Formal Charge

Look at nitric acid, HNO₃, and ask a simple question. How many bonds does the central nitrogen make? Does it "own" the right number of electrons to be neutral? The answer to that bookkeeping question is formal charge. It is a small piece of arithmetic that carries enormous predictive weight in organic chemistry. It tells you, atom by atom, whether a proposed Lewis structure is electronically sensible. It also shows which of several candidate structures is the best single picture of a molecule. Later, it shows which resonance contributor deserves the most weight in describing a real, delocalized electron distribution. Formal charge matters because Lewis structures are not unique. Given a molecular formula and a rule that says "satisfy the octet," a student can often draw two, three, or four different arrangements of dots and lines. All of them can look plausible on paper. Formal charge is the diagnostic that separates the chemically reasonable structures from the electronically absurd ones. Among the reasonable ones, it ranks them by plausibility. It is the referee for a game whose rules were laid out in Lewis Structures: Rules and Construction. The big picture is this: formal charge is a bookkeeping convention, not a measurement of real electron density. It assumes every bond is perfectly covalent — split exactly in half between the two atoms. This holds even when common sense (and electronegativity) says the electrons actually sit closer to one atom. That idealization is precisely what makes formal charge useful as a diagnostic. By holding electronegativity constant (pretending it doesn't exist), formal charge isolates a single question. Does this atom have its "expected" share of bonding electrons, given how many bonds it's making? Comparing formal charge to the real charge distribution (which does depend on electronegativity) matters greatly. That is exactly how chemists later decide which resonance structure of a delocalized system contributes the most to reality, as in the nitrate ion or an amide. This article builds formal charge from first principles. It offers a genuine "conservation of electrons" derivation, not a memorized formula. It shows the mechanism of assigning it atom-by-atom with curved-arrow-style electron partitioning. Then it applies this to molecules where getting it right or wrong changes the entire structural conclusion: ozone, the nitrate ion, isocyanide, and carbon monoxide. By the end you will be able to compute formal charge on any atom in any Lewis structure in seconds. More importantly, you will use it to choose correctly among competing structures. This is the essential skill that feeds directly into Evaluating Resonance Structures.

Key takeaways

Formal charge (FC) compares the electrons an atom "owns" in a Lewis structure to the electrons a neutral free atom of that element owns.
The formula is FC = (valence electrons of free atom) − (nonbonding electrons) − ½(bonding electrons).
Formal charge assumes every covalent bond is split exactly 50/50, ignoring real electronegativity differences — this is a deliberate idealization, not an error.
The sum of formal charges on all atoms in a structure must equal the overall charge on the species — this is a conservation law, not a coincidence.
Best Lewis structures minimize formal charges in magnitude, put negative formal charge on the more electronegative atom, and avoid same-sign adjacent formal charges.
Formal charge is not the same as oxidation state or true partial charge; it's a self-consistent bookkeeping tool, not a physical measurement.
Key idea: formal charge is electron bookkeeping under an artificial "bonds are always shared equally" assumption, and comparing it across candidate Lewis structures tells you which structure is the most electronically reasonable.

Where this lives today

Formal charge is not a historical curiosity confined to introductory courses — it is the everyday triage tool organic and inorganic chemists use before drawing a mechanism. When a chemist proposes a curved-arrow mechanism for, say, a Grignard addition or an SN2 reaction, they instinctively check that intermediates and products carry sensible formal charges (a carbanion-like carbon should show FC = −1; a protonated carbonyl oxygen should show FC = +1); a mechanism that produces an atom with formal charge ±2 or higher on a first-row element is a loud warning that a step has been drawn incorrectly. Reaction-prediction software and cheminformatics pipelines (used in drug discovery to enumerate tautomers and resonance structures of candidate molecules) run formal-charge and octet checks automatically, using exactly the arithmetic in this article, to filter out chemically nonsensical structures before they ever reach a chemist's screen. In medicinal chemistry, formal charge assignment on functional groups — carboxylates, ammoniums, phosphates, sulfonamides — determines a molecule's ionization state at physiological pH, which in turn governs solubility, membrane permeability, and protein binding; getting the Lewis structure and its formal charges right is the first step before any pKa or logP prediction can even be attempted. In inorganic and organometallic chemistry, formal charge on a metal center (distinct from, but related to, oxidation state) helps rationalize the electron count and geometry of coordination complexes, feeding into 18-electron-rule bookkeeping for transition metal catalysts used industrially in hydroformylation and olefin polymerization. And in spectroscopy, computed atomic charges (density-derived, not formal) are cross-checked against formal-charge predictions as a sanity test: if a computational method assigns a huge real charge where formal-charge bookkeeping expected something modest, that flags either an unusual electronic structure or a computational artifact worth investigating further. Every one of these downstream applications rests on the same arithmetic derived here, and every one of them depends on first getting the underlying Lewis Structures: Rules and Construction right before formal charge can say anything meaningful at all — which is exactly why formal charge sits immediately after Lewis structures and immediately before resonance in how organic chemistry builds its structural vocabulary, feeding directly into how The Major Functional Groups are recognized and drawn correctly from the very first day of the subject.

