Larmor Frequency Calculator
Place a nucleus with a magnetic moment in a magnetic field and it precesses like a spinning top, at a rate called the Larmor frequency. This frequency is what magnetic resonance imaging and nuclear magnetic resonance spectroscopy must match with their radio transmitters to excite the spins. This calculator multiplies the field strength by the gyromagnetic ratio of your chosen nucleus to give the precession frequency in megahertz and the angular frequency in radians per second. The proton default lets you read off standard MRI frequencies at a glance.
Larmor frequency formula
f = (gamma / 2pi) * B
omega = 2pi * f = gamma * B
gamma/2pi entered in MHz per tesla
f in MHz, omega in rad/s
The gyromagnetic ratio gamma over two pi is entered in megahertz per tesla, so the frequency comes out in megahertz directly. The angular frequency is two pi times that result, expressed in radians per second.
Magnetic resonance context
- The proton gyromagnetic ratio is about 42.577 megahertz per tesla.
- A clinical 1.5 tesla scanner runs at about 63.87 megahertz for hydrogen.
- A 3 tesla scanner runs at about 127.7 megahertz for hydrogen.
- Larmor frequency is exactly proportional to field strength.
- Carbon-13, fluorine-19 and phosphorus-31 each have a different gyromagnetic ratio.
Larmor frequency: frequently asked questions
What is the Larmor frequency?
The Larmor frequency is the rate at which the magnetic moment of a nucleus or electron precesses about an applied magnetic field. It equals the gyromagnetic ratio times the field strength: f = (gamma / 2pi) * B. It sets the radio frequency that an MRI scanner or NMR spectrometer must use to excite a given nucleus.
What is the gyromagnetic ratio?
The gyromagnetic ratio relates a particle's magnetic moment to its angular momentum and is specific to each nucleus. For the proton it is about 42.577 megahertz per tesla when expressed as gamma over two pi. Because it depends on the nucleus, it ships here as a user-editable input so you can select your species.
How does field strength affect MRI frequency?
Larmor frequency is directly proportional to field strength. A proton precesses at about 42.58 megahertz in a 1 tesla field, 63.87 megahertz at 1.5 tesla, and 127.7 megahertz at 3 tesla. Higher-field scanners therefore operate at higher radio frequencies and generally give better signal.
What is angular Larmor frequency?
The angular Larmor frequency, written omega, is the precession rate in radians per second and equals gamma times B, or two pi times the ordinary frequency. It is the form that appears directly in the equations of motion, while the ordinary frequency in hertz is what you tune a radio transmitter to.
Which nuclei are used in MRI and NMR?
Clinical MRI almost always images hydrogen-1 because the body is rich in water and fat. NMR chemistry also routinely uses carbon-13, fluorine-19 and phosphorus-31, each with its own gyromagnetic ratio and therefore its own Larmor frequency at a given field.
Official sources
- U.S. National Institute of Standards and Technology: Proton gyromagnetic ratio.
- U.S. National Institute of Standards and Technology: Physical Measurement Laboratory.
Reviewed by the CalculatorHub team, edited by James Graham, 16 June 2026. See our methodology.