Last updated: July 2, 2026
Electron Configuration Calculator
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Quick Answer
This calculator determines the electron configuration of any element (atomic numbers 1–118) or ion using the Aufbau principle. It outputs the full configuration (e.g. 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶ for iron), the noble-gas condensed shorthand (e.g. [Ar] 4s² 3d⁶), the number of valence electrons (highest-n shell), and the number of unpaired electrons by Hund's rule. Optional ionic charge input allows direct calculation for cations and anions.
To find the electron configuration of an element, enter its atomic number. For iron (Z=26), electrons fill in Aufbau order: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶, condensed as [Ar] 4s² 3d⁶. Iron has 2 valence electrons and 4 unpaired electrons. For sodium (Z=11) the configuration is 1s² 2s² 2p⁶ 3s¹, or [Ne] 3s¹, with 1 valence and 1 unpaired electron.
Key Takeaways
- Electrons fill orbitals in Aufbau order (1s→2s→2p→3s→3p→4s→3d→…), governed by the (n + l) rule.
- Each orbital holds at most 2 electrons with opposite spins (Pauli exclusion principle).
- Within a subshell, electrons occupy separate orbitals with parallel spin before pairing (Hund's rule).
- Chromium (Z=24) and copper (Z=29) are well-known exceptions where a half-filled or fully-filled d subshell is more stable.
- Valence electrons — those in the outermost n shell — determine an element's chemical behaviour and oxidation states.
Creators
Dharmendra SinghReviewers
Creators
Dharmendra SinghReviewers
Formula
electrons = Z − charge; fill subshells: 1s(2) 2s(2) 2p(6) 3s(2) 3p(6) 4s(2) 3d(10) 4p(6) 5s(2) 4d(10) 5p(6) 6s(2) 4f(14) 5d(10) 6p(6) 7s(2) 5f(14) 6d(10) 7p(6)
Where:
- Z=Atomic number(dimensionless)
- q=Ionic charge(dimensionless)
- e⁻=Number of electrons(dimensionless)
- n=Principal quantum number(dimensionless)
- l=Azimuthal quantum number (s=0, p=1, d=2, f=3)(dimensionless)
Worked Examples
Iron (Fe, Z = 26) — transition metal
Determine the electron configuration of neutral iron and its unpaired electrons.
- 1Electrons = Z − charge = 26 − 0 = 26.
- 2Fill in Aufbau order: 1s²(2) → 2s²(4) → 2p⁶(10) → 3s²(12) → 3p⁶(18) → 4s²(20) → 3d⁶(26).
- 3Full configuration: 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶.
- 4Ar covers the first 18 electrons (1s² through 3p⁶), so the condensed form is [Ar] 4s² 3d⁶.
- 5Highest principal quantum number is n = 4; valence electrons from 4s² = 2.
- 6Last subshell 3d has 6 electrons in 5 orbitals: 5 singly occupied, 1 pairs → 4 unpaired.
Sodium (Na, Z = 11) — alkali metal
Find the electron configuration of neutral sodium.
- 1Electrons = 11.
- 2Fill in Aufbau order: 1s²(2) → 2s²(4) → 2p⁶(10) → 3s¹(11).
- 3Full configuration: 1s² 2s² 2p⁶ 3s¹.
- 4Ne covers 10 electrons (1s² 2s² 2p⁶), so the condensed form is [Ne] 3s¹.
- 5Valence electrons: 1 (only 3s¹ in n = 3 shell).
- 6Last subshell 3s has 1 electron; 1 ≤ 1 orbital → 1 unpaired.
Chloride ion (Cl⁻, Z = 17, charge = −1)
Find the electron configuration of the chloride anion formed when chlorine gains one electron.
- 1Electrons = Z − charge = 17 − (−1) = 18.
- 2Fill in Aufbau order: 1s²(2) → 2s²(4) → 2p⁶(10) → 3s²(12) → 3p⁶(18).
- 3Full configuration: 1s² 2s² 2p⁶ 3s² 3p⁶.