Ask the tutor: In the nitrate ion NO₃⁻, three resonance structures each place a formal −1 on one different oxygen and a formal +1 on nitrogen — walk me through why all three are needed to describe the real ion, using formal charge as the guide.

The physical picture — thorough prose

Start from what a Lewis structure actually represents: a specific proposal for where all the valence electrons in a molecule live — some as lone pairs on individual atoms, some as shared pairs (bonds) between pairs of atoms. Every valence electron in the original set of free atoms has to end up somewhere in the final structure; none appear or disappear. This is nothing but conservation of electron count, applied atom by atom instead of molecule by molecule. Formal charge asks: for a given Lewis structure, if I now redistribute the bonding electrons in the most "fair" way imaginable — split every bond pair exactly in half regardless of which atom is more electronegative — how many electrons does each atom end up with, compared to the number it would have as a lone neutral atom? Any deficit shows up as a positive formal charge (the atom is "renting out" more electrons than it owns); any surplus shows up as a negative formal charge (the atom is "keeping" more than its fair share). Crucially, this fair-split assumption is a fiction. In real HF, the bonding electrons sit far closer to fluorine than to hydrogen — real electronegativity is not equal. Formal charge deliberately ignores this. That might seem like a defect, but it is the entire point: by fixing the same fictional rule (equal splitting) for every atom in every structure, formal charge becomes a controlled comparison. Structure A and Structure B for the same molecule are being judged by an identical, electronegativity-blind yardstick, so any difference in the formal charge pattern between A and B must come from the actual arrangement of bonds and lone pairs — the only thing that differs between them — not from an unfair application of electronegativity to one structure and not the other.

Figure

Assigning formal charge: bookkeeping the electrons around each atom in the nitrite ion, NO₂⁻

Formal charge also gives a rough, useful (though imperfect) rank-ordering of structures. Chemists prefer structures where (1) formal charges are as close to zero as possible, (2) any negative formal charge sits on the more electronegative atom, and (3) atoms bearing like-signed formal charges are not adjacent to each other. These preference rules are not arbitrary taste; each has a physical rationale rooted in electronegativity and electrostatics, which is unpacked in the mechanism section below. Finally, distinguish formal charge sharply from two things students often conflate it with: oxidation state (which assumes the opposite extreme — that every bond is 100% ionic, with both electrons going to the more electronegative atom) and real partial charge (the actual, physically measurable charge distribution, influenced by electronegativity, hybridization, and induction). Formal charge sits, quite deliberately, at the "equal-sharing" midpoint between these views.

Figure

Three views of the same C=O bond in formaldehyde: formal charge, oxidation state, real partial charge

The core ideas — the governing equation

The single equation governing everything in this article is:

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

where:

$V$ = number of valence electrons a neutral, isolated atom of that element has (its group number in the main-group sense: C = 4, N = 5, O = 6, halogens = 7, H = 1),
$N$ = number of nonbonding (lone-pair) electrons that atom has in this particular Lewis structure (each lone pair = 2 electrons),
$B$ = number of bonding electrons around that atom in this particular Lewis structure (each single bond contributes 2, each double bond 4, each triple bond 6 — count all electrons in every bond touching that atom, then divide the total by 2).

Reading it aloud: formal charge equals the electrons the free atom "should" have, minus the electrons it visibly keeps to itself, minus its half-share of every bond it's part of. If the result is 0, the atom's electron count in the structure exactly matches what a neutral free atom would have — no charge assigned. If it's positive, the atom is "missing" electrons relative to neutral (it is formally electron-poor); if negative, it has "extra" (formally electron-rich). A companion conservation law, essential for checking any completed structure:

\sum_{\text{all atoms}} \text{FC}_i = q_{\text{total}}

where $q_{\text{total}}$ is the net charge of the whole species (0 for a neutral molecule, $-1$ for an anion like OH⁻, $+1$ for a cation like NH₄⁺, and so on). This is not an independent postulate — it falls straight out of the fact that formal charge is just a redistribution of a fixed total electron count, as the first derivation below shows explicitly.

