Every roofing calculation starts with actual roof area, and almost nobody can measure that directly. What you can measure is the footprint of the building from the ground. The slope factor is what connects the two.
What pitch notation means
Roof pitch in the US is written as rise over run, in inches per twelve inches. A 6/12 roof climbs six inches for every twelve inches it travels horizontally.
That is not the same as a percentage or an angle. A 6/12 roof is 26.6 degrees; a 12/12 roof is exactly 45.
The slope factor
The slope factor is the hypotenuse of that triangle divided by the run — the square root of rise squared plus 144, all over 12. For a 6/12 roof it is 1.118, so the real roof surface is about 12 percent larger than the footprint it covers.
At 12/12 the factor is 1.414 and the roof is 41 percent bigger than the footprint. Skipping this step is the most common way people under-order shingles.
Finding the pitch without climbing up
Hold a level against a rafter or the underside of the roof in the attic. Measure twelve inches along the level from where it touches, then measure straight down to the rafter. That vertical distance is your rise.
From outside, a phone level app held flat against a gable end works well enough to identify a standard pitch.
Pitch decides what you can use
Below 2/12 asphalt shingles are not permitted at all — that needs a membrane roof. Between 2/12 and 4/12 shingles can be used but require doubled underlayment.
Above about 7/12 the roof becomes difficult to walk. That is a labour and safety question rather than a material one, but it changes the cost of the job more than the shingles do.
Pitch and drainage
The steeper a roof, the faster water leaves it and the less time it has to find a way in. That is why minimum pitches exist for each roofing material and why they are not suggestions.
Asphalt shingles are generally rated to 4/12 and above for a standard installation, and from 2/12 to 4/12 with a doubled underlayment and other specific details.
Below 2/12 no shingle is appropriate and the roof needs a membrane system. A roof that is close to a threshold should be measured properly rather than estimated, because the difference changes the whole material specification.
Pitch changes cost more than area
Two roofs with the same footprint but different pitches differ in material by the slope factor — perhaps ten or twenty percent. They differ in labour by much more.
Past about 7/12 a roof cannot be walked comfortably, and staging, roof jacks or harnesses become necessary. That changes the day rate and the time.
It also changes what can be stored on the roof while working. On a steep roof, bundles will not sit where you put them, which slows everything down.