# Magnetic Moment Calculator (Landé g-factor)

URL: https://speedycalculator.com/calculators/physics/magnetic-moment/
Last updated: 2026-10-30

> The magnetic moment calculator finds the Landé g-factor and the effective magnetic moment of an atom or ion from its spin, orbital and total angular momentum quantum numbers S, L and J.

## Inputs

- Spin quantum number S
- Orbital quantum number L
- Total angular momentum J

## Results

- Landé g-factor g_J
- Effective moment
- In J/T
- Check |L − S| ≤ J ≤ L + S

## Formula

```
g_J = 1 + [J(J+1) + S(S+1) − L(L+1)] / [2J(J+1)],  μ_eff = g_J·√(J(J+1))·μ_B
```

## Explanation

An atom's magnetic moment comes from both electron spin and orbital motion. The Landé g-factor combines them and explains how spectral lines split in a magnetic field (the Zeeman effect).

### How to use the Magnetic Moment Calculator

- **Spin quantum number S**
- **Orbital quantum number L**
- **Total angular momentum J**

Results update as you type, every field has its own unit menu, and everything is calculated in your browser.

### How it works

Enter S, L and J (half-integers allowed, e.g. 2.5).

### Inputs explained

FieldWhat to enterSpin quantum number SA numberOrbital quantum number LA numberTotal angular momentum JA number

### What each result means

- **Landé g-factor g_J** = 1 + ([Total angular momentum J]×([Total angular momentum J] + 1) + [Spin quantum number S]×([Spin quantum number S] + 1) - [Orbital quantum number L]×([Orbital quantum number L] + 1))÷(2×[Total angular momentum J]×([Total angular momentum J] + 1))
- **Effective moment** = [Landé g-factor g_J]×sqrt([Total angular momentum J]×([Total angular momentum J] + 1))
- **In J/T** = [Effective moment]×9.2740100783e-24

### Example values

How the main result changes when **Spin quantum number S** changes and everything else stays at the example values above:

Spin quantum number SLandé g-factor g_J1.251.66071.881.8082.523.132.23663.752.517953.2143

## Worked example

Inputs — Spin quantum number S: 2.5; Orbital quantum number L: 0; Total angular momentum J: 2.5.

Results — **Landé g-factor g_J = 2**; Effective moment = 5.91608 μ_B; In J/T = 5.4866e-23 J/T; Check |L − S| ≤ J ≤ L + S = Valid combination.

## Key terms

- **Landé g-factor**: Ratio of magnetic moment to angular momentum.

## FAQ

**What is g for a pure spin?**
About 2 (L = 0).

**What is g for pure orbital motion?**
1 (S = 0).

**What is Mn²⁺'s moment?**
S = 5/2, L = 0 → 5.92 μ_B.

**What is the Zeeman effect?**
Splitting of levels in a magnetic field, proportional to g_J.


## Sources

- [OpenStax – University Physics Volume 3](https://openstax.org/details/books/university-physics-volume-3)
- [NIST – Fundamental physical constants](https://physics.nist.gov/cuu/Constants/)