Derivation ADeriving the formal charge formula from conservation of electrons

Goal. Show that FC = V − N − B/2 is forced by nothing more than "electrons are neither created nor destroyed when we draw a Lewis structure," and that consequently ΣFC = overall charge.

Step 1 — Define "ownership" precisely. In a Lewis structure, every valence electron belongs to exactly one of two categories for a given atom X: (a) a lone pair centered entirely on X, contributing all of its electrons to X, or (b) a shared bonding pair between X and some neighbor Y, which formal-charge convention insists on splitting exactly in half between X and Y — one electron of the pair assigned to X, one to Y — regardless of the real identities of X and Y. This 50/50 split is the single idealizing assumption in the whole derivation; drop it and you get oxidation states instead (100/0 split) or true partial charges (whatever the actual electron density gives).

Step 2 — Count the electrons X "owns" under this rule. If atom X has $N$ nonbonding electrons (from lone pairs) and is party to bonds totaling $B$ bonding electrons (counting all electrons in every bond attached to X, single, double, or triple), then under the 50/50 splitting rule X's effective electron count is

n_X^{\text{eff}} = N + \frac{B}{2}.

This is because X keeps all $N$ of its lone-pair electrons, and gets exactly half of the $B$ bonding electrons surrounding it (the other half, by the same rule, is assigned to whichever neighbor(s) X is bonded to).

Step 3 — Compare to the neutral reference state. A free, neutral atom of X's element has $V$ valence electrons and, being neutral, has zero charge by definition. Formal charge is defined as the charge X would carry if the difference between "what it owns now" ( $n_X^{\text{eff}}$ ) and "what a neutral atom owns" ( $V$ ) were made up entirely of missing/extra electrons, each electron carrying charge $-1$ (in electron-charge units):

\text{FC} = -\bigl(n_X^{\text{eff}} - V\bigr) = V - n_X^{\text{eff}} = V - N - \frac{B}{2}.

This last line is exactly the formula stated above — it is not an ad hoc rule but the direct algebraic consequence of "count what the atom keeps under 50/50 splitting, and see how that compares to neutral."

Step 4 — Sum over all atoms and invoke total electron conservation. Let the molecule have atoms $X_1, \dots, X_k$ with valence electron counts $V_1,\dots,V_k$ , lone-pair counts $N_1,\dots,N_k$ , and bonding electron counts $B_1,\dots,B_k$ . Summing Step 3's result over all atoms,

\sum_i \text{FC}_i = \sum_i V_i - \sum_i N_i - \sum_i \frac{B_i}{2}.

Now, $\sum_i V_i$ is simply the total number of valence electrons that were assembled to build the structure — call it $E_{\text{total}}$ (for a neutral molecule this is the sum of each atom's group-valence count; for an ion, one electron is added for each unit of negative charge or removed for each unit of positive charge, exactly as in Lewis-structure electron counting). Also, $\sum_i N_i$ counts every lone-pair electron once (correct, since lone pairs belong to one atom only), while $\sum_i B_i/2$ counts every bond exactly once as well, because each bond's $B$ electrons get counted as " $B/2$ " from each of its two participating atoms, and summing over both atoms of a bond gives $B/2 + B/2 = B$ — the bond's full electron count — contributed once per bond, matching how those electrons were originally included in $E_{\text{total}}$ .

Step 5 — Conclude. Since every valence electron in $E_{\text{total}}$ ends up as either a counted lone-pair electron or a counted bonding electron (Lewis structures place every electron somewhere), $\sum_i N_i + \sum_i B_i = E_{\text{total}}$ exactly. Substituting,

\sum_i \text{FC}_i = E_{\text{total}} - \Bigl(\sum_i N_i + \sum_i \frac{B_i}{2}\Bigr).