- 418 electrons matches argon exactly, so condensed form is [Ar].
- 5Valence electrons: 8 (from the n = 3 shell: 3s² + 3p⁶).
- 6Last subshell 3p is fully filled (6/6) → 0 unpaired electrons.
Introduction
Electron configuration describes how electrons are distributed among the atomic orbitals of an atom or ion. Knowing an element's electron configuration is foundational to predicting its chemical reactivity, bonding behaviour, magnetic properties, and spectroscopic characteristics. This calculator applies the Aufbau principle, Pauli exclusion principle, and Hund's rule to distribute electrons across subshells for any element from hydrogen (Z = 1) to oganesson (Z = 118), and for common ionic species. It also reports the noble-gas condensed shorthand, valence electrons, and Hund's-rule unpaired electrons — the same quantities used in courses from general chemistry to advanced inorganic chemistry.
The Aufbau Principle and Filling Order
The Aufbau (German: *building-up*) principle states that electrons occupy the lowest available energy subshell before entering a higher one. The standard Aufbau filling order is: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p This order can be remembered with the diagonal mnemonic arrow diagram taught in most general chemistry textbooks. The capacity of each subshell follows from the quantum numbers: s = 2, p = 6, d = 10, f = 14. The IUPAC recommendations use this ordering as the standard definition of an electron configuration. It is important to note that the Aufbau order reflects *orbital energies in multi-electron atoms* as approximated by the (n + l) rule (Madelung rule): subshells with lower (n + l) fill first; when (n + l) is equal, lower n fills first.
Pauli Exclusion Principle and Hund's Rule
Two additional rules govern how electrons occupy orbitals within a subshell: Pauli Exclusion Principle: no two electrons in the same atom can have an identical set of all four quantum numbers. Consequently, each orbital holds a maximum of two electrons, which must have opposite spins (↑↓). This limits s subshells to 2 electrons, p to 6, d to 10, and f to 14. Hund's Rule of Maximum Multiplicity: when electrons occupy orbitals of equal energy (degenerate orbitals within the same subshell), they spread into separate orbitals with parallel spins before any orbital is doubly occupied. For example, nitrogen (Z = 7) has three 2p electrons occupying three separate p orbitals with parallel spin (↑ ↑ ↑), giving 3 unpaired electrons and a half-filled 2p subshell. This maximises spin multiplicity and minimises electron–electron repulsion. See the effective nuclear charge calculator for how nuclear shielding affects these energies.
Noble-Gas Condensed Notation
Writing the full configuration of a heavy element such as uranium (Z = 92) is cumbersome. Chemists use a condensed (noble-gas) shorthand by substituting the core electron configuration with the symbol of the preceding noble gas in brackets: | Noble gas | Z | Core configuration | |-----------|----|-----------------| | [He] | 2 | 1s² | | [Ne] | 10 | 1s² 2s² 2p⁶ | | [Ar] | 18 | 1s² 2s² 2p⁶ 3s² 3p⁶ | | [Kr] | 36 | [Ar] 4s² 3d¹⁰ 4p⁶ | | [Xe] | 54 | [Kr] 5s² 4d¹⁰ 5p⁶ | | [Rn] | 86 | [Xe] 6s² 4f¹⁴ 5d¹⁰ 6p⁶ | For example, iron's condensed configuration [Ar] 4s² 3d⁶ immediately shows the valence electrons beyond the argon core. This notation emphasises the chemically important valence shell and is the standard form used in inorganic chemistry texts. It is also directly connected to the electronegativity calculator, which depends on knowing the valence configuration.
