Formal Charge

Formal charge is a bookkeeping tool for judging Lewis structures. It answers a narrow but useful question. Imagine every bonding electron pair split perfectly evenly between the two atoms sharing it. Would a given atom in your drawn structure have gained or lost electrons? This is judged relative to its free, neutral state. A molecule or ion can often be drawn with more than one valid arrangement of bonds and lone pairs. Formal charge lets you rank these arrangements by chemical plausibility. It does not measure real charge distribution — that job belongs to electronegativity and dipole moments. But it is remarkably effective at flagging structures that are unreasonable. This article builds on Covalent Bonding and Lewis Structures. It assumes you can already count valence electrons. It also assumes you can draw a basic skeleton with bonds and lone pairs. The payoff here is a simple arithmetic rule. It turns "which Lewis structure is right?" from a guessing game into a calculation. The same logic will resurface when comparing contributing structures in Resonance Structures. There, formal charge helps decide which resonance forms matter most.

Key takeaways

Formal charge (FC) assigns each bonded atom the electrons it would have if all bonds were nonpolar (split 50/50), then compares that count to the atom's neutral valence electron count.
The formula: FC = V - N - \dfrac{B}{2} where $V$ = valence electrons of the free atom, $N$ = nonbonding (lone-pair) electrons, $B$ = bonding electrons around that atom.
The formal charges in a Lewis structure must sum to the overall charge of the species — this is a mandatory checksum, not optional.
Best Lewis structures minimize the magnitude of formal charges, and put any negative formal charge on the more electronegative atom.
Formal charge is a counting convention, not a measurement of actual electron density — real charge separation is smaller and depends on electronegativity.
Key idea: compute FC on every atom, check the structures sum correctly, then prefer the structure with formal charges closest to zero and correctly placed.

The core insight

Formal charge asks: "if bonds were shared perfectly evenly, would this atom look neutral?" The structure where the answer is "yes, almost everywhere" is usually the best Lewis structure.

The physical picture

Consider drawing a Lewis structure for a molecule like the thiocyanate ion, SCN⁻, or a simpler case like carbon dioxide, CO₂. The rules from Covalent Bonding and Lewis Structures — satisfy the octet, use the correct total valence electron count — can often be satisfied by more than one arrangement of double and triple bonds. Formal charge breaks the tie by asking how "comfortable" each atom is in that arrangement, using a simple accounting trick. The trick: pretend every shared electron pair is divided equally between its two atoms, regardless of which atom is more electronegative. Give each atom its full share of every bond it participates in, plus all of its own lone pairs. Compare that number to the number of valence electrons the atom would have as a free, neutral atom. Any difference is the formal charge. This is deliberately a simplified, idealized rule. It ignores electronegativity differences entirely — that's the point. Formal charge isolates the effect of "did this atom donate or receive more bonds than typical for its group," separate from the additional question of "which atom actually pulls electron density toward itself." That second question is handled by real charge distribution (partial charges, dipole moments), a separate and more physically accurate idea.

Figure

Counting electrons around nitrogen in the ammonium ion, NH₄⁺

Notice the arithmetic in the figure: nitrogen normally "owns" 5 valence electrons, but in NH₄⁺ it only gets to formally claim 4 (half of its 8 bonding electrons, with zero lone pairs). It is one electron short of neutral, so its formal charge is +1 — consistent with the ion's overall +1 charge, since every hydrogen comes out formally neutral.

The core relations

The formal charge of any atom in a Lewis structure is:

FC = V - N - \frac{B}{2}

where:

$V$ = number of valence electrons the atom has as a free, neutral atom (its group number in the main-group convention),
$N$ = number of nonbonding (lone-pair) electrons drawn directly on that atom in the structure,
$B$ = total number of bonding electrons around that atom (count 2 electrons per single bond, 4 per double bond, 6 per triple bond).

A necessary check on any completed structure is the charge conservation rule:

\sum_{\text{atoms}} FC_i = Q_{\text{total}}

where:

$FC_i$ = formal charge on atom $i$ ,
$Q_{\text{total}}$ = the overall charge of the molecule or ion (0 for a neutral molecule, $-1$ for an anion like NO₃⁻, etc.).

