# What is the difference between central rate of mortality and force of mortality? They seem to have the same formula

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The formula for the central rate of mortality is given as :

and the formula for the force of mortality is given as :

Are these not equivalent?

Thanks

So the force of mortality, $$\mu_x$$, represents the instantaneous rate of transition from alive to dead (i.e. the probability of dying right now given you are alive), and is estimated from data as $$\frac{d_x}{E^c_x}$$.
On the other hand, the central rate of mortality, $$m_x$$, represents the "average deaths" per person aged x (look back at the slides in the first section). It is calculated by $$\frac{number of deaths}{time spent alive and at risk}$$.