Entropy Calculator
Calculate entropy change for a chemical reaction, connect entropy to Gibbs free energy, or evaluate an isothermal ideal-gas expansion or compression.
Inputs
Live results
The products have a higher total entropy than the reactants, so the system entropy increases for the reaction as written.
How to use this entropy calculator
What this calculator does
This tool evaluates three closely related thermodynamic quantities. In Reaction entropy mode, it subtracts the total entropy of the reactants from the total entropy of the products. In Gibbs free energy mode, it applies ΔG = ΔH – TΔS after converting entropy from joules to kilojoules so the units are consistent. In Ideal gas mode, it calculates the entropy change of an isothermal ideal gas from a volume ratio or pressure ratio. The result is a thermodynamic estimate based on the values and idealized assumptions you supply; it does not by itself determine reaction rate, mechanism, safety, or whether a real gas behaves ideally.
When to use it
Use the reaction mode when comparing tabulated standard molar entropies for a balanced chemical equation. Use the Gibbs mode when you know ΔH, temperature, and ΔS and want to assess the sign of ΔG. Use the ideal-gas mode for reversible isothermal expansion or compression exercises, laboratory planning, and checks of textbook calculations. The LibreTexts overview of thermodynamic entropy provides useful conceptual background.
How to calculate
- The calculator opens with a complete demonstration: products at 377.4 J/K and reactants at 336.0 J/K. The first result is 41.40 J/K, and a validated example workbook is immediately available through Download Excel.
- Choose a Calculation mode. Replace the demonstration values with your own numbers. Inputs accept ordinary decimal notation with a period as the decimal separator; scientific notation and ambiguous comma-decimal formats are rejected.
- Read the large primary result, then use the direction, magnitude, ratio, or spontaneity summary to interpret the sign and scale.
- Select Download Excel to export the current validated inputs, formulas, outputs, and notes as a real .xlsx workbook.
- Select Reset to clear the demonstration data. Reset may disable the Excel download until a complete valid set of inputs is entered again.
Input guide
Calculation mode is required and selects one of the three formulas. In Reaction entropy mode, Total entropy of products and Total entropy of reactants are required finite values in J/K; values such as 377.4 and 336.0 are typical classroom totals. A higher product total raises ΔS, while a higher reactant total lowers it. Do not forget stoichiometric coefficients when forming either total.
In Gibbs free energy mode, Change in enthalpy, ΔH is required in kJ/mol and may be positive or negative; – 92.22 kJ/mol is a realistic exothermic example. Temperature is required in kelvin and must be greater than zero; 298.15 K represents 25 °C. Change in entropy, ΔS is required in J/(mol·K) and may be positive or negative; – 198.1 J/(mol·K) is the startup example. A common mistake is mixing J and kJ without conversion.
In Ideal gas mode, Base variable chooses either volume or pressure. Amount of substance is required in moles and must be positive. Initial volume and Final volume, or the corresponding pressure labels, must both be positive and use the same unit. Ten liters changing to twenty liters gives a ratio of 2. When pressure is selected, the formula uses the negative logarithm of final pressure divided by initial pressure. Only the ratio matters, so consistent units cancel.
Output guide
Entropy change, ΔS is the primary output in the reaction and ideal-gas modes. A positive value means the modeled system entropy increases; a negative value means it decreases; zero means no net change under the stated model. Change in Gibbs free energy, ΔG is the primary Gibbs output in kJ/mol. Negative ΔG indicates thermodynamic spontaneity under the specified constant-temperature, constant-pressure conditions, positive ΔG indicates a nonspontaneous direction, and zero indicates equilibrium. These signs do not predict how fast a process occurs.
The supporting cards report the direction or spontaneity classification, the magnitude, the dimensionless volume or pressure ratio, and the TΔS contribution in kJ/mol where applicable. The formula line shows the exact equation used for the current mode. The summary pills repeat the active mode, sign interpretation, and workbook readiness.
Worked example
For the startup reaction example, total product entropy is 377.4 J/K and total reactant entropy is 336.0 J/K. Applying ΔSreaction = ΣSproducts – ΣSreactants gives 377.4 – 336.0 = 41.4 J/K. Rounded to two decimals, the displayed primary result is 41.40 J/K. Because the result is positive, the direction card reads Entropy increases. The same typed values and result are written to the startup Excel workbook.
Formulas and interpretation
For a chemical reaction, entropy is a state function, so only the initial and final states matter: ΔSreaction = ΣSproducts – ΣSreactants. Standard molar entropy data are commonly reported at a defined standard state, and the coefficients from the balanced equation must multiply each species value. The IUPAC Gold Book definition of standard entropy helps distinguish molar standard values from a total system entropy.
Gibbs free energy combines enthalpy and entropy in ΔG = ΔH – TΔS. Because this calculator accepts ΔH in kJ/mol and ΔS in J/(mol·K), it divides TΔS by 1000 before subtraction. The LibreTexts guide to Gibbs energy explains why the sign of ΔG is tied to spontaneity at constant temperature and pressure.
For an isothermal ideal gas, ΔS = nR ln(V₂/V₁). The equivalent pressure form is ΔS = – nR ln(P₂/P₁). The gas constant used here is 8.314462618 J/(mol·K), consistent with the NIST value of the molar gas constant. Expansion at constant temperature gives a positive entropy change, while compression gives a negative one.