How to find oxidation numbers

An oxidation number (or oxidation state) is the charge an atom would have if every bond in the compound were fully ionic, with the shared electrons given to the more electronegative atom. It is a bookkeeping tool rather than a real charge, but it shows at a glance which atoms have lost or gained electrons, which is the key to redox reactions.

Oxidation number rules

These are the standard rules, as set out in OpenStax Chemistry. Apply them in this order of priority.

How to find an oxidation number: step by step

1. Write the formula and note the overall charge.
2. Fill in the atoms you know from the rules, such as H, O, F and group 1 and 2 metals.
3. Multiply each oxidation number by the number of those atoms in the formula.
4. Set up the sum: everything added together equals the overall charge.
5. Solve for the unknown, and divide if there is more than one of that atom.
6. Write the sign: oxidation numbers are written with the sign first, like +6 or −3.

Worked examples

Example 1: sulfur in H₂SO₄

Hydrogen is +1 and oxygen is −2, and the compound is neutral.

So 2 + S − 8 = 0, and S = +6.

Example 2: manganese in KMnO₄

Potassium is in group 1, so +1. Oxygen is −2. The compound is neutral: +1 + Mn + 4(−2) = 0, so Mn = +7. That high oxidation number is why potassium manganate(VII), also called potassium permanganate, is such a strong oxidising agent.

Example 3: chromium in Cr₂O₇²⁻

This is an ion with charge −2, and there are two chromium atoms.

So 2Cr = 12, and each Cr = +6. Remember to divide by the number of atoms.

Example 4: nitrogen in NH₄⁺

Hydrogen is +1 and the ion's charge is +1: N + 4(+1) = +1, so N = −3. Oxidation numbers can be negative.

Example 5: one element, many oxidation numbers

Carbon shows how oxidation numbers track electron gain and loss. In CH₄, C + 4(+1) = 0, so carbon is −4. In CO₂, C + 2(−2) = 0, so carbon is +4. Burning methane takes carbon from −4 to +4: it has been oxidised.

Example 6: the exceptions

• Hydrogen peroxide, H₂O₂: hydrogen is +1, so 2(+1) + 2O = 0 and each O = −1, not −2.
• Sodium hydride, NaH: sodium is +1 (group 1 outranks hydrogen), so H = −1.
• Fe₃O₄: 3Fe + 4(−2) = 0 gives Fe = +8/3. A fraction means the compound contains the element in more than one oxidation state: here one Fe²⁺ and two Fe³⁺, which average +8/3.

Oxidation numbers in names

When an element can have more than one oxidation number, chemical names show it as a Roman numeral in brackets. Iron(II) chloride is FeCl₂, with iron at +2, and iron(III) chloride is FeCl₃, with iron at +3. Copper(II) sulfate contains Cu²⁺. Working back from a name to a formula is a quick check on your oxidation numbers.

Using oxidation numbers to spot redox

Oxidation is an increase in oxidation number (loss of electrons). Reduction is a decrease in oxidation number (gain of electrons). The memory aid OIL RIG stands for Oxidation Is Loss, Reduction Is Gain, of electrons.

• Zinc goes from 0 to +2: its oxidation number rises, so zinc is oxidised. It is the reducing agent.
• Copper goes from +2 to 0: its oxidation number falls, so copper is reduced. Cu²⁺ is the oxidising agent.
• The total rise (+2) equals the total fall (−2), because the electrons zinc loses are the ones copper gains.

If no oxidation number changes in a reaction, it isn't a redox reaction. Neutralisation and precipitation reactions are common examples. Our Chemical Bonding course explains the ions behind these charges, and the Equation Balancer checks that redox equations balance.

Common mistakes

• Forgetting to multiply by the number of atoms: four oxygens at −2 make −8, not −2.
• Forgetting the ion's charge. For SO₄²⁻, the sum is −2, not 0.
• Forgetting to divide when there are two or more atoms of the unknown element, as in Cr₂O₇²⁻.
• Applying O = −2 to peroxides or H = +1 to metal hydrides.
• Writing the sign after the number. Oxidation numbers are +3 or −2. Ion charges are written 3+ or 2−.
• Mixing up oxidation and reduction. Oxidation number up means oxidised. Down means reduced.

Read next

Chemistry · Reactions and electrolysisWhat is oxidation? Definition, examples and OIL RIGWhat oxidation is: gain of oxygen, loss of hydrogen or loss of electrons. Redox reactions, half equations, oxidation numbers and everyday examples.