Quantum Numbers Calculator

Work out quantum numbers instantly with clear inputs, formula shown and shareable results.

About Quantum Numbers Calculator

The azimuthal number l must be smaller than n, and it fixes the shape: 0 is s, 1 is p, 2 is d, 3 is f. Each subshell has 2l+1 orbitals, one for every magnetic quantum number from -l to +l, and the Pauli principle allows two electrons per orbital. So 3d has five orbitals with ml from -2 to +2, holding ten electrons.

Formulas

Orbital count

orbitals = 2l + 1

Electron capacity

electrons = 2(2l + 1)

Worked example

With the default values below, Quantum Numbers Calculator returns Electrons The Subshell Holds of 10. Change any input above and every figure here is recalculated in your browser.

Inputs used

Principal quantum number naccepts 1–7: 3
Azimuthal quantum number laccepts 0–6: 2

Results

Electrons The Subshell Holds: 10
Subshell Label: 3d
Number Of Orbitals: 5
Allowed Magnetic Quantum Numbers: -2, -1, 0, +1, +2

Step by step

1Values used
2Orbital count
3Electron capacity
4Electrons The Subshell Holds= 10
5Subshell Label= 3d
6Number Of Orbitals= 5
7Allowed Magnetic Quantum Numbers= -2, -1, 0, +1, +2

Assumptions and limits

The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
Figures are rounded for display to whole numbers, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why must l be less than n?

The radial wavefunction needs at least l + 1 nodes-worth of room, so a 2d orbital cannot exist. Values above n-1 are clamped here.

What about the spin quantum number?

It is always +1/2 or -1/2, which is what puts the factor of two in the electron capacity.