Last updated: 2026-07-01

Electron configurations explained

An electron configuration describes how the electrons of an atom are arranged among its orbitals. It is one of the most useful pieces of information in chemistry: it explains an element's position in the periodic table, its typical oxidation states, its magnetic behavior, and the spectral lines it emits. Given an atomic number Z from 1 to 118, this calculator fills the orbitals in standard Aufbau order and returns the full configuration, the noble-gas shorthand, and the count of valence electrons.

Orbitals and subshells

Electrons occupy regions called orbitals, grouped into subshells labeled s, p, d, and f. Each subshell has a fixed capacity set by the number of orbitals it contains (each orbital holds two electrons of opposite spin):

A subshell is written as its principal quantum number followed by its letter and a superscript for the number of electrons — $2p^{4}$ means four electrons in the 2p subshell.

The Aufbau filling order

The Aufbau principle ("building up") says electrons occupy the lowest-energy orbitals first. Energies do not increase in simple numeric order: the 4s subshell fills before 3d, and 6s before 4f. The Madelung rule captures this by ordering subshells by increasing $n + l$, and by increasing $n$ when the sums are equal. The resulting sequence is:

Two more rules complete the picture. The Pauli exclusion principle limits each orbital to two electrons of opposite spin, which is why the capacities above are what they are. Hund's rule says that within a subshell, electrons occupy separate orbitals with parallel spins before pairing up — this governs how electrons distribute inside a subshell, though it does not change the occupancy total that the configuration reports.

Worked example: iron (Z = 26)

Iron has 26 electrons. Filling subshells in Aufbau order and stopping when all 26 are placed:

The first 18 electrons match the configuration of argon, so the noble-gas shorthand collapses them into [Ar]:

The outermost principal shell is $n = 4$, which holds the $4s^{2}$ electrons, giving iron 2 valence electrons under the main-group counting convention.

The noble-gas shorthand

Writing the full configuration for a heavy element is tedious, so chemists abbreviate the inner electrons with the preceding noble gas in brackets. The noble-gas cores are helium (2), neon (10), argon (18), krypton (36), xenon (54), and radon (86). For calcium (Z = 20), the first 18 electrons are the argon core, so 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² is written [Ar] 4s². The shorthand keeps the chemically active outer electrons in view while hiding the unreactive core.

Valence electrons

Valence electrons are the outermost electrons that participate in bonding. Under the standard main-group definition used here, they are the electrons in the highest occupied principal shell (the largest $n$), counting the ns and np subshells. Sodium (Z = 11) is [Ne] 3s¹, so it has one valence electron; chlorine (Z = 17) is [Ne] 3s² 3p⁵, with seven. For transition metals the picture is more nuanced because the (n−1)d electrons can also take part in bonding, but the outer-shell count gives the conventional group-based value.

Aufbau exceptions

Real atoms do not always follow the strict Aufbau prediction. Chromium (Z = 24) is observed as [Ar] 4s¹ 3d⁵ rather than the predicted [Ar] 4s² 3d⁴, and copper (Z = 29) is [Ar] 4s¹ 3d¹⁰ instead of [Ar] 4s² 3d⁹, because a half-filled or fully filled d subshell is slightly more stable. Similar irregularities appear among the lanthanides, actinides, and heavier transition metals. This calculator applies the standard Aufbau order and does not encode these anomalies, so a handful of d-block and f-block elements will differ from the experimentally measured ground state.