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The relationship between frequency (f) and wavelength (λ) in free space is λ = c / f, where c is the speed of light (≈ 299,792,458 m/s). Multiply or divide by the appropriate unit factors (1 kHz = 10³ Hz, 1 MHz = 10⁶ Hz, 1 GHz = 10⁹ Hz) to switch units. Wavelength shortens when the wave travels through a medium with a velocity factor less than 1.

A half-wave dipole is approximately λ/2 long, but real wire radiates a little slower than in free space, so the practical length uses the classic 468 / f(MHz) formula for feet (or 143 / f(MHz) for meters) which bakes in a ~0.95 velocity factor. A quarter-wave vertical is half of a dipole. A full-wave loop is ~1005 / f(MHz) feet.

SWR = (1 + |Γ|) / (1 − |Γ|) where Γ is the reflection coefficient. From forward/reflected power: |Γ| = √(Pr / Pf). Return loss (dB) = −20 log₁₀|Γ|. Mismatch loss (dB) = −10 log₁₀(1 − |Γ|²). SWR below 1.5 is excellent, 1.5–2.0 is acceptable, above 3 usually needs attention.