The formal charge of an atom is a bookkeeping value chemists use to determine how electrons are distributed in a molecule or polyatomic ion. It helps identify plausible Lewis structures, understand bonding patterns, and compare alternative arrangements of atoms and electrons.
To calculate formal charge, subtract the number of electrons assigned to an atom from the number of valence electrons in its neutral state. The assigned electrons include all nonbonding electrons, which belong to the atom alone, and half of the electrons shared in covalent bonds.
The formula is:
Formal charge = Valence electrons − Nonbonding electrons − ½(Bonding electrons)
Once you know how to count these three quantities, you can calculate the formal charge of nearly any atom represented in a Lewis structure.
Understand what formal charge means
Atoms contain positively charged protons and negatively charged electrons. In a neutral atom, the numbers of protons and electrons are equal. When atoms form chemical bonds, they share or transfer electrons, changing how electrons are distributed throughout the resulting chemical species.
Formal charge provides a simplified way to describe this distribution. It assumes that electrons in covalent bonds are shared equally between the bonded atoms, regardless of differences in electronegativity. Electronegativity is an atom’s ability to attract shared electrons toward itself.
Under this assumption, each atom receives all its nonbonding electrons and half of its bonding electrons. The difference between that assigned number and the number of valence electrons in the neutral atom is its formal charge.
Formal charge is not necessarily the actual electrical charge concentrated on an atom. It is a theoretical accounting tool based on a specific set of assumptions. An atom with a formal charge of zero may still carry a partial charge because electrons in its bonds are not always distributed equally.
Despite this limitation, formal charge is extremely useful for evaluating Lewis structures and understanding the relationships between bonding, electron distribution, and molecular stability.
Use the formal charge formula
The formal charge formula is:
FC = V − N − B/2
Here:
- FC is the formal charge of the atom.
- V is the number of valence electrons in the isolated, neutral atom.
- N is the number of nonbonding electrons assigned to the atom, also called lone-pair electrons.
- B is the total number of electrons shared in bonds involving that atom.
The formula can also be written as:
FC = V − N − ½B
Both forms mean the same thing.
Valence electrons are the electrons in an atom’s outermost occupied shell that are generally involved in chemical bonding. For the main-group elements, the periodic table provides a convenient way to determine their usual valence electron counts. For example, carbon has four, nitrogen has five, oxygen has six, and the halogens, such as fluorine and chlorine, have seven.
Nonbonding electrons appear as dots around an atom in a Lewis structure. A lone pair consists of two nonbonding electrons.
Bonding electrons are represented by lines between atoms. A single bond represents two electrons, a double bond represents four, and a triple bond represents six. When using the formula, count all bonding electrons associated with the atom, then divide that number by two.
Follow these steps to calculate formal charge
A reliable calculation begins with a correctly drawn Lewis structure. The Lewis structure shows which atoms are connected, how many bonds exist between them, and where lone pairs are located.
Step 1: Determine the atom’s valence electrons.
Find the number of valence electrons in the neutral atom using its position in the periodic table. For example, oxygen has six valence electrons, while nitrogen has five.
Step 2: Count the atom’s nonbonding electrons.
Count every electron represented by a dot around the atom. A lone pair contributes two electrons. If an atom has two lone pairs, it has four nonbonding electrons.
Step 3: Count the atom’s bonding electrons.
Count the electrons in every bond connected to the atom. Each single bond contributes two electrons, each double bond contributes four, and each triple bond contributes six.
Step 4: Divide the bonding electrons by two.
This assigns half of the shared electrons to the atom. For example, an atom involved in one double bond and one single bond is associated with six bonding electrons, so it is assigned three of them.
Step 5: Substitute the values into the formula.
Subtract the nonbonding electrons and half the bonding electrons from the atom’s valence electron count.
Step 6: Check the result.
Formal charges should be consistent with the overall charge of the molecule or ion. For a neutral molecule, the formal charges of all atoms must add up to zero. For an ion, their sum must equal the ion’s overall charge.
Example 1: Calculate the formal charge of oxygen in water
Water, H₂O, provides a straightforward example because its Lewis structure contains two O–H single bonds and two lone pairs on oxygen.
Oxygen has six valence electrons. In the water molecule, it has four nonbonding electrons and four bonding electrons, two from each O–H bond.