Because $E_{\text{total}}$ already equals $\sum N_i + \sum B_i$ (all electrons placed), and because $\sum B_i/2$ under-counts the bonding total by exactly half (each bond's electrons appear once, not twice, when divided among its two atoms), careful bookkeeping collapses this to

\sum_i \text{FC}_i = E_{\text{total}} - E_{\text{total,used}} = q_{\text{total}},

where $q_{\text{total}}$ is precisely the extra (or missing) electron count built into $E_{\text{total}}$ from the start — i.e., the ion's overall charge. This confirms the conservation law asserted above: the sum of formal charges must equal the overall charge of the species, for any correctly drawn Lewis structure, with no exceptions.

Go deeper · Derivation B · 4 minMechanism for assigning formal charge atom-by-atom, and using it to rank competing Lewis structures

Derivation BMechanism for assigning formal charge atom-by-atom, and using it to rank competing Lewis structures

Goal. Turn the formula into a repeatable, arrow-free "mechanism" — a fixed sequence of steps you apply to every atom — and then show why the three preference rules (minimize |FC|, put negative FC on the more electronegative atom, avoid adjacent like charges) actually follow from real physics, using formaldehyde's two candidate structures as the worked case.

Step 1 — Fix a correctly-drawn Lewis structure first. Formal charge is only meaningful once you have a legitimate Lewis structure — full octets (or valid exceptions), correct total electron count, all atoms with realistic bonding patterns — built according to the rules in Lewis Structures: Rules and Construction. Formal charge cannot fix a structure that violates the octet rule or miscounts electrons; it can only evaluate structures that are already electron-count-correct.

Step 2 — For each atom, identify $N$ : count dots directly on that atom. Each lone pair (two dots drawn next to the atomic symbol) contributes 2 to $N$ . This step requires no interpretation — it's a direct read of the diagram.

Step 3 — For each atom, identify $B$ : sum every electron in every bond touching that atom. A single line (bond) = 2 electrons; a double bond (two lines) = 4 electrons; a triple bond (three lines) = 6 electrons. Add these across all bonds emanating from the atom in question (an atom can be part of several bonds to different neighbors simultaneously).

Step 4 — Look up $V$ and compute. Identify the element's group-valence number, then evaluate $\text{FC} = V - N - B/2$ directly. Record the sign: FC = 0 means "unremarkable," FC ≠ 0 means "this atom departs from its neutral-atom electron count in this drawing."

Step 5 — Check the sum rule as an error trap. Add all the FC values. If the total does not equal the actual charge on the species, you have made an arithmetic slip or (more seriously) drawn a structure with the wrong total electron count — go back and recount electrons before trusting any conclusion.

Step 6 — Compare candidate structures using the preference rules, and understand why each rule works. Take formaldehyde-like reasoning applied to, say, the thiocyanate-type comparison of two Lewis structures for the same formula (illustrated concretely with formaldehyde's real structure versus a hypothetical miscounted alternative): Rule (a): minimize the magnitude of formal charges. A large formal charge (say ±2) means an atom's electron count deviates strongly from what a neutral atom of that element normally carries. Since real atoms resist large deviations from their preferred electron configuration (this is exactly why electronegativity and ionization energy exist as periodic trends), a structure demanding large formal charges is asking an atom to behave in a way its real electronic structure resists — such structures are high in energy and contribute little to the real molecule. Rule (b): negative formal charge should sit on the more electronegative atom, positive on the less electronegative one. Formal charge is electronegativity-blind by construction (Step 1 of the first derivation), but chemists apply real electronegativity afterward, as an external plausibility check. If a structure puts a formal negative charge (extra electron density, in the bookkeeping sense) on the less electronegative atom, that's fighting against the real tendency of electrons to prefer the more electronegative center — a real energetic penalty invisible to the formal-charge arithmetic itself but visible once you cross-reference electronegativity. This is why, comparing structures for cyanate versus a poor alternative, the structure with negative formal charge on oxygen (electronegativity ≈ 3.5) beats one with negative formal charge on carbon (electronegativity ≈ 2.5). Rule (c): avoid adjacent atoms carrying like-signed formal charges. Two adjacent centers both bearing, say, positive formal charge represent a bookkeeping picture in which two positively-charged-feeling atoms sit next to each other — by Coulomb's law, $E \propto q_1 q_2/r$ , same-sign charges at short bonding distances ( $r \sim 1.2$ –1.5 Å) cost real electrostatic energy. A structure forcing this arrangement is disfavored relative to one that avoids it, all else equal.

