A particle approaching a localized target with nonzero sideways offset follows a deflected trajectory rather than a head-on collision. In classical central-force scattering, the incoming trajectory is characterized by the impact parameter $b$: the perpendicular distance between the target center and the undeflected incoming line.

For an incident particle of momentum $p$ and speed $v$, the angular momentum about the target is $$L=bp.$$ Because a central force conserves angular momentum and energy, the effective-potential method determines the turning point and the final scattering angle $\theta$.

The relation $b(\theta)$ connects trajectories to measurable angular distributions. An annulus of incoming impact parameters between $b$ and $b+db$ has effective area $$d\sigma=2\pi b,db.$$ For an azimuthally symmetric interaction, the outgoing solid-angle element is $$d\Omega=2\pi\sin\theta,d\theta,$$ so $$\frac{d\sigma}{d\Omega} =\frac{b}{\sin\theta}\left|\frac{db}{d\theta}\right|.$$

For Coulomb scattering this leads to the Rutherford angular distribution, strongly peaked at small deflection angles. Large-angle events correspond to trajectories that pass closer to the scattering center.

The impact parameter is not directly measured in a typical beam experiment; it is the classical hidden geometric variable that maps an incoming area element to an outgoing angular interval.

Classical scattering turns central-force trajectories into cross sections. It provides both an experimental language for probing interactions and the classical reference point for quantum scattering, where individual trajectories are replaced by wave amplitudes.