Using the formula:
FC = 6 − 4 − ½(4)
FC = 6 − 4 − 2
FC = 0
Oxygen in water has a formal charge of zero.
Each hydrogen atom also has a formal charge of zero. Hydrogen has one valence electron, no nonbonding electrons, and two bonding electrons in its single bond:
FC = 1 − 0 − ½(2)
FC = 0
The formal charges add up to zero, matching the overall charge of the neutral water molecule.
Example 2: Calculate the formal charge of oxygen in hydroxide
The hydroxide ion, OH⁻, contains one oxygen atom bonded to one hydrogen atom. Oxygen has three lone pairs in its Lewis structure, while hydrogen shares one single bond with oxygen.
For oxygen:
- Valence electrons: 6
- Nonbonding electrons: 6
- Bonding electrons: 2
Substituting these values gives:
FC = 6 − 6 − ½(2)
FC = 6 − 6 − 1
FC = −1
Oxygen has a formal charge of −1.
For hydrogen:
FC = 1 − 0 − ½(2)
FC = 0
The sum of the formal charges is −1, which matches the overall charge of OH⁻. This example shows why the charge of an ion must be considered when checking a Lewis structure.
Example 3: Calculate formal charges in carbon dioxide
Carbon dioxide, CO₂, is commonly represented by the Lewis structure O=C=O. Carbon forms a double bond with each oxygen atom, and each oxygen has two lone pairs.
For carbon, the valence electron count is four. Carbon has no nonbonding electrons and participates in two double bonds, accounting for eight bonding electrons.
FC = 4 − 0 − ½(8)
FC = 4 − 4
FC = 0
For each oxygen atom, the valence electron count is six. Each oxygen has four nonbonding electrons and four bonding electrons in its double bond with carbon.
FC = 6 − 4 − ½(4)
FC = 6 − 4 − 2
FC = 0
All three atoms have formal charges of zero. Their charges sum to zero, consistent with the neutral carbon dioxide molecule.
This example illustrates how multiple bonds affect formal charge calculations. A double bond contributes four bonding electrons, but only two are assigned to each atom.
Example 4: Calculate formal charges in the ammonium ion
The ammonium ion, NH₄⁺, contains a central nitrogen atom connected to four hydrogen atoms by single bonds.
Nitrogen has five valence electrons. In the ammonium ion’s Lewis structure, it has no lone pairs and participates in four single bonds, accounting for eight bonding electrons.
FC = 5 − 0 − ½(8)
FC = 5 − 4
FC = +1
Nitrogen has a formal charge of +1.
Each hydrogen atom has one valence electron, no nonbonding electrons, and two bonding electrons:
FC = 1 − 0 − ½(2)
FC = 0
The total formal charge is +1, matching the charge of NH₄⁺.
This result may seem surprising because nitrogen ordinarily forms three covalent bonds in neutral ammonia, NH₃. In ammonium, nitrogen forms four bonds and has no lone pair. Its formal charge reflects that difference in its electron-counting arrangement.
Example 5: Calculate formal charges in the nitrate ion
The nitrate ion, NO₃⁻, demonstrates why formal charge is useful when evaluating alternative Lewis structures.
One common Lewis representation contains a central nitrogen atom with one double bond to oxygen and two single bonds to oxygen. The two singly bonded oxygen atoms each have three lone pairs, while the doubly bonded oxygen has two lone pairs.
For nitrogen, the valence electron count is five. It has no nonbonding electrons and participates in one double bond and two single bonds, totaling eight bonding electrons.
FC = 5 − 0 − ½(8)
FC = +1
For each singly bonded oxygen:
FC = 6 − 6 − ½(2)
FC = −1
For the doubly bonded oxygen:
FC = 6 − 4 − ½(4)
FC = 0
Adding the charges gives:
+1 + (−1) + (−1) + 0 = −1
The total matches the nitrate ion’s overall charge.
The double bond can be placed between nitrogen and any one of the three oxygen atoms, producing three equivalent Lewis structures. These are called resonance structures. The actual nitrate ion is not best described as having one permanently localized double bond and two permanently localized single bonds. Instead, its bonding and electron distribution are delocalized across the ion.
Formal charge helps distinguish the electron-counting patterns in the resonance structures, but it does not mean that the actual charge on each oxygen is exactly the formal charge shown in any single drawing.
