  A novel idea that the cosmic acceleration can be understood from the
perspective that spacetime dynamics is an emergent phenomena was proposed by T.
Padmanabhan. The Friedmann equations of FRW universe can be derived from
different gravity theories with different modifications of Padmanabhan's
proposal. In this paper, a unified formula is proposed, in which those
modifications can be treated as special cases when the formula is applied to
different universe radii. Furthermore, the dynamic equations of FRW universe in
the $ f(R) $ theory and deformed Ho{\v{r}}ava-Lifshitz theory are investigated.
The results show the validity of our proposed formula.
