Calculate gyromagnetic ratio, magnetic moment, or angular momentum by entering any two values and converting between supported units.
Gyromagnetic Ratio Formula
The gyromagnetic ratio relates magnetic moment to angular momentum. The calculator uses the scalar form of this relationship, so you enter any two values and solve for the third.
\gamma = \frac{\mu}{L}\mu = \gamma L
L = \frac{\mu}{\gamma}- γ = gyromagnetic ratio, usually in rad/(s·T)
- μ = magnetic moment, usually in J/T
- L = angular momentum, usually in J·s
The calculator has three functions:
- Calculate gyromagnetic ratio: if you enter magnetic moment and angular momentum, it uses γ = μ / L.
- Calculate magnetic moment: if you enter gyromagnetic ratio and angular momentum, it uses μ = γL.
- Calculate angular momentum: if you enter magnetic moment and gyromagnetic ratio, it uses L = μ / γ.
Before applying the formula, values are converted to base units: rad/(s·T), J/T, and J·s. The result is then converted back to the unit selected in the missing field.
Gyromagnetic Ratio Unit Conversions
These are the unit conversions used for the inputs and outputs.
| Quantity | Unit | Base-unit conversion |
|---|---|---|
| Gyromagnetic ratio | rad/(s·T) | 1 rad/(s·T) |
| Gyromagnetic ratio | GHz/T | 1 GHz/T = 1 × 109 rad/(s·T) |
| Gyromagnetic ratio | MHz/T | 1 MHz/T = 1 × 106 rad/(s·T) |
| Magnetic moment | J/T or A·m² | 1 J/T = 1 A·m² |
| Magnetic moment | erg/G | 1 erg/G = 1 × 10-7 J/T |
| Angular momentum | J·s or kg·m²/s | 1 J·s = 1 kg·m²/s |
| Angular momentum | erg·s | 1 erg·s = 1 × 10-7 J·s |
Input and Result Meaning
| Value | What it represents | Zero-value note |
|---|---|---|
| Gyromagnetic ratio | How strongly magnetic moment is related to angular momentum | Cannot be zero when solving for angular momentum |
| Magnetic moment | Magnetic strength associated with the system | Can be zero if the physical case allows no magnetic moment |
| Angular momentum | Rotational momentum associated with the magnetic moment | Cannot be zero when solving for gyromagnetic ratio |
Examples
Example 1: Calculate gyromagnetic ratio
Suppose the magnetic moment is 4 J/T and the angular momentum is 2 J·s.
\gamma = \frac{4}{2} = 2 \text{ rad/(s·T)}The gyromagnetic ratio is 2 rad/(s·T).
Example 2: Calculate magnetic moment
Suppose the gyromagnetic ratio is 3 rad/(s·T) and the angular momentum is 5 J·s.
\mu = 3 \times 5 = 15 \text{ J/T}The magnetic moment is 15 J/T.
FAQ
What is the gyromagnetic ratio?
The gyromagnetic ratio is the ratio of magnetic moment to angular momentum. In simple scalar form, it tells you how much magnetic moment corresponds to a given amount of angular momentum.
Why do J/T and A·m² both appear for magnetic moment?
They are equivalent units for magnetic moment. A magnetic moment of 1 J/T is the same as 1 A·m², so the calculator treats them with the same conversion factor.
Can the gyromagnetic ratio be negative?
Yes. In physics, the sign can indicate that the magnetic moment and angular momentum point in opposite directions. If you are working only with magnitudes, use positive values. If direction matters in your problem, keep the sign from your source data.