The bronze English one penny piece, as minted between 1971 and 1992, was 1.52 millimetres thick.
The steel one penny piece, as minted since 1992, measures 1.65 millimetres in thickness.
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The height of a penny is the thickness: 1.55 mm (millimeters)
millimeters
There are many countries which use a penny as its minor currency unit and these coins are not the same size. Furthermore, the citizens of the US refer to their cent as a penny - for some bizarre reason. Without any indication as to which country's currency the question is about, it is not possible to give an answer.
19mm, Thickness is 1.55mm
it is approx the thickness of a penny