Valence Electrons and Chemical Reactivity
Valence electrons are those in the outermost principal quantum number shell (highest n). They determine how an element bonds and reacts: - Main-group elements (s- and p-block): valence electrons in the ns and np subshells directly dictate the group number and oxidation states. - Transition metals (d-block): the highest-n s electrons are the primary valence electrons. Iron ([Ar] 4s² 3d⁶) has 2 valence electrons (4s²), which is why +2 is its most common oxidation state. - Lanthanides/actinides (f-block): f electrons participate in bonding, giving complex and variable oxidation states. The number of valence electrons is also needed by the bond order calculator and the percent composition calculator when predicting stoichiometry. For a neutral element, the valence electron count equals the group number for main-group elements (IUPAC groups 1, 2, 13–18), making periodic table navigation intuitive. For more on how electrons are counted relative to the nucleus, see the effective nuclear charge calculator.
Chromium, Copper, and Other Aufbau Exceptions
The Aufbau principle predicts configurations that occasionally disagree with experimental spectroscopic measurements for certain transition metals and lanthanides. The two most-cited textbook exceptions are: Chromium (Z = 24): Aufbau predicts [Ar] 4s² 3d⁴, but the actual configuration is [Ar] 4s¹ 3d⁵ (half-filled 3d subshell). The half-filled d⁵ arrangement provides extra stability through exchange energy, so one 4s electron migrates to 3d. Copper (Z = 29): Aufbau predicts [Ar] 4s² 3d⁹, but the actual configuration is [Ar] 4s¹ 3d¹⁰ (full 3d subshell). A filled d¹⁰ is particularly stable. This calculator reports the strict Aufbau result for all elements, which is accurate for the vast majority (Z = 1–118) and is the standard taught in general chemistry courses. For advanced work with Cr, Cu, and about 19 other known anomalies (Mo, Ag, Au, Pd, etc.), consult spectroscopic databases such as the NIST Atomic Spectra Database. The exceptions arise from the near-degeneracy of 3d and 4s orbital energies in those elements — a subtlety beyond the scope of the simple Aufbau model.
Electron Configurations of Ions and Real-World Applications
Forming ions changes the electron count and therefore the configuration. For cations, electrons are removed from the highest-energy occupied orbital (4s before 3d in transition metals when forming ions, despite 4s filling before 3d in neutral atoms — an important and frequently-tested subtlety). For anions, electrons are added to the next available subshell. Real-world applications of electron configurations include: - Magnetic materials: unpaired electrons give paramagnetic (attracted to magnets) behaviour. Fe²⁺ ([Ar] 3d⁶) has 4 unpaired electrons; Fe³⁺ ([Ar] 3d⁵) has 5, making it more paramagnetic. MRI contrast agents exploit this property. - Laser technology: Nd:YAG lasers rely on the 4f³ configuration of Nd³⁺ for specific optical transitions. - Catalyst design: the d-electron count of transition metals determines which ligands bind and how. The electronegativity calculator provides complementary data for predicting bond polarity. - Semiconductor doping: adding phosphorus (Z = 15, [Ne] 3s² 3p³) to silicon (Z = 14, [Ne] 3s² 3p²) introduces an extra valence electron, creating an n-type semiconductor. - Spectroscopy: electron configuration determines allowed optical transitions and underpins both emission and absorption spectroscopy, from flame tests to X-ray photoelectron spectroscopy (XPS). For chemical bonding analysis, also see the bond order calculator.
Quick Reference Card
Electron Configuration Quick Reference
Quick reference • Electron Configuration Calculator
electrons = Z − charge; fill 1s 2s 2p 3s 3p 4s 3d 4p … in orderValid range: Z = 1 to 118; charge range typically −4 to +8 for stable ions
Common Values
⚠ Watch Out
- •Cr (Z=24) and Cu (Z=29) — and ~19 other transition/lanthanide elements — have configurations that differ from strict Aufbau; always verify against spectroscopic data for these elements.
- •When ionising transition metals, electrons are removed from the highest-n shell (4s) before the d subshell, even though 4s fills before 3d in neutral atoms.
- •The calculator uses the Aufbau model, which is an approximation; relativistic effects become significant for very heavy elements (Z > 80).
- •Noble-gas configuration assumes complete filling of the noble gas core; always verify for elements immediately following a noble gas in edge cases.
