Larmor Frequency Calculator
Protons in a 1.5 T MRI scanner precess at 63.8662 MHz, from f = (γ/2π)B₀ with 42.58 MHz/T.
63.866217777 MHz
Full answer, then cut to fewer decimals (not rounded):
- 63.866217777 MHz
- 63.86621777 MHz
- 63.8662177 MHz
- 63.866217 MHz
- 63.86621 MHz
- 63.8662 MHz
- 63.866 MHz
- 63.86 MHz
- 63.8 MHz
- Angular frequency ω = 2πf
- 401283281.2 rad/s
- γ/2π for this nucleus
- 42.57747852 MHz/T
- At 3 T
- 127.7324356 MHz
Step-by-step solution
- f = (γ/2π) × B₀ = 42.57747852 MHz/T × 1.5 T
- f = 63.86621778 MHz
Larmor Frequency Formula
f = (γ/2π) B₀
γ/2π for ¹H = 42.577478518 MHz/T (CODATA 2018)
Worked Example
Hydrogen nuclei (protons) in a 1.5 T scanner:
- f = (γ/2π) × B₀ = 42.57747852 MHz/T × 1.5 T
- f = 63.86621778 MHz
γ/2π for this nucleus: 42.57747852 MHz/T · At 3 T: 127.7324356 MHz
GATE tip
With a gradient G (T/m), the frequency changes by (γ/2π)G per metre: 10 mT/m gives 425.8 kHz/m, so a 1 kHz bandwidth slice is about 2.3 mm thick.
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Frequently asked questions
Why does MRI image hydrogen?
Water and fat are full of hydrogen nuclei, which have the largest gyromagnetic ratio of common nuclei and so the strongest signal.
How is position encoded?
Gradient coils make B₀ vary with position, so the Larmor frequency, and phase, label where each signal comes from.
Sources
- The International System of Units (SI), 9th edition (SI Brochure), Bureau International des Poids et Mesures .
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
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APA
Scientific Converters. (2026, October 15). Larmor Frequency Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/larmor-frequency-calculator/
IEEE
Scientific Converters, "Larmor Frequency Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/larmor-frequency-calculator/