Use our spin quantum number calculator for quick and accurate calculations. Free online tool.
mₛ = +1/2
mₛ = -1/2
Maximum 2 electrons per orbital (one of each spin)
Only two possible values: +1/2 (spin up ↑) and -1/2 (spin down ↓)
Electron spin is a form of intrinsic angular momentum that has no classical analogue. The Stern-Gerlach experiment (1922) first demonstrated spin quantization by showing that a beam of silver atoms splits into exactly two distinct bands when passed through an inhomogeneous magnetic field — direct evidence that the electron possesses a two-valued magnetic moment corresponding to ms = +½ and ms = −½.
The spin quantum number is central to the Pauli Exclusion Principle, which states that no two electrons in the same atom can share the same set of four quantum numbers. Because ms can only be +½ or −½, an atomic orbital (defined by n, ℓ, and mℓ) can hold at most two electrons, and those two electrons must have opposite spins. This requirement directly determines the electron capacity of every subshell and shapes the periodic table's structure.
The spin magnetic moment arising from ms is responsible for paramagnetism and diamagnetism: atoms or ions with unpaired electrons (ms contributions that do not cancel) are paramagnetic and are attracted to external magnetic fields, while those with all electrons paired are diamagnetic. Spin is also the quantum-mechanical foundation of NMR spectroscopy, MRI technology, and spintronic devices, making it one of the most practically consequential quantum properties.
The spin quantum number ms can only be +½ (spin up, ↑) or −½ (spin down, ↓); these are the only two quantum mechanically allowed spin states for an electron.
The Stern-Gerlach experiment (1922) passed a beam of silver atoms through an inhomogeneous magnetic field and observed exactly two deflected beams, demonstrating that the electron has a two-valued intrinsic magnetic moment.
The Pauli Exclusion Principle requires that no two electrons share all four quantum numbers; since ms has only two values, each orbital can hold exactly two electrons with opposite spins (+½ and −½).
Electrons are spin-½ particles (fermions); the spin angular momentum quantum number s = ½ gives 2s + 1 = 2 states with ms = +½ and −½, which are half-integers rather than integers by the nature of fermionic spin.
If an atom has unpaired electrons whose ms values do not cancel, it possesses a net magnetic moment and is paramagnetic; if all electrons are paired with opposite ms values, the moments cancel and the atom is diamagnetic.