Pro Tips
- →Use the (n + l) rule: subshells fill in order of increasing (n + l); for equal (n + l), lower n fills first — e.g. 4s (4+0=4) before 3d (3+2=5).
- →The number of unpaired electrons = e if e ≤ (capacity/2), else capacity − e, for any subshell.
- →For main-group elements, valence electrons = group number (IUPAC groups 1, 2, 13–18).
- →Counting d electrons (d^n) from the noble-gas shorthand directly gives the oxidation state for many common transition-metal complexes.
FAQs
What is the electron configuration of iron (Fe)?
Iron (Z = 26) has the electron configuration 1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁶. In noble-gas shorthand this is written [Ar] 4s² 3d⁶. Iron has 2 valence electrons (in the 4s shell) and 4 unpaired electrons (in the 3d subshell, by Hund's rule). These 4 unpaired electrons make neutral iron paramagnetic.
Why does chromium have a different configuration than the Aufbau rule predicts?
Chromium (Z =
- 1is predicted by the Aufbau principle to have [Ar] 4s² 3d⁴, but its actual ground-state configuration is [Ar] 4s¹ 3d⁵. The half-filled 3d⁵ configuration is especially stable because of maximised exchange energy between electrons of parallel spin. The energy gain from achieving a half-filled d subshell exceeds the cost of moving one electron from 4s to 3d. Similarly, copper (Z =
- 2has [Ar] 4s¹ 3d¹⁰ rather than the predicted [Ar] 4s² 3d⁹, because a fully filled 3d¹⁰ is particularly stable
How do I find the electron configuration of an ion?
To find the configuration of an ion, adjust the electron count: for a cation with charge +n, remove n electrons from the neutral atom starting with the highest-energy occupied orbital. For transition-metal cations this means removing 4s electrons before 3d electrons, even though 4s fills before 3d in the neutral atom. For an anion with charge −n, add n electrons to the next available subshell. For example, Fe²⁺ (charge +2) has 26 − 2 = 24 electrons: [Ar] 3d⁶. Our calculator supports the charge input and reports the Aufbau result for electrons = Z − charge.
What are valence electrons and why do they matter?
Valence electrons are those in the outermost principal quantum number (n) shell of an atom. They are responsible for chemical bonding and reactions. For main-group elements, the number of valence electrons equals the IUPAC group number (e.g. oxygen in group 16 has 6 valence electrons). For transition metals, only the outermost s electrons are counted as valence electrons by the highest-n definition (e.g. iron has 2 valence electrons in 4s²). Valence electrons determine oxidation states, bond types, and molecular geometry, making them the single most important output of an electron configuration analysis.
How are unpaired electrons calculated, and why do they matter?
Unpaired electrons are calculated using Hund's rule: in a degenerate subshell, each orbital is singly occupied with parallel spin before any pairing occurs. For a subshell with capacity C and electron count e: if e ≤ C/2, all electrons are unpaired (e unpaired); if e > C/2, pairing occurs and the number of unpaired electrons = C − e. Unpaired electrons determine magnetic behaviour. Atoms or ions with unpaired electrons are paramagnetic (attracted to external magnetic fields); those with all electrons paired are diamagnetic. The number of unpaired electrons also influences colour, spectroscopic selection rules, and reactivity.
What is the noble-gas shorthand and how is it written?
The noble-gas (condensed) shorthand replaces the inner-core electron configuration of an element with the symbol of the preceding noble gas in square brackets. For example, sodium (Z = 11, full config: 1s² 2s² 2p⁶ 3s¹) can be written [Ne] 3s¹ because neon covers the first 10 electrons. The shorthand highlights the chemically active valence electrons while omitting the stable, non-reactive core. Noble gases used as cores are He (Z=2), Ne (Z=10), Ar (Z=18), Kr (Z=36), Xe (Z=54), Rn (Z=86), and Og (Z=118). Elements that are themselves noble gases are simply written [He], [Ne], [Ar], etc.