The differential cross section is defined as the number of events of a particular type p per unit of time, divided by the total flux F, where F is the number of particles crossing a unit of transverse area per unit of time.
For the process of elastic scattering sketched in figure MACROm3cdiffF1, the differential cross section per unit solid angle is given by
The number of particles passing through the transverse area
per time unit is given by
.
The number of particles is conserved in the scattering process, such that all particles passing through the ring
must be scattered through an angle between
and
:
This leads to


Thus the differential cross section can be calculated if the deflection function is known.