When multiple valid skeletons exist, the preferred Lewis structure is chosen using these guidelines, in order of priority:

\text{Preference rank: } \min\left(\sum_i |FC_i|\right) \;\;\text{then}\;\; (-)\,FC \text{ on more electronegative atom}

where:

$\sum_i |FC_i|$ = the sum of the absolute values of all formal charges in the structure (smaller is better),
"more electronegative atom" refers to placing any unavoidable negative formal charge on the atom that most easily tolerates extra electron density.

Derivation ADeriving the formal charge formula from first principles

The goal is to justify why $FC = V - N - B/2$ correctly counts "electrons this atom would have under equal sharing," and to show the conservation identity follows automatically from a proper Lewis structure.

Step 1. Count the atom's assigned electrons under equal sharing. In a genuine Lewis structure, every electron is accounted for either as a lone pair on one specific atom or as a bonding pair shared between exactly two atoms. If sharing is assumed perfectly equal, each atom keeps all $N$ of its own nonbonding electrons and additionally keeps half of each bonding pair it participates in. If an atom has $B$ total bonding electrons distributed across its bonds, its equal-sharing allotment is

\text{Assigned electrons} = N + \frac{B}{2}.

Step 2. Compare to the free-atom baseline. The neutral free atom has $V$ valence electrons. Formal charge is defined as the deficit (or surplus) relative to this neutral baseline:

FC = V - \left(N + \frac{B}{2}\right) = V - N - \frac{B}{2}.

This is exactly the working formula. If the atom's equal-sharing allotment matches its free-atom valence count, $FC = 0$ : the atom looks electronically "normal" in this structure.

Step 3. Show that formal charges must sum to the total charge. Sum the formula over every atom $i$ in the structure:

\sum_i FC_i = \sum_i V_i - \sum_i N_i - \sum_i \frac{B_i}{2}.

The term $\sum_i V_i$ is, by construction, the total number of valence electrons used to build the structure (call it $V_{\text{tot}}$ , computed from group numbers plus/minus the ionic charge, exactly as in the electron-counting step of drawing a Lewis structure). The term $\sum_i N_i$ counts every lone-pair electron exactly once — each lone pair belongs to one atom only. The term $\sum_i B_i$ counts every bonding electron twice, because each bond contributes to the $B$ count of both atoms sharing it; therefore $\sum_i B_i / 2$ equals the total number of bonding electrons, counted once per bond.

Step 4. Recognize that lone-pair electrons plus bonding electrons equal the total electron count. By the way a Lewis structure is built, every valence electron placed in the structure is either a lone-pair electron or a bonding electron, so

\sum_i N_i + \left(\sum_i \frac{B_i}{2}\right) = V_{\text{tot}}.

Substituting into Step 3,

\sum_i FC_i = V_{\text{tot}} - V_{\text{tot}} = 0 \quad \text{for a neutral molecule's total electron budget}.

More generally, since $V_{\text{tot}}$ already includes the adjustment for ionic charge (add 1 electron per unit negative charge, remove 1 per unit positive charge), the identity becomes

\sum_i FC_i = Q_{\text{total}},

which is the conservation rule stated above. This is not a separate assumption — it is a direct consequence of correctly counting valence electrons when the structure was first drawn.

Worked examples

Example 1 — Nitrate ion, NO₃⁻, choosing among resonance-like skeletons. Total valence electrons: N contributes 5, each O contributes 6 (three oxygens), plus 1 extra electron for the $-1$ charge:

V_{\text{tot}} = 5 + 3(6) + 1 = 24.

Draw nitrogen centrally bonded to three oxygens. One reasonable structure has one N=O double bond and two N–O single bonds, with each singly-bonded oxygen carrying three lone pairs and the doubly-bonded oxygen carrying two lone pairs, and nitrogen with no lone pairs. Formal charge on nitrogen:

FC(N) = 5 - 0 - \frac{8}{2} = 5 - 4 = +1

(nitrogen has one double bond (4 electrons) and two single bonds (2 + 2 electrons) = 8 bonding electrons total, zero lone pairs). Formal charge on the double-bonded oxygen (2 lone pairs = 4 nonbonding electrons, 4 bonding electrons from the double bond):

FC(O_{=}) = 6 - 4 - \frac{4}{2} = 6 - 4 - 2 = 0.

