Rolling reduces thickness by drawing metal through a gap between rotating rolls.

For strip width $b$ that changes little, approximate volume conservation gives

$$bh_0v_0\approx bh_1v_1,$$

so a thinner outgoing strip moves faster than the incoming strip.

The thickness reduction or draft is

$$\Delta h=h_0-h_1,$$

and percentage reduction is

$$r=\frac{h_0-h_1}{h_0}\times100%.$$

A strip reduced from 10 mm to 8 mm has

$$r=\frac{10-8}{10}\times100%=20%.$$

Friction between rolls and workpiece is essential because it draws the material into the roll gap. Too little friction and the rolls cannot bite the strip; excessive friction raises force and can worsen nonuniform flow.

Elastic roll flattening, roll bending and temperature variation can make the exit thickness vary across the width. Industrial rolling mills therefore use roll profiles, support rolls and active control to manage thickness and flatness.

Hot rolling permits large reductions and can refine or reshape microstructure. Cold rolling gives better dimensional control and surface condition but raises flow stress and work-hardens the material.

Rolling is therefore both a geometric thickness-reduction process and a microstructure-processing step.