A flat footprint area understates roof surface area the moment there's any pitch — and the steeper the roof, the bigger that gap gets.
The math
The relationship is straightforward trigonometry: roof surface area equals footprint area divided by the cosine of the pitch angle, where the pitch angle is the arctangent of rise over run. In practice, most estimators use a pitch multiplier lookup instead of doing the trig by hand:
A real example
That means a 2,000 sq ft footprint under a 10/12 roof actually needs sheathing for roughly 2,604 sq ft of surface — a 30% difference that a flat-footprint estimate would completely miss.
Do not forget waste factor
On top of the pitch multiplier, waste factor still applies — 10% for a simple gable roof, 12–15% or more for hip roofs and rooflines with dormers or valleys, where cutting to fit the angles wastes more material.