Step 7 — Apply to formaldehyde, H₂C=O, versus a deliberately poor alternative H₂C–O with three lone pairs redistributed to give C a positive and O a compensating extra lone pair (making O formally more negative than needed and C formally positive without any real driving force). For the standard structure (C=O double bond, two C–H bonds, two lone pairs on O):

\text{FC(C)} = 4 - 0 - \frac{8}{2} = 0, \qquad \text{FC(O)} = 6 - 4 - \frac{4}{2} = 0.

Both atoms carry zero formal charge — the maximally favorable outcome, satisfying rule (a) trivially (all magnitudes are already zero, nothing to improve). For the alternative structure with a C–O single bond and an extra lone pair moved onto oxygen (three lone pairs on O, and correspondingly C left electron-deficient with only 6 electrons, an incomplete octet, and a formal +1):

\text{FC(C)} = 4 - 0 - \frac{6}{2} = +1 \quad(\text{octet-deficient, disfavored on structural grounds alone}), \qquad \text{FC(O)} = 6 - 6 - \frac{2}{2} = -1.

This alternative both violates the octet rule at carbon (already disqualifying on the grounds from Lewis Structures: Rules and Construction) and fails rule (a) — nonzero formal charges where a zero-formal-charge structure was available with the same atom connectivity and the same total electron count. The standard double-bonded structure wins decisively on every criterion, exactly matching the structure organic chemists actually draw for formaldehyde.

Worked examples

Example 1 (foundational): Formal charge on every atom in ammonium, NH₄⁺. Ammonium has a central nitrogen singly bonded to four hydrogens, net charge +1. First confirm the total valence electron count: N contributes 5, each of 4 H contributes 1, giving $5 + 4(1) = 9$ electrons from neutral atoms; because the ion carries a +1 charge, one electron has been removed, giving $9 - 1 = 8$ valence electrons to place — exactly four N–H bonds (4 × 2 = 8 electrons), with zero left over for lone pairs. This matches the structure: N has four bonds and no lone pairs. For nitrogen: $V = 5$ (group 15), $N = 0$ (no lone pairs drawn), $B = 8$ (four single bonds × 2 electrons each, all touching N).

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

For each hydrogen: $V = 1$ , $N = 0$ , $B = 2$ (one bond, single, touching that H).

\text{FC(H)} = 1 - 0 - \frac{2}{2} = 1 - 0 - 1 = 0.

Sum check: $\text{FC(N)} + 4 \times \text{FC(H)} = (+1) + 4(0) = +1$ , matching the ion's overall charge of +1 exactly, as the conservation law demands. This is the correct, standard picture of ammonium: the positive charge is formally localized on nitrogen because it is making one bond more than its neutral valence (three) would predict, having "lent out" an extra electron pair's worth of sharing to pick up the fourth N–H bond.

Example 2 (applied): Comparing two candidate structures for thiocyanate, SCN⁻, to select the better one. Thiocyanate has 5 (S) + 4 (C) + 5 (N) + 1 (extra electron for the −1 charge) = 16 valence electrons to distribute among three atoms in a row, S–C–N (or N–C–S — the arrangement itself is not in question here, only the bonding pattern). Consider two candidate Lewis structures, both with the connectivity S–C–N and both correctly totaling 16 electrons. Structure I: S=C=N, with two lone pairs on S and one lone pair on N (cumulated double bonds, like an isocyanate-type skeleton). Electron count check: 2 double bonds (4 + 4 = 8 electrons) + 2 lone pairs on S (4 electrons) + 1 lone pair on N (2 electrons) = 8 + 4 + 2 = 14... this needs an additional lone pair to reach 16; place a second lone pair on N as well, giving N two lone pairs total, for 8 + 4 + 4 = 16. ✓. Formal charges for Structure I:

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

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

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

Sum: $0 + 0 + (-1) = -1$ ✓, matching the ion charge. Structure II: S≡C–N, a triple bond between S and C, single bond between C and N, three lone pairs on N and one lone pair on S. Electron count: triple bond (6 electrons) + single bond (2 electrons) + 1 lone pair on S (2 electrons) + 3 lone pairs on N (6 electrons) = 6 + 2 + 2 + 6 = 16 ✓. Formal charges for Structure II:

\text{FC(S)} = 6 - 2 - \frac{6}{2} = 6 - 2 - 3 = +1.

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

\text{FC(N)} = 5 - 6 - \frac{2}{2} = 5 - 6 - 1 = -2.

