Use our quantum numbers calculator for quick and accurate calculations. Free online tool.
The Quantum Numbers Calculator helps you determine all four quantum numbers (n, l, ml, ms) that uniquely describe an electron within an atom. These four quantum numbers — principal, angular momentum, magnetic, and spin — together define the exact quantum state of any electron, following the Pauli Exclusion Principle which states no two electrons can share the same set of four quantum numbers.
For example, an electron in a 2p orbital has n=2, l=1, and possible ml values of -1, 0, or +1, with ms of +½ or -½. This gives six distinct quantum states for the 2p subshell, explaining why p subshells hold a maximum of 6 electrons. The set {2, 1, 0, +½} fully specifies one unique electron in a 2p orbital.
Enter the principal quantum number n to automatically generate all valid combinations of l, ml, and ms. This tool is essential for chemistry and physics students studying electron configuration, orbital theory, and atomic spectroscopy. It is also useful for verifying electron configurations and understanding how electrons populate atomic orbitals.
The four quantum numbers are the principal (n), angular momentum (l), magnetic (ml), and spin (ms) quantum numbers. Together they uniquely identify every electron in an atom.
This is the Pauli Exclusion Principle: two electrons in the same atom cannot occupy the exact same quantum state, ensuring that each electron has a unique identity.
The n=3 shell has 18 quantum states (2n² = 18), corresponding to the 3s, 3p, and 3d subshells holding 2, 6, and 10 electrons respectively.
The spin quantum number ms can only be +½ (spin up) or -½ (spin down), representing the two intrinsic spin states of an electron.
Electron configuration is a shorthand notation derived directly from quantum numbers; each subshell designation (1s², 2p⁶, etc.) corresponds to specific sets of n and l values.