Gyromagnetic Ratio Calculator
Calculate the gyromagnetic ratio (γ) for particles, nuclei, and magnetic systems.
Calculation Parameters
Particle Presets
Calculation Results
Select a calculation method and enter values to see the gyromagnetic ratio
Gyromagnetic Ratio Calculator
The gyromagnetic ratio (γ) connects a particle's magnetic behavior with its angular motion. It plays a key role in nuclear magnetic resonance (NMR), MRI scans, and quantum physics. This calculator helps you compute γ quickly, accurately, and in the units you need.
You can calculate γ using different approaches depending on what you know: magnetic moment and angular momentum, or resonance frequency and magnetic field strength. The calculator handles all the unit conversions and physics constants automatically.
How the Calculator Works
Using Magnetic Moment
When you know the magnetic moment and angular momentum:
γ = μ / J
Where μ is magnetic moment and J is angular momentum.
Using Resonance Frequency
For NMR and MRI applications:
γ = 2πf / B
γ = f / B
Choose angular frequency (with 2π) or linear frequency based on your data.
Example Calculations
| Particle/System | Input Method | Values | Gyromagnetic Ratio | Application |
|---|---|---|---|---|
| Proton | Resonance Frequency | 42.58 MHz, 1 T | 2.675 × 10⁸ rad/s·T | NMR Spectroscopy |
| Electron | Particle Preset | Built-in value | -1.761 × 10¹¹ rad/s·T | ESR Spectroscopy |
| ¹³C Nucleus | Resonance Frequency | 10.71 MHz, 1 T | 6.728 × 10⁷ rad/s·T | NMR Imaging |
| ²³Na Nucleus | Resonance Frequency | 11.27 MHz, 1 T | 7.080 × 10⁷ rad/s·T | Medical MRI |
| ³¹P Nucleus | Resonance Frequency | 17.24 MHz, 1 T | 1.083 × 10⁸ rad/s·T | Biochemistry |
| ¹⁹F Nucleus | Resonance Frequency | 40.08 MHz, 1 T | 2.518 × 10⁸ rad/s·T | Drug Research |
| ²H (Deuterium) | Resonance Frequency | 6.54 MHz, 1 T | 4.107 × 10⁷ rad/s·T | Isotope Studies |
| ¹⁷O Nucleus | Resonance Frequency | 5.77 MHz, 1 T | 3.626 × 10⁷ rad/s·T | Metabolomics |
| ¹⁵N Nucleus | Resonance Frequency | 4.32 MHz, 1 T | 2.712 × 10⁷ rad/s·T | Protein Studies |
| ²⁷Al Nucleus | Resonance Frequency | 11.10 MHz, 1 T | 6.976 × 10⁷ rad/s·T | Materials Science |
This table shows gyromagnetic ratios for common nuclei used in NMR and MRI applications. All values are calculated for a 1 Tesla magnetic field.