Formula: λ = c ÷ f (c = 299,792,458 m/s). Quarter-wave monopole length = (λ/4)×velocity factor — the standard whip/PCB-trace antenna length for a ground-plane-referenced antenna (most ESP32/ESP8266 module antennas). Half-wave dipole = (λ/2)×velocity factor total, split as two equal legs fed at the center. Velocity factor accounts for the wire not being in a perfect vacuum; real copper wire is typically 0.95–0.98, PCB trace antennas vary more by substrate and need EM simulation for precision — treat this as a solid starting point, not a substitute for tuning/measurement on a real board.