An injection-locked divider (ILD) can provide good synchronization at lower input signal to noise ratio, which is its advantage over other types of divider. The general expression of phase equation and equivalent model are presented for the ILD with an input additive noise. In the absence of noise the performance of the phase-modulated signal through the ILD and synchronous ranges of the ILD are given. The effects of the additive noise on the ILD are discussed. The injuction-locked amplifier (ILA) is only a particular case in which n=1, therefore the given results are applicable to the ILA.