Quantum Numbers Calculator

Enter a principal quantum number to see all valid sets of n, l, ml, and ms values with orbital names and electron counts.

Quantum Number Inputs

Determines the energy level and shell (1–7).

0 = s, 1 = p, 2 = d, 3 = f. Range: 0 to n−1.

Shell Summary

Quantum Number Rules

n

Principal

Positive integer ≥ 1. Sets energy level and shell.

l

Azimuthal

Integer from 0 to n−1. Defines orbital shape.

ml

Magnetic

Integer from −l to +l. Specifies orbital orientation.

ms

Spin

Either +½ (spin up) or −½ (spin down). Pauli exclusion.

Valid Quantum Number Sets

0 sets
# n l ml ms Orbital Spin

Summary

Enter a principal quantum number to see all valid sets of n, l, ml, and ms values with orbital names and electron counts.

How it works

  1. Enter the principal quantum number n (1–7).
  2. Choose a specific subshell (l value) or view all subshells for that n.
  3. The calculator lists every valid (n, l, ml, ms) combination.
  4. Each row shows the orbital name (e.g. 2p), orientation (ml), and spin (ms = +½ or −½).
  5. The summary table shows total electrons per subshell and per shell.

Use cases

  • Verify which quantum number sets are allowed for a given energy level.
  • Study for chemistry or physics exams on atomic structure.
  • Find the number of orbitals and electrons in any subshell.
  • Understand the Pauli exclusion principle through enumerated combinations.
  • Cross-check electron configurations with quantum number rules.
  • Teach or visualize quantum mechanics concepts interactively.

Frequently Asked Questions

Last updated: 2026-06-18 · Reviewed by Nham Vu