A formula for the energy of the lower edge of doubly excited states of a many-electron atom is derived using the approximate solution of the Schrodinger equation. This formula is a generalisation of Rydberg's formula for single-electron excitations and correctly takes into account the interaction of the electrons and between themselves and with the core. Comparison with the experimental data shows that the generalised Rydberg formula well reproduces the energies for ground states of the type (core)(n s²¹S) as well as those for highly excited resonances and autoionising states of atoms and negative and positive ions. The accuracy of the estimate increases with n. For example, the energy for negative-ion He^- resonances at n<or=9 is reproduced with a maximum error of 18 meV. It is shown that at large n the energy for the lower edge of double excitations is given by the expression E(n, Z)=-Z-0.18169/n².