Enter field values, choose units, and use particle presets. Get frequency, period, and energy results. Simple inputs support fast laboratory and classroom physics checks.
| Particle | Magnetic Field | Gamma (MHz/T) | Larmor Frequency (MHz) |
|---|---|---|---|
| Proton (1H) | 1.5 T | 42.577479 | 63.866218 |
| Carbon-13 (13C) | 3.0 T | 10.708400 | 32.125200 |
| Fluorine-19 (19F) | 3.0 T | 40.052000 | 120.156000 |
| Phosphorus-31 (31P) | 7.0 T | 17.235000 | 120.645000 |
| Electron | 10 mT | 28024.951640 | 280.249516 |
Angular Larmor frequency: ω = |γ| × B
Cyclic Larmor frequency: f = ω / (2π)
Equivalent form when γ is already in Hz/T: f = |γ| × B
Precession period: T = 1 / f
Spin energy splitting: ΔE = ħω
Here, γ is the gyromagnetic ratio and B is the magnetic field in tesla.
Larmor frequency describes the precession rate of a magnetic moment inside an external magnetic field. It is a core quantity in modern physics. It appears in NMR, MRI, ESR, quantum mechanics, and magnetic resonance spectroscopy. The value depends on the applied field strength and the gyromagnetic ratio of the selected particle.
This calculator helps you estimate that precession rate quickly. You can choose a common particle preset such as a proton, electron, carbon-13 nucleus, fluorine-19 nucleus, sodium-23 nucleus, neutron, or phosphorus-31 nucleus. You can also enter a custom gyromagnetic ratio. That option is useful for research tasks, teaching examples, and specialized resonance work.
The calculator does more than return one number. It also provides angular frequency, precession period, and spin energy splitting. These extra outputs are helpful when you need to compare resonance conditions, set instrument expectations, or check lab notes. By converting field values into tesla internally, the tool also reduces unit mistakes.
In magnetic resonance experiments, small input differences can change the output significantly. A stronger magnetic field increases the Larmor frequency directly. A larger gyromagnetic ratio does the same. That is why protons, electrons, and other nuclei behave differently under the same field. The relationship is simple, but the consequences are important for imaging, detection, and frequency planning.
Students can use this page to study spin precession and verify homework. Engineers can use it to estimate resonance values in sensing systems. Researchers can use it to test field conversions and compare particle behavior. The included table, formula section, export tools, and FAQ section make the page useful for both quick checks and more detailed physics work.
Larmor frequency is the rate at which a magnetic moment precesses around an applied magnetic field. It is central to resonance physics, MRI, NMR, and ESR calculations.
Each particle has its own gyromagnetic ratio. That constant changes the precession rate. A proton, neutron, and electron therefore produce different frequencies under the same magnetic field.
You can use tesla, millitesla, microtesla, or gauss. The calculator converts the selected unit into tesla before applying the Larmor frequency formula.
Angular frequency is measured in radians per second. Cyclic frequency is measured in hertz. They are related by ω = 2πf.
Yes. Switch the input mode to custom gyromagnetic ratio. Then enter the value using rad/s/T, Hz/T, kHz/T, MHz/T, or GHz/T.
A negative gyromagnetic ratio means the precession sense is reversed relative to positive values. The displayed frequency magnitude remains positive for practical comparison.
It is the energy difference associated with spin precession in the magnetic field. The calculator estimates it using ΔE = ħω.
It is useful in MRI, NMR, ESR, spectroscopy, quantum physics, laboratory planning, resonance hardware setup, and classroom demonstrations involving magnetic fields and spin behavior.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.