Formal charge on each single-bonded oxygen (3 lone pairs = 6 nonbonding electrons, 2 bonding electrons from the single bond):

FC(O_{-}) = 6 - 6 - \frac{2}{2} = 6 - 6 - 1 = -1.

Check the sum:

FC(N) + FC(O_{=}) + 2\,FC(O_{-}) = (+1) + (0) + 2(-1) = +1 + 0 - 2 = -1,

which correctly matches the ion's overall charge of $-1$ . This structure is chemically sensible: the single negative formal charge sits on oxygen, the most electronegative atom present, and the magnitudes involved are small ( $+1, 0, -1, -1$ ). Compare this against a structure with all three N–O single bonds (no double bond at all), which would require an expanded octet or an electron-deficient nitrogen to keep the electron count correct — check nitrogen's formal charge there:

FC(N) = 5 - 0 - \frac{6}{2} = 5 - 3 = +2,

with all three oxygens single-bonded and carrying $FC = -1$ each. The sum is $+2 + 3(-1) = -1$ — still charge-balanced, but the sum of magnitudes, $2 + 1+1+1 = 5$ , is larger than the first structure's sum of magnitudes, $1 + 0 + 1 + 1 = 3$ . The double-bond structure is preferred because it minimizes total formal charge magnitude. (Real nitrate is best described as a resonance average of three equivalent double-bond placements — a preview of Resonance Structures.)

Example 2 — Carbonic acid skeleton test: distinguishing a good structure from a bad one for HCNO (fictional connectivity check). Take a slightly asymmetric, less common test case: the cyanate ion, OCN⁻, and compare two different atom orderings to show formal charge catching an implausible skeleton. Total valence electrons: O (6) + C (4) + N (5) + 1 (extra electron for $-1$ charge) = 16.

Structure A: O=C=N⁻ ordering (oxygen first, cumulated double bonds), i.e., :O=C=N:⁻ Here oxygen has two lone pairs (4 nonbonding electrons) and one double bond (4 bonding electrons); carbon has two double bonds (8 bonding electrons, 0 lone pairs); nitrogen has two lone pairs (4 nonbonding electrons) and one double bond (4 bonding electrons).

FC(O) = 6 - 4 - \frac{4}{2} = 6 - 4 - 2 = 0

FC(C) = 4 - 0 - \frac{8}{2} = 4 - 4 = 0

FC(N) = 5 - 4 - \frac{4}{2} = 5 - 4 - 2 = -1

Sum check:

0 + 0 + (-1) = -1,

which matches the ion's charge. Magnitudes sum to $0+0+1=1$ — extremely favorable, and the negative charge sits on nitrogen, which is more electronegative than carbon (though less so than oxygen; this is the accepted major structure for cyanate, with a minor contributor placing the negative charge on oxygen instead).

Structure B: force a version with a C–O single bond and C≡N triple bond, i.e., ⁻:O–C≡N: Oxygen now has three lone pairs (6 nonbonding electrons) and one single bond (2 bonding electrons); carbon has one single bond plus one triple bond (2 + 6 = 8 bonding electrons, 0 lone pairs); nitrogen has one lone pair (2 nonbonding electrons) and one triple bond (6 bonding electrons).

FC(O) = 6 - 6 - \frac{2}{2} = 6 - 6 - 1 = -1

FC(C) = 4 - 0 - \frac{8}{2} = 4 - 4 = 0

FC(N) = 5 - 2 - \frac{6}{2} = 5 - 2 - 3 = 0

Sum check:

(-1) + 0 + 0 = -1,

also correctly charge-balanced, with the same total magnitude of 1. This structure is actually the accepted major contributor for cyanate (negative charge on oxygen, the most electronegative atom), while Structure A is a close, energetically reasonable minor contributor. Both pass the formal-charge sum-of-magnitudes test almost equally, illustrating a genuine case where more than one structure is chemically important — exactly the situation that motivates Resonance Structures. As a limiting-case sanity check on the whole method: for a simple neutral diatomic-style fragment where each atom keeps exactly its own valence electron count under equal sharing (for example, two identical atoms joined by one nonpolar single bond, like two chlorine atoms in Cl₂, each with 3 lone pairs and 1 shared bond), formal charge must vanish on both atoms:

FC(Cl) = 7 - 6 - \frac{2}{2} = 7 - 6 - 1 = 0,

confirming that a "textbook normal" bonding pattern returns zero formal charge everywhere, as it should.

