Orbital Diagram Calculator

An orbital diagram is a visual representation of how electrons are distributed among the atomic orbitals of an element. Each orbital is depicted as a box or line, and electrons are shown as arrows pointing up or down to indicate their spin direction. Orbital diagrams follow three fundamental principles: the Aufbau principle (electrons fill the lowest energy orbitals first), Hund's rule (electrons occupy degenerate orbitals singly before pairing), and the Pauli exclusion principle (no two electrons in an atom can have the same set of four quantum numbers).

Unlike electron configuration notation, which uses shorthand like 1s² 2s² 2p⁶, orbital diagrams explicitly show the spin arrangement of every electron. This is important because the spin arrangement determines whether an atom is paramagnetic (has unpaired electrons and is attracted to a magnetic field) or diamagnetic (all electrons are paired and is weakly repelled by a magnetic field). Understanding orbital diagrams is essential for predicting chemical bonding behavior, magnetic properties, and reactivity patterns.

This calculator generates complete orbital diagrams for elements up to krypton (Z = 36), showing each subshell's boxes with up and down arrows. It also reports the total number of electrons, unpaired electrons, valence electrons, and whether the atom is paramagnetic or diamagnetic. You can also explore ion formation by specifying an ionic charge, which changes the electron count and thus the orbital filling pattern.

Electrons fill atomic orbitals in a specific order determined by increasing energy. The filling sequence follows the pattern: 1s, 2s, 2p, 3s, 3p, 4s, 3d, 4p, 5s, 4d, 5p, 6s, 4f, 5d, 6p, and so on. This order arises from the interplay between the principal quantum number (n) and the azimuthal quantum number (l), and is summarized by the (n + l) rule: orbitals with lower (n + l) values are filled first, and when two orbitals have the same (n + l) value, the one with the lower n is filled first.

Hund's rule governs how electrons occupy orbitals within a subshell. Electrons first fill each orbital in a subshell with a single electron (all spinning in the same direction) before pairing begins. This arrangement minimizes electron-electron repulsion and is the lowest energy configuration. For example, in a 2p subshell with three orbitals, the first three electrons each go into separate orbitals with parallel spins, and only the fourth electron begins pairing.

The Pauli exclusion principle states that no two electrons in an atom can share the same four quantum numbers. This means each orbital can hold a maximum of two electrons, and those two electrons must have opposite spins (one spin-up, one spin-down). This principle is what gives orbital diagrams their characteristic arrow notation, where each box contains at most two arrows pointing in opposite directions.

Use this calculator to explore the orbital diagrams of elements and their ions:

1. Select an Element: Choose an element from the dropdown by its atomic number (Z). The calculator supports elements from hydrogen (Z = 1) through krypton (Z = 36).
2. Set the Ionic Charge: Use the charge selector to specify an ion. For example, setting charge to +2 for iron (Fe, Z = 26) gives Fe²⁺, which has 24 electrons instead of 26.
3. Use Quick Select: Click common element buttons (H, C, N, O, Na, Cl, Fe) for fast access.
4. Read the Results: The orbital diagram displays each subshell with boxes containing spin arrows. The summary cards show total electrons, unpaired electrons, valence electrons, and magnetic properties.

The orbital diagram visually shows which orbitals are fully occupied, which are half-filled, and which are empty. This information is directly useful for understanding an element's chemical reactivity and bonding preferences.

One of the most important outputs of an orbital diagram is the magnetic property of the atom or ion. Paramagnetic substances have one or more unpaired electrons, which create a net magnetic moment. When placed in an external magnetic field, paramagnetic materials are attracted toward the field. This property is exploited in applications ranging from MRI contrast agents (which contain paramagnetic gadolinium ions) to magnetic separation in mineral processing.

Diamagnetic substances have all electrons paired, resulting in no net magnetic moment. Diamagnetic materials are very weakly repelled by magnetic fields. While this effect is much weaker than paramagnetic attraction, it is detectable and is the basis for measuring magnetic susceptibility in research laboratories.

The number of unpaired electrons directly determines the strength of paramagnetic behavior. For example, iron (Fe) in its ground state has four unpaired electrons in the 3d subshell, making it strongly paramagnetic. When iron forms Fe²⁺, it loses two 4s electrons and retains four unpaired 3d electrons. Fe³⁺ loses an additional 3d electron, leaving five unpaired electrons — the maximum possible for a 3d element — making it even more paramagnetic.

Orbital diagrams and the principles they illustrate are fundamental to many areas of chemistry and materials science:

Transition Metal Chemistry: The partially filled d-orbitals of transition metals give rise to their characteristic properties: colorful compounds (d-d electronic transitions), variable oxidation states, and catalytic activity. Understanding which d-orbitals are occupied explains why Cu²⁺ forms blue solutions while Ni²⁺ forms green ones.

Magnetic Materials: The magnetic properties of materials are determined by the orbital diagrams of their constituent atoms. Ferromagnetic materials like iron, cobalt, and nickel have unpaired d-electrons that align cooperatively to produce strong permanent magnets. This is the basis for data storage, electric motors, and magnetic resonance imaging.

Chemical Bonding: Orbital diagrams predict how atoms will bond. Atoms with half-filled or nearly half-filled subshells tend to be more stable and less reactive (e.g., nitrogen's half-filled 2p subshell makes N₂ exceptionally inert). Elements at the end of a subshell (like noble gases) have all orbitals filled, explaining their chemical inertness.

Bioinorganic Chemistry: Metalloenzymes use transition metal ions with specific orbital configurations to catalyze biological reactions. Hemoglobin contains Fe²⁺ with a specific d-orbital configuration that enables reversible oxygen binding. The orbital diagram explains why Fe²⁺ binds O₂ while Fe³⁺ does not.