Orbital Quantum Number Calculator

Explore allowed subshells for each energy level. Validate l values and reveal angular momentum details. Download tables, compare cases, and learn patterns quickly here.

Calculator
Allowed range here: 1 to 50.
Must satisfy 0 ≤ l ≤ n−1.
Leave empty to use a standard value.
Auto lists all if l is empty.
Reset

Formula used

The orbital quantum number l sets the electron subshell and orbital angular momentum. For a given principal level n, the allowed values are:

  • l = 0, 1, 2, …, n−1
  • Number of orbitals in a subshell: 2l + 1
  • Maximum electrons in a subshell: 2(2l + 1)
  • Angular momentum magnitude: L = √(l(l+1)) ħ
  • Nodes: angular nodes = l, radial nodes = n−l−1

Subshell letters follow the common sequence: s, p, d, f, then g, h, i…

How to use this calculator

  1. Enter an integer value for n.
  2. Optionally enter l to evaluate one subshell.
  3. Keep l empty to list all allowed values.
  4. Adjust ħ only if you need custom units.
  5. Click Calculate to view results above the form.

Example data table

n Allowed l Subshells Orbitals per subshell Max electrons per subshell
1 0 s 1 2
2 0, 1 s, p 1, 3 2, 6
3 0, 1, 2 s, p, d 1, 3, 5 2, 6, 10
4 0, 1, 2, 3 s, p, d, f 1, 3, 5, 7 2, 6, 10, 14
Example: for n=3, the allowed set is l=0..2.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.