Limiting cases & common traps

Situation	What to check	Common mistake
Multiple skeletons possible	Compute FC on every atom for each skeleton; prefer minimum $\sum \|FC_i\|$	Stopping after checking only the central atom
Charge-balance check	$\sum FC_i$ must equal the ion/molecule's overall charge	Forgetting to add/subtract electrons for ionic charge in the total valence count
Negative FC placement	Prefer negative FC on the more electronegative atom	Placing a negative formal charge on a less electronegative atom (e.g., carbon) when oxygen is available
Expanded octets (period 3+)	Elements like S, P, Cl can exceed 8 electrons, sometimes lowering FC	Assuming every atom must obey the strict octet even when a low-FC expanded structure exists
Formal charge vs. real charge	FC is a counting device; it is not the actual partial charge	Treating FC values as literal charges or as identical to dipole-derived partial charges

The chemist behind it

The idea of assigning "formal" oxidation-like charges to atoms within a covalently bonded Lewis structure grew directly out of the electron-pair bonding theory developed in the early twentieth century. The essential leap — that a shared electron pair could be split evenly for bookkeeping purposes, regardless of the true polarity of the bond — traces back to the broader program of representing molecules with dots and lines for electron pairs, a convention formalized well before quantum mechanical bonding theories existed and refined as chemists needed a reliable way to choose between competing valid structures for the same molecule.

Origins · 1 minGilbert N. Lewis and how this was discovered

Gilbert N. Lewis

1875–1946 · American physical chemist who introduced electron-dot structures and the shared electron-pair bond

Lewis proposed in 1916 that a covalent bond consists of a shared pair of electrons between two atoms, and that atoms tend toward stable arrangements of eight valence electrons (the octet rule). His electron-dot notation — the same dots-and-lines structures used throughout introductory chemistry — created the very framework in which formal charge became a meaningful, calculable quantity: without a defined picture of shared bonding pairs and localized lone pairs, there would be nothing to "split evenly" in the first place. Formal charge is best understood as a natural extension of Lewis's bonding model, used to discriminate between multiple structures that all satisfy his original octet and electron-counting rules.

Ask the tutor: How does formal charge help decide which resonance structures contribute most to a molecule like ozone or benzene?

Is formal charge the same thing as oxidation state?

No. Oxidation state assumes bonding electrons are given entirely to the more electronegative atom (maximally unequal sharing), while formal charge assumes bonding electrons are split exactly evenly (maximally equal sharing). They are opposite idealizations built from the same Lewis structure, and they usually give different numbers for the same atom.

Can formal charge be a non-integer?

No, not for ordinary Lewis structures with whole bonds and whole lone pairs. Since $B$ (bonding electrons) is always even for a properly drawn structure — single bonds contribute 2, double bonds 4, triple bonds 6 — and $N$ is always a whole number of electrons, $B/2$ is always an integer, so $FC = V - N - B/2$ is always an integer.

Does a structure with all formal charges equal to zero always win?

Almost always, but not automatically over every other consideration. If two structures both have low or zero formal charges, other criteria such as electronegativity-based placement of any remaining nonzero charge, or whether resonance genuinely applies, can matter. Formal charge is the primary filter, not the only one.

Why does the "extra electron" get added for anions and removed for cations when computing total valence electrons?

Because the total valence electron count used to build the Lewis structure must represent the actual number of electrons present in that specific ion, not just the sum of neutral-atom valence electrons. An anion has gained electrons (add one per unit negative charge); a cation has lost electrons (subtract one per unit positive charge). This adjusted total is what eventually shows up as $Q_{\text{total}}$ in the formal charge sum rule.

If two different atoms in a molecule both come out with formal charge zero, does that guarantee the structure is correct?

It's a strong positive sign but not an absolute guarantee. You still need to confirm the correct total valence electron count, valid octets (or accepted expanded octets for period 3+ elements), and a sensible skeleton with the least electronegative atom typically central. Formal charge of zero across the board is consistent with a good structure, but should be checked alongside these other rules from Covalent Bonding and Lewis Structures.