Gyromagnetic Ratio Calculator

Are you trying to figure out the gyromagnetic ratio of a particle but finding it tricky to juggle values like g-factor, charge, and mass? Understanding the relationship between a particle’s magnetic moment and angular momentum can feel overwhelming without the right tool. That’s why we built this simple Gyromagnetic Ratio Calculator. In this article, you’ll not only get a free tool to calculate instantly, but you’ll also learn how the formula works and what the result means. By the end of this page, you’ll be able to confidently calculate gyromagnetic ratios and interpret the numbers with ease.

How to Use This Calculator:

1. Enter g-factor: This is the dimensionless number specific to the particle.
2. Input particle charge (q): The electric charge in coulombs.
3. Add particle mass (m): The mass in kilograms.
4. Click Calculate: Your result, the gyromagnetic ratio (γ), will appear instantly.

The Formula Explained: How It All Works

For those who like to see the magic behind the curtain, here is the exact formula our Gyromagnetic Ratio Calculator uses:

γ = (g × q) / (2 × m)

Variable Breakdown

γ: Gyromagnetic ratio (in rad·s⁻¹·T⁻¹)
g: g-factor of the particle (dimensionless constant)
q: Electric charge of the particle (in coulombs)
m: Mass of the particle (in kilograms)

Supporting Concepts

• g-factor: Specific to each particle. For an electron, g ≈ 2.0023. For a proton, g ≈ 5.586.
• Charge (q): For an electron, q ≈ -1.602 × 10⁻¹⁹ C. For a proton, q ≈ +1.602 × 10⁻¹⁹ C.
• Mass (m): Electron mass ≈ 9.109 × 10⁻³¹ kg. Proton mass ≈ 1.672 × 10⁻²⁷ kg.

Practical Example: Let’s Walk Through It

Let’s imagine you want to calculate the gyromagnetic ratio of an electron.

Scenario Data

g-factor (g): 2.0023
Charge (q): -1.602 × 10⁻¹⁹ C
Mass (m): 9.109 × 10⁻³¹ kg

Calculation

γ = (2.0023 × -1.602 × 10⁻¹⁹) / (2 × 9.109 × 10⁻³¹)
γ ≈ -1.76 × 10¹¹ rad·s⁻¹·T⁻¹

The Result

The gyromagnetic ratio of the electron is approximately -1.76 × 10¹¹ rad·s⁻¹·T⁻¹. This negative sign indicates that the electron’s spin is opposite to the applied magnetic field direction.

Reference Table for Common Gyromagnetic Ratios

Particle	g-factor	Charge (C)	Mass (kg)	Gyromagnetic Ratio (γ)
Electron	2.0023	-1.602 × 10⁻¹⁹	9.109 × 10⁻³¹	-1.76 × 10¹¹ rad·s⁻¹·T⁻¹
Proton	5.586	+1.602 × 10⁻¹⁹	1.672 × 10⁻²⁷	2.68 × 10⁸ rad·s⁻¹·T⁻¹
Neutron	-3.826	0	1.675 × 10⁻²⁷	-1.83 × 10⁸ rad·s⁻¹·T⁻¹

Helpful Tips & Tricks

1. Always double-check whether you are using the correct g-factor for your particle.
2. Remember that the sign of the gyromagnetic ratio has physical meaning—it indicates orientation.
3. Use known constants for standard particles like electrons or protons to speed up calculations.

FAQs