Sum: $1 + 0 + (-2) = -1$ ✓ — also charge-consistent, so the sum rule alone cannot distinguish them; formal charge magnitude and placement must be used. Comparing: Structure I has formal charges $\{0, 0, -1\}$ — magnitudes summing to 1 in absolute value, with the single unit of negative charge on nitrogen (electronegativity 3.0). Structure II has formal charges $\{+1, 0, -2\}$ — magnitudes summing to 3, with a formal −2 (a large deviation, disfavored by rule (a)) again on nitrogen, plus a positive charge on sulfur. By rule (a) (minimize magnitude) Structure I is clearly superior — total |FC| of 1 versus 3. This matches the accepted experimental and computational picture: the true structure of thiocyanate is best represented as a resonance blend dominated by structures resembling Structure I (and its mirror image with charge distributed differently along the chain), not by high-formal-charge structures like Structure II.

Example 3 (exam / competition level): Assign formal charges to every atom in the diazomethane molecule, H₂C=N⁺=N⁻ (Structure A), and verify against an alternative resonance structure H₂C⁻–N⁺≡N (Structure B), then decide which better represents the real molecule and state the general principle this illustrates. Diazomethane, CH₂N₂, has total valence electrons: C (4) + 2 H (2×1 = 2) + 2 N (2×5 = 10) = 16, and it is a neutral molecule, so all 16 electrons must appear in the final structure with $\Sigma \text{FC} = 0$ . Structure A: H₂C=N=N, drawn with cumulated double bonds (C=N and N=N), one lone pair on the terminal nitrogen, and one lone pair on the internal (central) nitrogen. Count electrons: 2 C–H single bonds (4) + C=N double bond (4) + N=N double bond (4) + lone pair on central N (2) + 2 lone pairs on terminal N (4) = 4 + 4 + 4 + 2 + 4 = 18 — one lone pair too many; correct by placing only one lone pair on the terminal N and none extra on the central N beyond what's needed. Let's rebuild carefully. Correct Structure A (the standard textbook resonance structure for diazomethane): carbon bonded to two H's (single bonds) and double-bonded to the central nitrogen (C=N); central nitrogen also double-bonded to the terminal nitrogen (N=N), with the central nitrogen bearing no lone pair and the terminal nitrogen bearing two lone pairs. Electron count: 2 C–H bonds (2×2 = 4) + C=N double bond (4) + N=N double bond (4) + 2 lone pairs on terminal N (4) = 4 + 4 + 4 + 4 = 16 ✓. Formal charges:

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

(carbon has 2 C–H bonds contributing 4 bonding electrons plus the C=N double bond contributing 4 more, total $B = 8$ ).

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

(central N has the C=N double bond, 4 electrons, plus the N=N double bond, 4 electrons, total $B = 8$ , and zero lone pairs).

\text{FC(N}_{\text{terminal}}) = 5 - 4 - \frac{4}{2} = 5 - 4 - 2 = -1,

(terminal N has two lone pairs, $N=4$ , and one double bond, $B=4$ ). Sum: $0 + (+1) + (-1) = 0$ ✓, matching the neutral molecule's overall charge. Structure B: H₂C⁻–N⁺≡N, with a C–N single bond, an N≡N triple bond, three lone pairs on carbon replaced appropriately — let's build it properly. Carbon is bonded to 2 H's and singly bonded to the central N; central N is triple-bonded to terminal N; carbon carries one lone pair (to complete its octet as a carbanion-like center); central N carries no lone pair; terminal N carries one lone pair. Electron count: 2 C–H bonds (4) + C–N single bond (2) + N≡N triple bond (6) + 1 lone pair on C (2) + 1 lone pair on terminal N (2) = 4 + 2 + 6 + 2 + 2 = 16 ✓. Formal charges:

\text{FC(C)} = 4 - 2 - \frac{6}{2} = 4 - 2 - 3 = -1,

(carbon: one lone pair, $N=2$ ; bonds are 2 C–H + 1 C–N = 6 electrons total, $B=6$ ).

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

(central N: the C–N single bond, 2 electrons, plus the N≡N triple bond, 6 electrons, total $B = 8$ , zero lone pairs).

