Every way to express a roof slope
A roof’s steepness is one number wearing several costumes. The slope — also called the roof gradient — is just the rise over the run: how far the roof climbs vertically for a given horizontal distance, and from that single ratio you can read four different figures that all describe the same roof:
- x-in-12 — the framing convention in the US and Canada: inches of rise per 12 inches of run, written 6/12 or 6:12.
- Degrees — the angle off horizontal, handy for a circular-saw bevel or a phone inclinometer.
- Slope % — rise ÷ run × 100, common in metric and on plans.
- Multiplier — the factor that turns flat plan measurements into real sloped lengths and areas.
x-in-12 = rise ÷ run × 12
angle° = atan(rise ÷ run)
slope % = rise ÷ run × 100
multiplier = √((rise÷run)² + 1) = √(x² + 144) ÷ 12
Rafter length from the pitch
The rafter is the hypotenuse of the slope triangle, so its line length is the run times the multiplier — identical to √(rise² + run²) by the Pythagorean theorem. That line length runs from the heel of the birdsmouth cut to the centreline of the ridge. Two adjustments turn it into a board length: add your tail overhang past the wall, and subtract half the thickness of the ridge board if your run was measured to the ridge centre rather than its face.
rafter line length = run × multiplier = √(rise² + run²)
Common pitches and what they mean
| Pitch | Angle | Slope % | Multiplier | Typical use |
|---|---|---|---|---|
| 2/12 | 9.46° | 16.7% | 1.014 | Low slope, near the shingle minimum |
| 4/12 | 18.43° | 33.3% | 1.054 | Common conventional roof |
| 6/12 | 26.57° | 50.0% | 1.118 | Very common, comfortable to walk |
| 8/12 | 33.69° | 66.7% | 1.202 | Steeper, getting hard to walk |
| 10/12 | 39.81° | 83.3% | 1.302 | Steep, staging usually needed |
| 12/12 | 45.0° | 100% | 1.414 | 45°, steep architectural look |
Most walkable residential roofs sit between roughly 4/12 and 9/12. A shed or lean-to is just a single sloped plane — one pitch, no ridge. A hip roof carries the same common-rafter pitch on its main planes, but the hip and valley rafters run at a shallower angle and have their own (longer) factor; size those separately. Anything under about 3/12 is treated as low-slope and typically needs a membrane rather than standard shingles — always confirm the minimum slope for your covering with the manufacturer and your local code.
Turning pitch into shingle squares
A roofing square is 100 ft² of roof surface. Multiply the plan footprint by the pitch multiplier to get the true sloped area, divide by 100 for squares, and figure architectural shingles at about three bundles per square. The area mode here does this quick estimate and adds your waste allowance. For full square-footage and material estimation across several sections or shapes — L-shaped, hip and shed roofs, with bundle counts and a slope-factor table — use the dedicated roof area calculator.
How to measure pitch without climbing on the roof
From the attic, hold a level horizontally against a rafter, mark 12″ along it, and measure straight down from that mark to the rafter — that drop is your x-in-12. From the ground, sight along a gable end with a phone inclinometer to read degrees. Either number drops straight into the boxes above.