The exact formula for the intensity of synchrotron radiation emitted by a single charged particle in vacuo was given by Schott, for the case of circular orbits, and Takakura for the case of helical orbits. In the general case the radiated power is expressed in terms of four variables which appear in (among other places) the arguments or orders of a Bessel function and its first derivative; hence the general formula gives little insight into the interpretation of synchrotron radiation and allows evaluation only in particular cases. There is a particular need for approximate formulae that yield the spectrum of the radiation in explicit form. Such approximate formulae were found by Vladimirskii and Schwinger for the case of highly relativistic electrons. In the present paper we outline the derivation of approximate formulae applicable to mildly relativistic electrons, especially those with velocity βc such that 0 ≪ β ≲ O.9. These approximations are also relevant to the case of highly relativistic electrons in a plasma with refractive index appreciably less than unity.