Electron Configuration Calculator — full, noble-gas and orbital diagram

The electron configuration calculator on this page fills orbitals in the Madelung (aufbau) order, then checks the result against a table of the elements that genuinely break that order, and returns four things at once: the full configuration, the noble-gas shorthand, an orbital box diagram with arrows, and the counts that follow from it — valence electrons and unpaired electrons. Set a charge and it rebuilds the configuration for the ion using the removal rule that trips up most students.

Arb Digital builds free reference tools for the calculations people repeatedly get wrong by hand, and electron configuration is near the top of that list. Not because the filling rule is hard, but because roughly twenty elements do not obey it, and because ions do not lose electrons from the orbital they most recently filled. Both of those are handled explicitly here rather than glossed over.

What This Electron Configuration Calculator Does

Give it an element symbol, an element name or a bare atomic number between 1 and 118, and it returns the electron configuration written two ways. The full form lists every subshell from 1s upward. The noble-gas shorthand replaces the filled core with the preceding noble gas in brackets, so chromium becomes [Ar]3d⁵4s¹ instead of a twenty-four-electron string you have to read character by character.

Alongside that, it draws an orbital diagram. Each subshell is shown as its individual orbitals — one box for s, three for p, five for d, seven for f — filled according to Hund's rule, which puts one electron in every orbital of a subshell before any orbital takes a second. From that diagram the calculator counts unpaired electrons, the number that predicts whether a species is paramagnetic or diamagnetic. It also reports the block (s, p, d or f) and a valence electron count.

A charge field turns any element into an ion. Enter +2 for a magnesium cation or −1 for a chloride anion and the configuration is rebuilt, not merely relabelled. If you need atomic masses rather than electron structure, the molar mass calculator handles that side; the molar mass converter is a unit converter and a different job again.

How to Use It

1. Enter the element. Type a symbol (Fe), a full name (iron) or the atomic number (26). Capitalisation does not matter.
2. Set the charge. Leave it at 0 for a neutral atom. Use a positive integer for a cation, a negative one for an anion.
3. Pick the writing order. Shell order groups everything by principal quantum number, which is how most textbooks print a final answer. Filling order lists subshells in the sequence they were actually occupied.
4. Read the hero line for the noble-gas shorthand, then the note below the grid for the full configuration and the orbital diagram.
5. Check the unpaired count if you care about magnetism, and the valence count if you are heading toward bonding or Lewis structures.

The Formula: How the Configuration Is Built

There is no single equation here, but there is a strict procedure. Electrons occupy subshells in order of increasing n + l, and where two subshells share the same n + l value, the one with the lower n fills first. That is the Madelung rule, and it produces this sequence: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, 7s, 5f, 6d, 7p. Compare 4s (n + l = 4 + 0 = 4) with 3d (3 + 2 = 5) and the famous inversion falls straight out of the arithmetic: 4s has the lower sum, so it fills first.

Each subshell holds 2(2l + 1) electrons: two in s, six in p, ten in d, fourteen in f. The Pauli exclusion principle is what caps each individual orbital at two electrons, and it requires those two to have opposite spin. Hund's rule of maximum multiplicity governs the order within a subshell — electrons spread out singly with parallel spins before pairing, because pairing two electrons in the same small region of space costs energy. The calculator applies all three rules in that order, then applies a fourth step that most simple scripts skip entirely: it looks the element up in an exceptions table. The subshell energies used here follow the standard ground-state assignments published in the NIST Periodic Table of the Elements and in the IUPAC Periodic Table of the Elements.

The Exceptions Table, and Why It Exists

Aufbau filling is a useful approximation, not a law. Around twenty elements have measured ground states that differ from what strict n + l ordering predicts, and pretending otherwise is the single most common flaw in electron configuration tools. This calculator carries them as explicit data.

• Chromium (24) is [Ar]3d⁵4s¹, not [Ar]3d⁴4s². Copper (29) is [Ar]3d¹⁰4s¹.
• In the second transition row the departures are the norm rather than the exception: niobium (41) [Kr]4d⁴5s¹, molybdenum (42) [Kr]4d⁵5s¹, ruthenium (44) [Kr]4d⁷5s¹, rhodium (45) [Kr]4d⁸5s¹, silver (47) [Kr]4d¹⁰5s¹.
• Palladium (46) is the outlier among outliers: [Kr]4d¹⁰ with an empty 5s subshell, the only neutral atom in the d block with no outer s electrons at all.
• At the top of the f block, lanthanum (57) [Xe]5d¹6s² and cerium (58) [Xe]4f¹5d¹6s² put an electron into 5d before 4f is comfortably underway, and gadolinium (64) [Xe]4f⁷5d¹6s² holds a half-filled 4f set.
• In the third transition row, platinum (78) [Xe]4f¹⁴5d⁹6s¹ and gold (79) [Xe]4f¹⁴5d¹⁰6s¹.
• The actinides break repeatedly: actinium (89) [Rn]6d¹7s², thorium (90) [Rn]6d²7s² with no 5f electrons at all, protactinium (91), uranium (92) [Rn]5f³6d¹7s², neptunium (93), curium (96) [Rn]5f⁷6d¹7s², and lawrencium (103) [Rn]5f¹⁴7s²7p¹.

The usual classroom explanation for chromium and copper is that half-filled and completely filled d subshells carry extra stability. That story is a simplification. The fuller account is that 3d and 4s sit extremely close in energy here, and the deciding factor is the balance between electron-electron repulsion and exchange energy: two electrons paired in one 4s orbital repel strongly, while spreading them across five 3d orbitals with parallel spins maximises exchange stabilisation. Whether the half-filled shell wins is a close-run numerical contest, which is why it happens for chromium and molybdenum but not for tungsten, whose ground state is the ordinary [Xe]4f¹⁴5d⁴6s². If a rule were doing the work, tungsten would break too. It does not, and that is the tell.

