An oxidation number is a number assigned to an atom in a chemical substance to represent its apparent loss, gain, or sharing of electrons. Chemists use oxidation numbers to track how electrons are redistributed during chemical reactions, identify oxidation and reduction, and determine which atoms change their chemical behavior.
Oxidation numbers are especially useful in redox reactions, in which one substance loses electrons while another gains them. They also help chemists balance chemical equations, understand the chemistry of metals and nonmetals, and describe how elements behave in compounds.
To calculate an oxidation number, start with a set of established rules, identify the known oxidation numbers of the other atoms in the substance, and use the overall charge to determine the unknown value. The process becomes straightforward once you understand how the rules fit together.
What an oxidation number represents
An oxidation number, also called an oxidation state, is a bookkeeping tool for tracking electrons in chemical compounds. It assigns electrons in chemical bonds to atoms according to a consistent set of conventions, even when the atoms share electrons unequally.
In an ionic compound such as sodium chloride (NaCl), sodium forms a positive ion, Na⁺, and chlorine forms a negative ion, Cl⁻. Their oxidation numbers are +1 and −1, respectively, reflecting the charges of these ions.
In a covalent compound, atoms share electrons rather than transferring them completely. Water (H₂O), for example, contains covalent bonds between hydrogen and oxygen. Oxygen attracts the shared electrons more strongly than hydrogen does. Under oxidation-number conventions, the bonding electrons are assigned to oxygen, giving oxygen an oxidation number of −2 and each hydrogen an oxidation number of +1.
This assignment does not mean that every oxygen atom in water carries an actual charge of −2. The molecule is electrically neutral, and its electrons are shared. The oxidation numbers are formal values used to describe the distribution of electrons according to a standardized accounting system.
Oxidation numbers can be positive, negative, or zero. They may also be fractional in certain compounds when an average value is assigned to atoms of the same element. These numbers help distinguish different chemical environments and reveal changes that occur during reactions.
The rules for assigning oxidation numbers
Most oxidation-number calculations rely on a small number of rules. Applying them in the right order makes it possible to solve problems involving both simple compounds and more complicated substances.
An element in its free form has an oxidation number of zero. This applies whether the element exists as individual atoms or as molecules made from identical atoms. Examples include iron (Fe), copper (Cu), hydrogen gas (H₂), oxygen gas (O₂), and sulfur (S₈). The oxidation number is zero because the atoms are not combined with a different element.
A monatomic ion has an oxidation number equal to its charge. A monatomic ion consists of a single charged atom. Sodium in Na⁺ has an oxidation number of +1, while magnesium in Mg²⁺ has an oxidation number of +2. Chloride in Cl⁻ has an oxidation number of −1.
The sum of oxidation numbers in a neutral compound is zero. A compound has no net electrical charge, so the oxidation numbers of all its atoms must add up to zero. In carbon dioxide (CO₂), for example, each oxygen has an oxidation number of −2. The two oxygen atoms contribute −4 in total, so carbon must have an oxidation number of +4.
The sum of oxidation numbers in a polyatomic ion equals the ion’s overall charge. A polyatomic ion contains two or more atoms bonded together and carries a net charge. In sulfate (SO₄²⁻), the oxidation numbers of sulfur and four oxygen atoms must add up to −2, the charge of the entire ion.
Group 1 metals have an oxidation number of +1 in their compounds. These elements include lithium, sodium, and potassium. Group 2 metals, including magnesium and calcium, generally have an oxidation number of +2 in their compounds.
Fluorine has an oxidation number of −1 in its compounds. Fluorine attracts bonding electrons more strongly than any other element, so it is assigned those electrons under the standard rules.
Oxygen usually has an oxidation number of −2. This rule applies to most compounds, including water, carbon dioxide, and many metal oxides. There are important exceptions. In peroxides, such as hydrogen peroxide (H₂O₂), oxygen has an oxidation number of −1. In compounds with fluorine, oxygen can have a positive oxidation number because fluorine attracts the bonding electrons more strongly.
Hydrogen usually has an oxidation number of +1 when bonded to nonmetals. In water and methane, for example, hydrogen is assigned +1. When hydrogen bonds to a metal in a metal hydride, such as sodium hydride (NaH), it generally has an oxidation number of −1.
Chlorine, bromine, and iodine usually have an oxidation number of −1 in compounds. However, they can have positive oxidation numbers when bonded to oxygen or fluorine, which attract electrons more strongly.
These rules are not all equally broad. The sum rule for compounds and ions is fundamental, while rules such as the usual oxidation numbers of oxygen and hydrogen have exceptions. Recognizing those exceptions prevents many calculation errors.
How to calculate an oxidation number step by step
The most reliable method is to identify the known oxidation numbers first, represent the unknown value with a variable, and use the total charge to create an equation.
