Physics Formulas Reference
Comprehensive collection of essential physics formulas for FRCR Part 1 exam preparation. Quick reference guide covering X-ray, CT, MRI, ultrasound, nuclear medicine, and radiation protection.
X-ray Physics Formulas
Essential formulas for X-ray production, interactions, and image quality
X-ray Production
Maximum X-ray Energy
Emax = e × kVp
Where e = electron charge (1.6 × 10-19 C)
Minimum Wavelength
λmin = hc / (e × kVp)
Where h = Planck's constant, c = speed of light
X-ray Tube Heat Units
HU = kVp × mAs × 1.35
For single-phase generators
X-ray Interactions
Linear Attenuation
I = I0 × e-μt
Where μ = linear attenuation coefficient
Half-Value Layer
HVL = ln(2) / μ = 0.693 / μ
Thickness reducing intensity to 50%
Mass Attenuation
μm = μ / ρ
Where ρ = density of material
CT Physics Formulas
Key calculations for CT image reconstruction and quality parameters
CT Numbers & Reconstruction
CT Number (Hounsfield Unit)
CT = 1000 × (μ - μwater) / μwater
Water = 0 HU, Air = -1000 HU
Slice Thickness
FWHM = 2.35 × σ
From slice sensitivity profile
Pitch Factor
Pitch = Table feed / Beam width
Per rotation in helical CT
CT Dose & Image Quality
CT Dose Index (CTDI)
CTDI = (1/T) ∫ D(z)dz
Integrated over slice thickness T
Noise
σ ∝ 1/√(mAs)
Quantum noise relationship
Spatial Resolution
MTF = |FT{LSF}|
Modulation Transfer Function
MRI Physics Formulas
Fundamental equations for magnetic resonance imaging principles
Basic MRI Physics
Larmor Frequency
f = γB0 / 2π
γ = gyromagnetic ratio (42.6 MHz/T for 1H)
T1 Relaxation
Mz(t) = M0(1 - e-t/T1)
Longitudinal magnetization recovery
T2 Relaxation
Mxy(t) = M0 × e-t/T2
Transverse magnetization decay
MRI Imaging Parameters
Slice Thickness
Δz = Δf / (γGz)
RF bandwidth and slice gradient
Pixel Size
Δx = FOV / Matrix
Field of view and matrix size
SNR Relationship
SNR ∝ Voxel × √(NEX)
Voxel volume and number of excitations
Ultrasound & Nuclear Medicine Formulas
Ultrasound Physics
Wave Equation
c = f × λ
Speed = frequency × wavelength
Doppler Shift
Δf = 2f0v cos(θ) / c
For moving reflector
Acoustic Impedance
Z = ρ × c
Density × speed of sound
Nuclear Medicine
Radioactive Decay
N(t) = N0 × e-λt
λ = decay constant
Half-life
T½ = ln(2) / λ = 0.693 / λ
Time for 50% decay
Activity
A = λN = 0.693N / T½
Becquerels (disintegrations/sec)
Radiation Protection Formulas
Essential calculations for radiation dosimetry and protection
Dose Calculations
Absorbed Dose
D = E / m
Energy per unit mass (Gy)
Effective Dose
E = Σ wT × HT
Tissue weighting factors
Distance & Shielding
Inverse Square Law
I2 / I1 = (d1 / d2)2
Point source radiation
Shielding
I = I0 × e-μt
Exponential attenuation
Units & Conversions
SI Units
• Gray (Gy) = J/kg
• Sievert (Sv) = weighted Gy
• Becquerel (Bq) = s-1
Old Units
• 1 rad = 0.01 Gy
• 1 rem = 0.01 Sv
• 1 Ci = 3.7 × 1010 Bq
Quick Reference Constants
Physical Constants for FRCR Part 1
| Constant | Symbol | Value | Units |
|---|---|---|---|
| Speed of light | c | 3.0 × 108 | m/s |
| Planck constant | h | 6.63 × 10-34 | J⋅s |
| Electron charge | e | 1.6 × 10-19 | C |
| Proton gyromagnetic ratio | γ | 42.6 | MHz/T |
| Avogadro number | NA | 6.02 × 1023 | mol-1 |
Master Physics Formulas with Practice
Use these formulas to solve real FRCR Part 1 Physics MCQ questions and build confidence for your exam.