Why the Filling Order Is Not the Energy Order

Here is the point that causes the most confusion in a first-year course. 4s fills before 3d, and yet in a transition metal atom the 3d orbitals lie below 4s in energy once they are occupied. Both statements are true, and they are not in conflict, because orbital energies are not fixed properties of an element — they depend on how many electrons are already present and how they shield one another.

In a nearly empty potassium or calcium shell, 4s penetrates closer to the nucleus than 3d and feels a higher effective nuclear charge, so it is the lower-energy home for the next electron. As soon as d electrons accumulate, the 3d set contracts and drops below 4s. The atom therefore fills 4s first and then holds 4s electrons that are the highest in energy it has. Every oddity about transition metal ions follows from that one fact.

Ions: Why 4s Leaves Before 3d

Ask a student to write Fe³⁺ and the common answer is [Ar]3d³4s² — remove three electrons from the last thing you filled. The correct answer is [Ar]3d⁵. Cations lose electrons from the orbital with the highest principal quantum number first, which for a first-row transition metal means 4s empties completely before 3d gives up a single electron.

This surprises people because it looks like the reverse of the filling rule, and in a sense it is. But you are no longer filling a nearly empty shell; you are ionising an atom that already has its 3d set contracted and stabilised. The 4s electrons are further out, more shielded, and easier to remove. The practical rule the calculator applies is: strip from the largest n, and within a shell strip from the highest l first. So Fe (26) is [Ar]3d⁶4s²; removing two electrons gives Fe²⁺ as [Ar]3d⁶, and removing a third gives Fe³⁺ as [Ar]3d⁵ — a half-filled d shell, which is part of why iron(III) is such a common and stable oxidation state.

Anions are easier: added electrons go into the next available slot in the ordinary filling sequence. Chloride takes its extra electron into 3p and becomes [Ne]3s²3p⁶, isoelectronic with argon but not identical to it, since the nuclear charge differs.

Reading a Configuration Straight Off the Periodic Table

You rarely need a table of subshell orders if you can read the periodic table as a map of blocks. Groups 1 and 2 form the s block, groups 13 to 18 the p block, groups 3 to 12 the d block, and the two detached rows the f block. Start at hydrogen and read left to right, row by row, writing down the block and period you pass through: period 1 gives 1s, period 2 gives 2s then 2p, period 3 gives 3s then 3p, period 4 gives 4s then 3d then 4p, and so on.

Remember that a d block in period n means (n − 1)d, and an f block in period n means (n − 2)f. Stop at your element and count how far into its block it sits — that count is the superscript on the final subshell. Selenium, in period 4, group 16, is the fourth element of the 4p block, so it ends 4p⁴ and the whole configuration reads [Ar]3d¹⁰4s²4p⁴. The method is fast and reliable for everything except the exceptions listed above, which is precisely why a table of exceptions is worth memorising separately.

What the Configuration Predicts About Magnetism

The unpaired electron count is the most directly useful output on this page. A species with at least one unpaired electron is paramagnetic and is attracted into a magnetic field. A species with every electron paired is diamagnetic and is weakly repelled. Zinc, [Ar]3d¹⁰4s², has no unpaired electrons and is diamagnetic. Manganese, [Ar]3d⁵4s², has five, the maximum possible for a first-row transition metal.

For a free atom or simple ion, the spin-only magnetic moment follows from that count alone. Once ligands enter the picture the d orbitals split, so the free-ion configuration is only a starting point for high-spin and low-spin complexes. Gadolinium, with seven unpaired 4f electrons plus one in 5d, has one of the largest ground-state moments of any element, readable directly from the exception-corrected configuration.

Valence Electrons, and Why the Definition Shifts

For a main-group element, valence electrons are simply those in the highest occupied principal shell: sulfur, [Ne]3s²3p⁴, has six. That count maps straight onto the group number and onto Lewis structures. For a transition metal the definition is less tidy, because the incompletely filled (n − 1)d subshell participates in bonding too. This calculator counts the outer s electrons plus any incomplete d or f electrons, which is the convention that best matches observed oxidation states — iron gets eight, and its common +2 and +3 states both sit within that range.

Different textbooks answer this question differently, so an answer marked wrong is often a definition disagreement rather than an error. If a question asks for the valence electrons of a d-block element without qualification, state which definition you are using.

Common Mistakes to Avoid

• Assuming aufbau order is universal — around twenty elements, chromium and copper among them, have measured ground states that differ from the predicted filling.
• Removing 3d electrons before 4s when forming a cation — the highest principal quantum number always empties first, so Fe³⁺ is [Ar]3d⁵, not [Ar]3d³4s².
• Pairing electrons within a subshell too early — Hund's rule puts one electron in every orbital of a subshell before any orbital gets a second.
• Writing the noble-gas core of the wrong element — the bracket holds the noble gas preceding your element, so bromine uses [Ar], not [Kr].
• Treating isoelectronic species as chemically identical — Cl⁻, Ar and K⁺ share a configuration but have different nuclear charges, radii and reactivity.

Related Free Tools From Arb Digital

Configurations lead naturally into stoichiometry, so pair this page with the moles to grams calculator when you move from structure to quantity, use the chemical equation balancer for the reaction side, and try the Gibbs free energy calculator for the energetics. The full free online tools hub lists everything else.

Frequently Asked Questions

This tool is an educational reference for ground-state electron configurations and provides no laboratory procedure, handling, or chemical safety guidance of any kind.