This oxidation number calculator runs the bookkeeping rule of redox chemistry: the oxidation numbers in a species sum to its overall charge. Enter the species’ charge, the combined contribution of all the OTHER atoms (their oxidation number × count, summed), and how many atoms of the target element there are — it returns the target’s oxidation state, alongside a quick-check table for famous species.

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The Rules, the Algebra, and the Traps

Oxidation numbers are assigned by a rule hierarchy: free elements are 0; monatomic ions equal their charge; fluorine is always −1; oxygen is −2 EXCEPT peroxides (−1), superoxides (−½) and OF₂ (+2); hydrogen is +1 EXCEPT metal hydrides (−1); Group 1 metals +1, Group 2 +2 — and everything sums to the species’ charge. The calculator automates the final step: demarcate the knowns, solve for the unknown. Defaults run dichromate, Cr₂O₇²⁻: seven oxygens contribute −14, the ion’s charge is −2, two chromiums share the difference: x = (−2 + 14)/2 = +6 — chromium’s maximum, matching CrO₃ and chromic acid: hexavalent chromium, the oxidizer of breathalyzers and the villain of water-contamination cases, identified by one line of algebra.

The traps cluster around the exceptions: KMnO₄’s manganese is +7 only because oxygen is honestly −2 there; in H₂O₂ oxygen is −1 (peroxide) making hydrogen still +1; in NaH hydrogen is −1 (hydride) flipping Na to its usual +1 by necessity; Fe₃O₄ returns the famous +8/3 average because the solid really contains Fe²⁺ and 2 Fe³⁺ — mixed valence, where a fractional calculator answer is the CORRECT signal, and this page says so instead of rounding it away. Organic chemistry adds the per-carbon reality: carbons in one molecule differ (ethanol’s carbons are −3 and −1), so “the oxidation number of carbon in glucose” is an average (0) that hides the chemistry — averages sum correctly and inform loosely.

Quick-Check Table (Verified Classics)

  • KMnO₄: knowns K +1, O₄ −8; charge 0 → Mn = 0 − (−7) = +7.
  • H₂SO₄: H₂ +2, O₄ −8 → S = +6. (H₂SO₃: S = +4 — sulfite vs sulfate by 2.)
  • NH₄⁺: H₄ +4, charge +1 → N = −3. (NO₃⁻: N = +5; the nitrogen ladder −3 → +5 spans 8 electrons.)
  • Cr₂O₇²⁻ (defaults): Cr = +6.
  • H₂O₂: H₂ +2, charge 0 → each O = −1 (the peroxide exception).

Oxidation Number Discipline

  • Apply the hierarchy in order: F first, then metals’ fixed states, oxygen, hydrogen — assign the confident atoms before solving for the interesting one.
  • Peroxide/superoxide check before assuming O = −2: any O–O bond changes the rules (H₂O₂, Na₂O₂, KO₂).
  • Polyatomic ions keep their internal numbers wherever they travel: sulfate’s S is +6 in H₂SO₄, Na₂SO₄ and CuSO₄ alike — solve once, reuse forever.
  • Oxidation number ≠ actual charge: carbon in CO₂ is +4 without bearing a +4 charge; these are bookkeeping integers for electron accounting, and the bookkeeping is what redox balancing spends.
  • A fractional result is diagnostic, not wrong: mixed valence (Fe₃O₄, Pb₃O₄) or an equivalent-atom average (thiosulfate’s sulfurs are +5 and −1, averaging +2).

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Frequently Asked Questions

How do you find an oxidation number?

Sum the known atoms’ contributions (fixed rules: O usually −2, H usually +1, Group 1 +1, F −1), set (target × its count) + known sum = overall charge, and solve. Dichromate: 2x + 7(−2) = −2 → x = +6. This calculator does that algebra from three inputs — charge, the knowns’ sum, and the target’s atom count — and flags fractional (mixed-valence) answers.

What are the oxidation number rules in order?

(1) Free elements: 0. (2) Monatomic ions: their charge. (3) Fluorine: −1, always. (4) Group 1: +1, Group 2: +2 in compounds. (5) Hydrogen: +1, except metal hydrides −1. (6) Oxygen: −2, except peroxides −1, superoxides −½, OF₂ +2. (7) The sum equals the species’ overall charge (0 for neutral compounds). Apply the confident rules first; the remaining element absorbs the balance — which is what the calculator solves.

Why is oxygen −1 in peroxides?

Because the O–O bond splits its electrons evenly between identical atoms, leaving each oxygen with only one electron gained from its partner atom (vs two in water/oxides). H₂O₂: the two hydrogens contribute +2, so the two oxygens share −2 → −1 each. The structural clue is the O–O bond itself; superoxides (O₂⁻) split further to −½ each — fractional per-atom values that are genuinely correct here.

What does a fractional oxidation number mean?

Mixed valence or averaged non-equivalent atoms. Fe₃O₄: the +8/3 average resolves into one Fe²⁺ and two Fe³⁺ — real ions, integer states, mixed population. Thiosulfate S₂O₃²⁻: average +2, actual +5 and −1 on structurally different sulfurs. The calculator’s non-integer warning points you at the resolution rather than letting you report +2.67 as a physical state.

Oxidation number vs charge vs valence — what’s the difference?

Charge is physical (ions carry it; atoms in covalent compounds mostly don’t carry full charges). Valence is bonding capacity (how many bonds). Oxidation number is the accounting construct: the charge an atom WOULD have if all bonds were ionic, assigned by electronegativity. It exists to track electron transfer — oxidation is an INCREASE in oxidation number, reduction a decrease (OIL RIG), regardless of actual charge distributions.

Which elements have only one oxidation state?

Fluorine (−1 in compounds), Group 1 (+1), Group 2 (+2), aluminium (+3), and (nearly) zinc (+2) and silver (+1) — the fixed points that make the algebra solvable. Transition metals are the interesting variables: Fe +2/+3, Cu +1/+2, Mn +2 through +7, Cr +2/+3/+6 — their multi-state flexibility is precisely why a calculator earns its place on this page.

How are oxidation numbers used to balance redox equations?

The oxidation-number method: assign all states, find each element’s change, and scale so total electrons lost = total gained (the change in oxidation number × atoms must balance between the oxidized and reduced species). In dichromate–iron titrations: Cr goes +6 → +3 (gain 3 per Cr, 6 per Cr₂O₇²⁻), Fe²⁺ → Fe³⁺ (lose 1) — hence the famous 1:6 ratio Cr₂O₇²⁻ : Fe²⁺ before waters and protons tidy the rest.

Is this oxidation number calculator free?

Yes — free, instant, no sign-up. Enter the species’ charge, the other atoms’ summed contributions and the target atom count for the oxidation state, with a classic-species quick-check table included.