Consider sulfur in sulfur trioxide (SO₃).
First, identify the unknown oxidation number. Let sulfur’s oxidation number be x.
Next, assign oxidation numbers to the other atoms. Oxygen normally has an oxidation number of −2. Because there are three oxygen atoms, their combined contribution is 3 × (−2) = −6.
Then use the rule for a neutral compound. The sum of all oxidation numbers must equal zero:
x + 3(−2) = 0
Simplifying gives:
x − 6 = 0
Therefore:
x = +6
Sulfur has an oxidation number of +6 in sulfur trioxide.
The same approach works for polyatomic ions. The only difference is that the sum must equal the ion’s charge rather than zero. It also works when the unknown atom appears more than once in a formula, provided the number of atoms is included in the equation.
Worked examples of oxidation-number calculations
Working through several examples shows how the rules apply to substances with different formulas and charges.
Water (H₂O)
Water contains two hydrogen atoms and one oxygen atom. Hydrogen normally has an oxidation number of +1, and oxygen normally has an oxidation number of −2.
The sum is:
2(+1) + (−2) = 0
The result matches the zero net charge of water. Each hydrogen has an oxidation number of +1, and oxygen has an oxidation number of −2.
Carbon dioxide (CO₂)
To determine carbon’s oxidation number, let it equal x. Each of the two oxygen atoms has an oxidation number of −2.
The equation is:
x + 2(−2) = 0
x − 4 = 0
x = +4
Carbon has an oxidation number of +4 in carbon dioxide.
Ammonia (NH₃)
Ammonia contains one nitrogen atom and three hydrogen atoms. Hydrogen has an oxidation number of +1 because it is bonded to a nonmetal.
Let nitrogen’s oxidation number be x:
x + 3(+1) = 0
x + 3 = 0
x = −3
Nitrogen has an oxidation number of −3 in ammonia.
Sulfate ion (SO₄²⁻)
The sulfate ion has an overall charge of −2. Oxygen normally has an oxidation number of −2, and four oxygen atoms contribute a total of −8.
Let sulfur’s oxidation number be x:
x + 4(−2) = −2
x − 8 = −2
x = +6
Sulfur has an oxidation number of +6 in sulfate.
The right side of the equation is −2, not zero, because sulfate is an ion with a net negative charge.
Potassium permanganate (KMnO₄)
Potassium permanganate contains potassium, manganese, and oxygen. Potassium is a Group 1 metal, so its oxidation number is +1. Oxygen normally has an oxidation number of −2.
Let manganese’s oxidation number be x. Because the compound is neutral, the equation is:
(+1) + x + 4(−2) = 0
1 + x − 8 = 0
x = +7
Manganese has an oxidation number of +7 in potassium permanganate.
This example illustrates why knowing the periodic table and the common oxidation-number rules is useful. Once the familiar values are assigned, the unknown value follows from the overall charge.
Hydrogen peroxide (H₂O₂)
Hydrogen peroxide demonstrates why exceptions matter. Hydrogen has an oxidation number of +1, but oxygen in a peroxide has an oxidation number of −1 rather than its usual −2.
The calculation is:
2(+1) + 2(−1) = 0
The sum is zero, as required for a neutral compound.
If oxygen were incorrectly assigned −2, the oxidation numbers would add up to −2 instead of zero. Recognizing the peroxide exception avoids that mistake.
How oxidation numbers relate to oxidation and reduction
Oxidation numbers are particularly valuable because they help identify electron-transfer processes, even when electrons are not explicitly shown in a chemical equation.
Oxidation is an increase in oxidation number. It corresponds to the loss of electrons in the standard electron-transfer description of redox chemistry.
Reduction is a decrease in oxidation number. It corresponds to the gain of electrons.
The two processes always occur together in a redox reaction. When one substance loses electrons, another substance gains them.
For example, consider the reaction between magnesium and oxygen:
2Mg + O₂ → 2MgO
Before the reaction, magnesium and oxygen are in their elemental forms, so each has an oxidation number of zero.
In magnesium oxide (MgO), magnesium has an oxidation number of +2 and oxygen has an oxidation number of −2.
Magnesium’s oxidation number increases from 0 to +2, so magnesium is oxidized. Oxygen’s oxidation number decreases from 0 to −2, so oxygen is reduced.
Magnesium supplies electrons, while oxygen accepts them. The increase in magnesium’s oxidation number and the decrease in oxygen’s oxidation number provide a convenient way to track this change.
The substance that causes another substance to be oxidized is called the reducing agent because it supplies electrons. The substance that causes another substance to be reduced is called the oxidizing agent because it accepts electrons. In the magnesium reaction, magnesium is the reducing agent and oxygen is the oxidizing agent.
