Entropy is the thermodynamic measure of disorder — how many ways a system's particles and energy can be arranged while still looking the same from the outside. Calculating the entropy change of a reaction, ΔS, tells you whether a process makes the world more or less random, which is half of what determines whether a reaction happens spontaneously.
Entropy as a state function
Like enthalpy, entropy is a state function — it depends only on a system's current state, not on the path taken to get there. That means every substance has an absolute standard molar entropy S° that can be tabulated (unlike enthalpy, where only differences ΔH are meaningful, since there's no true zero point for energy). This is a consequence of the third law of thermodynamics, which sets the entropy of a perfect crystal at absolute zero to exactly zero.
Two equivalent ways to find ΔS
You can calculate ΔS for a reaction two ways that agree with each other. The standard-entropy method sums ΣS°(products) − ΣS°(reactants) using tabulated values, the same way ΔH is found from formation enthalpies. The heat-based method, ΔS = q/T, applies to any reversible process and is especially useful for phase changes like melting or boiling, which happen at a constant temperature — this is, in fact, the operational definition entropy was originally built from.
Reading the sign of ΔS
A positive ΔS means the products are more disordered than the reactants — common when a reaction produces more moles of gas, dissolves a solid, or breaks a large molecule into smaller pieces. A negative ΔS means the system becomes more ordered, such as when gas molecules combine into a liquid or solid, or when several small molecules combine into one larger one. Predicting the sign from molecular reasoning is a useful sanity check before trusting a calculated number.
Entropy and spontaneity
The second law of thermodynamics says the total entropy of the universe never decreases for a spontaneous process — but a system's own entropy can decrease locally, as long as the surroundings' entropy increases by at least as much. Whether a reaction is spontaneous overall depends on Gibbs free energy, ΔG = ΔH − TΔS, which weighs entropy against enthalpy. A reaction with negative ΔS can still be spontaneous if it releases enough heat (very negative ΔH) to compensate — see the Gibbs Free Energy calculator to combine both effects.