and ΔS?
Any consistent energy unit family. If ΔH is in kJ/mol, use ΔS in kJ/(mol·K). If ΔH is in J/mol, use ΔS in J/(mol·K). The calculator does not convert between kilojoules and joules for you.
How is spontaneity decided?
Kinetics and non-standard activities are out of scope.
What does it cost?
The browser tool is free and runs locally.
Related tools
For developers — API access
Everything on this page is available programmatically. This section is for teams who want to wire it into their own systems; everyone else can just use the tool above.
API endpoint
Prefer to automate it? One authenticated POST creates the task; the result comes back by webhook or a signed link. The same capability also runs here on the web, by email and from Telegram — and soon from our app too.
Call it from your stack
curl -X POST https://api.kit.forhosting.com/chem/gibbs-free-energy \
-H "Authorization: Bearer $KIT_KEY" \
-H "Content-Type: application/json" \
-d '{"delta_h":-100,"delta_s":-0.2,"temperature_k":298.15}'const res = await fetch("https://api.kit.forhosting.com/chem/gibbs-free-energy", {
method: "POST",
headers: {
"Authorization": `Bearer ${process.env.KIT_KEY}`,
"Content-Type": "application/json"
},
body: JSON.stringify({
"delta_h": -100,
"delta_s": -0.2,
"temperature_k": 298.15
})
});
const { task_id } = await res.json();import os, requests
res = requests.post(
"https://api.kit.forhosting.com/chem/gibbs-free-energy",
headers={"Authorization": f"Bearer {os.environ['KIT_KEY']}"},
json={
"delta_h": -100,
"delta_s": -0.2,
"temperature_k": 298.15
},
)
task_id = res.json()["task_id"]<?php
$res = file_get_contents("https://api.kit.forhosting.com/chem/gibbs-free-energy", false, stream_context_create([
"http" => [
"method" => "POST",
"header" => "Authorization: Bearer " . getenv("KIT_KEY") . "\r\nContent-Type: application/json",
"content" => '{"delta_h":-100,"delta_s":-0.2,"temperature_k":298.15}',
],
]));
$task = json_decode($res, true);body := bytes.NewBufferString(`{"delta_h":-100,"delta_s":-0.2,"temperature_k":298.15}`)
req, _ := http.NewRequest("POST", "https://api.kit.forhosting.com/chem/gibbs-free-energy", body)
req.Header.Set("Authorization", "Bearer "+os.Getenv("KIT_KEY"))
req.Header.Set("Content-Type", "application/json")
res, _ := http.DefaultClient.Do(req)Example request
{
"delta_h": -100,
"delta_s": -0.2,
"temperature_k": 298.15
}Example response
{
"task_id": "tsk_a1b2c3d4e5f6a1b2c3d4e5f6",
"type": "chem.gibbs_free_energy",
"status": "queued",
"_links": {
"result": "/tasks/tsk_…/result"
}
}The API is asynchronous: the call returns a task_id immediately and the result arrives by webhook. Polling is capped at 1 req/s per task.
Pricing
Published price — no tokens, no invented credits. A failed task is never charged.
Errors
| HTTP | Code | Meaning |
|---|---|---|
401 | unauthorized | Missing or invalid API key. |
402 | insufficient_balance | Your balance doesn't cover the task price. |
404 | unknown_type | That task type doesn't exist. |
429 | rate_limited | Too many requests. Use the webhook instead of polling. |
Technical notes
How Gibbs free energy is computed from ΔH, ΔS and T
The entire pipeline is deterministic floating-point arithmetic with no random seeds, no wall-clock timestamps, no network calls, and no model drift, so identical numbers always produce identical JSON.
What you send and what you get back
The formula and method strings document the closed form for audits and teaching slides. Classic checks include room-temperature values near two hundred ninety-eight point one five kelvin with a large negative enthalpy and modest entropy, high-temperature entropy-driven cases where positive Delta S overcomes positive Delta H, and the equilibrium edge where Delta H equals T Delta S exactly. Send three finite numbers under the fields delta_h, delta_s, and temperature_k. All three fields are required. delta_h is the enthalpy change in your chosen energy unit, such as kilojoules per mole or joules per mole. delta_s is the entropy change in energy per kelvin with the same energy unit family, for example kilojoules per mole per kelvin when delta_h is in kilojoules per mole. temperature_k is absolute temperature in kelvin and must be greater than or equal to zero; any negative value fails with invalid_input and a message that absolute temperature cannot be below zero. On success the response echoes the cleaned inputs, reports t_delta_s as the product of temperature and entropy change, reports delta_g as Delta H minus that product, and sets spontaneity to spontaneous when Delta G is negative, non_spontaneous when positive, or equilibrium when Delta G is numerically zero within a tiny floating-point tolerance. Pricing for successful API calls is the published base of $0.002 per item; validation failures do not consume prepaid balance.
Where Gibbs free energy calculations show up in real work
Because this capability is a pure parse engine, API pricing is the published base of $0.002 per successful item and failed validation does not consume balance.