Oxidation numbers are also useful when the reaction involves covalent compounds, where electrons may be shared rather than transferred completely. In such cases, a change in oxidation number reflects a change in the formal assignment of bonding electrons, not necessarily the movement of a whole electron from one atom to another.
Why oxidation numbers can be positive or negative
The sign of an oxidation number depends on how bonding electrons are assigned and on the overall electrical charge of the substance.
A positive oxidation number generally indicates that an atom is assigned fewer electrons from its bonds than it would have in its neutral elemental form. A negative oxidation number generally indicates that it is assigned more. These are formal comparisons, not direct measurements of an atom’s actual charge in a molecule.
For example, carbon has an oxidation number of −4 in methane (CH₄) and +4 in carbon dioxide (CO₂). In methane, hydrogen is assigned an oxidation number of +1, so carbon must be −4 to make the molecule neutral. In carbon dioxide, oxygen is assigned −2, so carbon must be +4.
Carbon therefore has different oxidation numbers in different compounds. This reflects differences in the elements to which it is bonded and how the bonding electrons are assigned.
An oxidation number of zero can also occur in a compound or molecule when the contributions of different atoms balance. The overall sum for a neutral compound is always zero, but that does not mean each individual atom has an oxidation number of zero. In elemental oxygen (O₂), both atoms have oxidation number zero because the substance consists of the element in its free form.
What fractional oxidation numbers mean
Some compounds have an average oxidation number that is fractional. This does not necessarily mean that an individual atom carries a fractional electrical charge or that its oxidation state is literally divided into a fraction.
Iron oxide Fe₃O₄, commonly called magnetite, provides an example. Oxygen has an oxidation number of −2, so the four oxygen atoms contribute −8. The three iron atoms must contribute a total of +8 to make the compound neutral.
The average oxidation number of iron is therefore:
+8 ÷ 3 = +8/3
This average does not mean that every iron atom has an oxidation number of +8/3. Magnetite contains iron in more than one oxidation state: iron(II) and iron(III). In the conventional description, one iron atom is in the +2 state and two are in the +3 state.
Their combined contribution is:
(+2) + 2(+3) = +8
Dividing that total by three gives the average of +8/3.
Fractional averages can therefore describe a mixture of oxidation states within a compound. In some solids, electron behavior is more complicated than a simple division into distinct integer oxidation states, so the chemical structure must be considered before interpreting an average value as a description of individual atoms.
Common mistakes when calculating oxidation numbers
One frequent mistake is confusing oxidation number with ionic charge. These values coincide for a monatomic ion, but they are not always the same for atoms in covalent compounds. Oxygen in water has an oxidation number of −2, for instance, even though the water molecule is neutral and oxygen does not exist as a free O²⁻ ion in the molecule.
Another mistake is assuming that oxygen always has an oxidation number of −2. Peroxides contain oxygen at −1, and oxygen can have positive oxidation numbers in compounds with fluorine. Hydrogen also changes from its usual +1 to −1 in metal hydrides.
It is equally important to account for every atom in a chemical formula. In CO₂, the contribution from oxygen is 2 × (−2), not simply −2. Ignoring subscripts produces an incorrect equation.
A related error is setting the sum of oxidation numbers equal to zero for every substance. That rule applies to neutral compounds, but the sum for an ion must equal its overall charge. For example, the oxidation numbers in nitrate (NO₃⁻) must add up to −1.
Finally, a positive oxidation number does not always indicate a literal loss of a whole number of electrons, and a negative value does not always indicate a literal gain of that many electrons. Oxidation numbers are formal accounting values. They are most useful when interpreted within the chemical bonding and reaction context.
When oxidation numbers are useful
Oxidation numbers help chemists analyze a wide range of chemical processes. In combustion, they show how elements change as fuels react with oxygen. In corrosion, they help describe how metals are oxidized as they react with substances in their surroundings. In batteries, changes in oxidation numbers help explain the chemical reactions that release or store electrical energy.
They are also useful in balancing redox equations. By comparing oxidation numbers before and after a reaction, chemists can identify which elements are oxidized and reduced and determine whether the electron loss and gain are balanced. This is particularly valuable when equations involve multiple reactants, products, or polyatomic ions.
In biological chemistry, oxidation-number changes help describe processes such as cellular respiration, in which compounds derived from food are oxidized and oxygen is reduced. In environmental chemistry, they help explain transformations involving nitrogen, sulfur, iron, and other elements in soil, water, and air.
The central principle remains the same in each application: oxidation numbers provide a consistent way to track how electrons are assigned to atoms and how those assignments change during chemical reactions.
To calculate an oxidation number, identify the known values, account for every atom in the formula, and make the sum equal to the total charge of the compound or ion. With practice, this method makes it easier to interpret chemical formulas, recognize redox reactions, and understand the electron changes underlying many important chemical processes.