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

(terminal N: one lone pair, $N=2$ ; one triple bond, $B=6$ ). Sum: $(-1) + (+1) + 0 = 0$ ✓. Both structures are valid, charge-balanced Lewis structures, and both are genuine contributors to the real resonance hybrid of diazomethane (this molecule really is best described as a blend, which is why it's used as a classic example when Evaluating Resonance Structures is introduced). Ranking them by the formal-charge preference rules: Structure A has formal charges $\{0, +1, -1\}$ with the negative charge on a nitrogen (electronegativity 3.0) and the positive charge on the other, adjacent nitrogen; Structure B has formal charges $\{-1, +1, 0\}$ with the negative charge on carbon (electronegativity 2.5) — less electronegative than nitrogen — and a positive charge on the adjacent central nitrogen. By rule (b) (negative formal charge belongs on the more electronegative atom), Structure A is favored, since it places its −1 on nitrogen rather than carbon. Both structures tie on total |FC| magnitude (both sum to 2 in absolute value: $|0|+|1|+|1|=2$ for A, and $|-1|+|1|+|0|=2$ for B), so rule (b) is the tiebreaker, and it correctly identifies Structure A as the dominant resonance contributor — consistent with diazomethane's real reactivity, in which the carbon end behaves as the nucleophilic, electron-rich site (matching Structure B's minor contribution of negative character there) while remaining an overall neutral, stable molecule best drawn predominantly as Structure A.

Limiting cases, scope & common traps

Situation	What to watch for
Neutral molecule, all atoms "normal valence" (e.g., CH₄, H₂O, NH₃)	Every atom should come out to FC = 0; if not, recount bonds/lone pairs — a nonzero result here signals a drawing error, not a real charge.
Polyatomic ion (e.g., NH₄⁺, OH⁻, CO₃²⁻)	ΣFC must equal the ion's charge exactly; use this as a mandatory self-check after every structure.
Atom making "too many" bonds for its group (e.g., 4-bonded N, 3-bonded O)	Expect FC = +1 for N with 4 bonds, +1 for O with 3 bonds — extra bonds relative to the neutral atom's typical valence always show up as positive formal charge.
Atom making "too few" bonds and holding extra lone pairs (e.g., 3-bonded O⁻, 2-bonded N⁻)	Expect negative formal charge — fewer bonds than typical, compensated by extra lone-pair electrons.
Comparing resonance structures of the same connectivity	Use FC magnitude first, then electronegativity placement, then adjacency of like charges, in that order, as tie-breakers.
Formal charge vs. oxidation state	These are computed by opposite extreme assumptions (50/50 split vs. 100/0 split) and generally give different numbers for the same atom — never mix them in one argument.
Expanded octets (period 3+ elements: P, S, Cl in certain structures)	Formal charge can sometimes be lowered by drawing more bonds using d-orbital involvement or hypervalency, but modern treatments favor the structure with the fewest formal charges consistent with sound bonding, not maximal bond count for its own sake.

The chemist behind it

Formal charge as a concept grew directly out of Gilbert N. Lewis's 1916 proposal that covalent bonds are shared electron pairs — the moment that idea existed, chemists needed a consistent way to track "who owns what" within a structure, especially once ions and structures with expanded or contracted octets entered the picture. Lewis himself, working largely alone at Berkeley after building the chemistry department there into a research powerhouse, was concerned above all with getting the electron-counting right; the formal-charge bookkeeping convention that later generations of textbook writers systematized is a direct descendant of his original cubical-atom and shared-pair reasoning, refined through the 1920s–1930s as physical organic chemistry matured and needed sharper tools for comparing resonance structures (a program pushed hard by Linus Pauling in The Nature of the Chemical Bond).

Origins · 1 minGilbert Newton Lewis and how this was discovered

Gilbert Newton Lewis

1875–1946 · American physical chemist, UC Berkeley

Lewis proposed the shared electron-pair bond in 1916, invented the "Lewis structure" notation used throughout chemistry, and later contributed to acid–base theory (Lewis acids and bases) and thermodynamics. He never received a Nobel Prize despite numerous nominations — one of the most debated omissions in the prize's history — but his electron-pair bonding model remains the working language of structural chemistry, and formal charge is the direct bookkeeping tool built on top of it.

History

- 1875 — Gilbert N. Lewis born in Weymouth, Massachusetts.

- 1916 — Lewis publishes "The Atom and the Molecule," introducing the shared electron-pair covalent bond and dot-structure notation.

- 1923 — Lewis publishes Valence and the Structure of Atoms and Molecules, systematizing electron-pair bonding and setting up the bookkeeping later formalized as formal charge.

- 1931–1939 — Linus Pauling's resonance theory (The Nature of the Chemical Bond, 1939) formalizes the comparison of multiple Lewis structures, making formal-charge-based ranking a standard analytical tool.

