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Oxidation numbers (oxidation states) are a bookkeeping tool that tracks the hypothetical charge an atom would have if all bonds were fully ionic. A set of rules governs assignment: free elements are 0, monatomic ions equal their charge, oxygen is usually −2 (except in peroxides), hydrogen is usually +1 (except in metal hydrides), and the sum of oxidation numbers in a neutral compound is 0 (or equals the ion charge for polyatomic ions). Changes in oxidation number across a reaction identify which atoms are oxidized (increase) and which are reduced (decrease).
Memorize the priority rules in order, then practice assigning oxidation numbers to atoms in progressively complex molecules and polyatomic ions. Compare oxidation numbers before and after a reaction to confirm redox has occurred and to identify the number of electrons transferred.
From the periodic table, you know that atoms have characteristic tendencies to gain or lose electrons based on their position — metals tend to lose, nonmetals tend to gain. Oxidation numbers extend this idea into a universal bookkeeping system that tracks where electrons "belong" in any compound, even covalent ones where electrons are actually shared. The trick is to pretend that every bond is fully ionic: assign all shared electrons to the more electronegative atom, then count up the hypothetical charge on each atom. The resulting number is the oxidation state.
A set of priority rules makes assignment systematic. Free elements (like O₂, Fe, or S₈) have an oxidation number of 0 — atoms bonded only to identical atoms have no reason to shift electrons. Monatomic ions have oxidation numbers equal to their charge (Na⁺ is +1, Cl⁻ is −1). Fluorine is always −1 because it is the most electronegative element — nothing pulls electrons away from it. Oxygen is almost always −2 (except in peroxides like H₂O₂, where it is −1, because each oxygen shares electrons equally with the other oxygen). Hydrogen is +1 when bonded to nonmetals and −1 in metal hydrides like NaH. And crucially, the oxidation numbers in any neutral compound must sum to zero, while in a polyatomic ion they must sum to the ion's charge. This last rule is your algebraic handle: when you know the oxidation numbers of all atoms but one, you can solve for the unknown.
Consider the permanganate ion, MnO₄⁻. Oxygen is −2, and there are four oxygens: 4(−2) = −8. The overall charge is −1. So manganese must be +7, because +7 + (−8) = −1. In Cr₂O₇²⁻, the seven oxygens contribute −14, the ion charge is −2, so two chromiums share +12, making each Cr +6. This algebraic approach works for any compound or ion, no matter how complex.
The real power of oxidation numbers appears when you compare them across a reaction. If an atom's oxidation number increases from reactant to product, that atom has been oxidized — it has lost electrons (or behaves as if it did). If the number decreases, the atom has been reduced — it has gained electrons. This is how you identify redox reactions and figure out which species is the oxidizing agent (contains the atom being reduced) and which is the reducing agent (contains the atom being oxidized). For example, in the reaction 2Fe₂O₃ + 3C → 4Fe + 3CO₂, iron goes from +3 to 0 (reduced) and carbon goes from 0 to +4 (oxidized). The number of electrons lost must equal the number gained, which is the principle you will use when you begin writing and balancing half-reactions.