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Exemplo λ/4 monopole = 164.1 mm — ground plane REQUIRED. λ is 690.9 mm in free space; at k = 0.95 a full wave of wire is 656.3 mm, and every length above is cut from that.

$\lambda =\frac{c}{f}$ — the element is then a fraction of that wavelength, trimmed by a shortening factor k: $L=\frac{k\times \lambda }{4}$ for a quarter-wave. Two things trip people up. A λ/4 whip is only half an antenna and does almost nothing without a ground plane. And a real conductor resonates a few per cent short of the free-space figure — end effect, the fringing capacitance off its tips, which grows with the element's thickness — so wire and whips are cut at about k = 0.95 and trimmed from there. k is not a coax velocity factor: that number belongs to the feedline, not to the radiator.

A λ/4 whip is only half an antenna — the ground plane is the other half, mirrored. Give it a solid copper pour, or 3–4 radials of the same length sloped about 45°. With no counterpoise the coax braid and whatever the board is screwed to become one by default, which is why a module can work on the bench and lose most of its range inside an enclosure.