How formal charge differs from oxidation state and partial charge
Formal charge, oxidation state, and partial charge all describe aspects of electron distribution, but they answer different questions.
Formal charge assumes that electrons in covalent bonds are divided equally between the bonded atoms. It is calculated directly from a Lewis structure.
Oxidation state uses a different accounting rule: bonding electrons are assigned to the more electronegative atom, or divided equally when the bonded atoms are identical. This convention helps track electron transfer in chemical reactions, particularly oxidation-reduction reactions.
Partial charge describes an unequal distribution of electron density in a real molecule. It often arises because one atom attracts shared electrons more strongly than another. Partial charges are commonly represented using δ⁺ and δ⁻ rather than whole-number charges.
For example, the O–H bonds in water are polar because oxygen attracts shared electrons more strongly than hydrogen. Oxygen therefore has greater electron density than hydrogen, even though the formal charges on all three atoms in the Lewis structure of water are zero.
A formal charge of zero does not mean an atom has no influence on molecular polarity, and a formal charge of +1 does not necessarily mean that exactly one unit of positive charge is physically concentrated on that atom.
How to use formal charge to evaluate Lewis structures
A molecule or ion can sometimes be represented by more than one plausible Lewis structure. Formal charge helps chemists compare these possibilities.
In general, a favorable Lewis structure tends to have formal charges as close to zero as possible. This preference is not an absolute rule, but it provides a useful starting point when several structures satisfy the basic electron-counting requirements.
When formal charges are unavoidable, a structure is often preferred if it minimizes the separation of positive and negative formal charges. A structure with fewer atoms carrying nonzero formal charges is often more favorable than one with many such charges, provided other important considerations are comparable.
The placement of formal charges also matters. Negative formal charges are generally more favorable on more electronegative atoms, while positive formal charges are often more favorable on less electronegative atoms. For example, oxygen can accommodate a negative formal charge more readily than carbon in many common Lewis structures.
These guidelines must be used alongside other chemical principles, including the total number of available valence electrons, typical bonding patterns, and the octet rule. The octet rule states that many main-group atoms tend to form bonds that give them eight electrons in their valence shell. Hydrogen is an important exception because its first shell holds a maximum of two electrons.
Formal charge alone cannot establish the exact structure or stability of a molecule. Some species have incomplete octets, unpaired electrons, or bonding arrangements that do not fit simple octet-based expectations. In such cases, a correct interpretation requires considering the relevant chemical context rather than relying on formal-charge minimization alone.
Common mistakes when calculating formal charge
Several counting errors can lead to incorrect results.
Counting bonds instead of bonding electrons. A single bond contains two electrons, a double bond contains four, and a triple bond contains six. The formula requires the number of bonding electrons, not simply the number of bonds.
Forgetting to divide bonding electrons by two. Because covalent bonding electrons are shared between two atoms in the formal-charge model, each atom receives half of the bonding electrons. Omitting this division can produce incorrect charges.
Counting lone pairs incorrectly. Each lone pair contains two electrons. An atom with three lone pairs has six nonbonding electrons, not three.
Ignoring the overall charge of an ion. Individual formal charges must add up to the total charge of the chemical species. If they do not, the electron count or Lewis structure should be checked.
Assuming formal charge equals actual charge. Formal charge is a calculated value based on equal sharing of bonding electrons. It does not directly measure the real electron density around an atom.
Treating one resonance structure as the complete physical picture. When resonance is important, a single Lewis structure may not adequately represent the actual distribution of electrons. Formal charges should be interpreted in the context of all relevant resonance structures.
Check the total formal charge
The most dependable final check is to add the formal charges of every atom in the Lewis structure. The sum must equal the overall electrical charge of the molecule or ion.
For a neutral molecule, the sum is zero. For a singly charged positive ion, the sum is +1. For a singly charged negative ion, the sum is −1. The same principle applies to ions with larger charges.
This check is valuable because an individual atom’s formal charge depends on the Lewis structure used for the calculation. If the total does not match the known charge of the species, revisit the number of valence electrons, the placement of lone pairs, and the number of bonding electrons.
The essential principle is simple: subtract the nonbonding electrons and half the bonding electrons from the atom’s neutral valence electron count. Applying this rule consistently, then checking the sum of all atomic formal charges, provides a reliable way to analyze Lewis structures and understand how chemists represent bonding in molecules and ions.