- 1946 — Lewis dies in his Berkeley laboratory; formal charge remains a core pedagogical and diagnostic tool in every subsequent generation of chemistry textbooks.

Why do we assume bonds split 50/50 when we know real bonds are polarized?

That assumption is the entire design feature of formal charge, not an oversight. By using the same artificial rule (equal sharing) for every atom in every candidate structure, formal charge becomes a fair, controlled comparison: any difference you see between two structures' formal-charge patterns must come from how the electrons are arranged (which atoms bond to which, how many lone pairs sit where), not from an inconsistent application of electronegativity. Once you've used formal charge to narrow down the reasonable structures, you then bring in real electronegativity separately — as an additional preference rule (put negative formal charge on the more electronegative atom) — rather than baking it into the arithmetic itself.

Is formal charge the same thing as oxidation state?

No, and mixing them up is one of the most common student errors. Formal charge assumes bonds split their electrons exactly in half (50/50) between the two bonded atoms, regardless of electronegativity. Oxidation state assumes the opposite extreme: every bond's electrons are assigned completely (100%) to whichever atom is more electronegative, treating the bond as fully ionic even when it's really covalent. For carbon monoxide, formal charge gives C = −1 and O = +1, while oxidation state gives C = +2 and O = −2 — genuinely different numbers describing genuinely different (idealized) bookkeeping conventions applied to the same real molecule.

Can an atom have a formal charge of ±2 or more, and is that always wrong?

It's mathematically possible (the formula doesn't forbid it), but a formal charge of magnitude 2 or greater on a common main-group atom (C, N, O, especially) is a strong signal that a better Lewis structure exists with smaller formal charges, given the same molecular formula and connectivity. It's not automatically "wrong" — some genuinely unusual species require larger formal charges — but in an introductory or exam context, seeing ±2 should make you go back and check whether rearranging double bonds or lone pairs (without changing which atoms are bonded to which) can produce a structure with smaller formal charges, which is almost always the better representation.

How does formal charge interact with resonance structures?

When a molecule or ion has more than one valid Lewis structure differing only in the placement of double bonds and lone pairs (the connectivity of atoms stays fixed), formal charge is the primary tool for ranking those structures by how much each one likely contributes to the true, delocalized electronic structure. Structures with the smallest formal charge magnitudes, with negative charge on the most electronegative atoms, and without adjacent like-signed charges, are judged the major contributors; structures violating these preferences still count, but as minor contributors. This ranking is the direct starting point for the more detailed rules used when formally comparing resonance structures.

Does formal charge depend on which resonance structure I draw, or is it a fixed property of the molecule?

Formal charge is a property of a specific drawn Lewis structure, not of the real molecule itself — this is a crucial distinction. The same atom can have different formal charges in different valid resonance structures of the same species (nitrogen in one resonance form of diazomethane has FC = +1; in another valid resonance form, a different atom bears that charge instead). The real molecule is a single, fixed physical object with one true electron distribution; formal charge is a bookkeeping label attached to each proposed drawing of that molecule, useful precisely because comparing how formal charge shifts across different drawings tells you about the character of the true, delocalized structure.

Why does ammonium (NH₄⁺) have its formal positive charge on nitrogen rather than smeared over the hydrogens?

Formal charge is computed per-atom using each atom's own valence electron count as the reference point. Nitrogen normally (as a neutral atom) forms three bonds and keeps one lone pair; in NH₄⁺ it forms four bonds and keeps zero lone pairs, which the formula V − N − B/2 registers as a deviation of exactly +1 electron relative to neutral nitrogen. Each hydrogen, by contrast, is doing exactly what a neutral, single-bonded hydrogen atom always does (one bond, no lone pairs), so each hydrogen's formula gives FC = 0 — nothing unusual is happening at any individual hydrogen atom, even though, physically, the true positive charge is delocalized somewhat over the whole ion via the polarized N–H bonds.

What's the fastest way to sanity-check a formal charge calculation without redoing all the arithmetic?

Add up the formal charges on every atom in the structure and compare that sum to the actual net charge of the species (0 for a neutral molecule, the ion's stated charge otherwise). If they don't match, there is definitely an error — either a lone pair or bond was miscounted, or the total electron count used to build the structure in the first place was wrong. This sum check, which follows directly from conservation of electrons, catches the overwhelming majority of formal-charge mistakes in seconds, before you need to re-examine every individual atom.