  The radiation efficiency from simple vibrating planar surfaces is often used
as a basis to describe the sound radiation from more complex structures, having
important applications in various fields of acoustics. The low-frequency
radiation efficiency of a baffled piston can easily be represented by a simple
monopole source. Notably, the equivalent source strength is dependent on the
piston surface area. However, the unbaffled case presents additional
difficulties as the so-called ``edge effects'' significantly alter the piston
radiation impedance. Consequently, a low-frequency equivalence between dipoles
and an unbaffled pistons is not as straight forward, since not only the piston
area but also its shape will have an effect on the radiated sound. In this
work, the search for a simple and generic, equivalence between dipoles and
unbaffled pistons is pursued. A finite element model is used to calculate the
radiation efficiency from unbaffled pistons with the same surface area but
different shapes. A broad set of results indicate that the ``edge effects'' can
be accurately represented by a simple term dependent on the piston compactness
(ratio of area to perimeter). Effectively, pistons with smaller area to
perimeter ratio will be less efficient radiators. Such term allows the
definition of an equivalent dipole source strength that approximates the
low-frequency behavior of an unbaffled piston of arbitrary shape.
