Roof pitch conversion

Why roofers count rise in twelfths, and what the slope factor is for

Rise-per-12 is the carpenter’s notation, and it survives because it is the shape of the tool. A framing square held against a rafter reads rise directly: for every twelve units the roof runs horizontally, the pitch number is how far it climbs — a 6-in-12 roof climbs six inches per foot of run. The notation is a ratio, indifferent to units, which is why it travels between a plan set, a lumber yard and a conversation on a ladder without losing anything.

Degrees are the same triangle read with trigonometry: the angle whose tangent is rise over run. Degrees matter when the pitch was measured rather than specified — an inclinometer on the existing roof reports an angle, and turning it back into rise-per-12 is how a re-roofing job recovers the notation the rest of the arithmetic wants. The pack declares a reverse workflow that solves for the rise producing a given angle.

Percent slope is rise over run scaled to a hundred — the language of drainage and of low-slope roofing, where the question is not how steep the roof looks but whether water leaves it. The three notations are strict translations of one another; a take-off that mixes them without converting is a classic way a roof estimate goes wrong.

The slope factor is the output that earns this page its place at the front of the cluster: the ratio of length measured along the slope to length measured flat. Every horizontal measurement a plan or a tape gives you becomes a roof measurement by multiplying through the factor — a rafter’s run becomes its length, a footprint becomes a roof-plane area. The gable layout page is that multiplication carried out in full.

The factor also explains why steep roofs consume so much more material than they appear to. A footprint says nothing about pitch, but the surface a shingle bundle has to cover grows with the factor — gently near flat, then fast. An estimate built from a satellite photo or a floor plan alone, with no pitch behind it, is systematically short on every steep roof it touches.

What none of these notations can say is whether a pitch is appropriate — for a shingle product’s minimum slope, for local snow, for a walkable surface. Those are questions for the construction documents and the people responsible for them. This page only makes sure that when the answer arrives, everyone was talking about the same triangle.

When this calculation is used

• Recovering rise-per-12 from a measured angle before re-roofing, using the declared reverse workflow.
• Converting a specified pitch to degrees to set a saw or check an inclinometer reading against the plans.
• Reading off the slope factor the rafter-length and roof-area arithmetic downstream will multiply by.
• Expressing a low-slope pitch as percent to set beside the minimum a covering product is rated for — the comparison is the reader’s; the conversion is the engine’s.

Worked example

The reference roof this cluster follows is pitched at 6-in-12 — the pack’s own anchor vector, and the middle of the range most walkable shingle roofs occupy. Enter a rise of six.

Three figures come back. The angle in degrees is what an inclinometer on this roof should read — a quick site check that plans and reality agree. The percent slope is the same ratio in drainage language. The slope factor is the one to carry forward: it is the multiplier the gable layout page applies to every horizontal run on this building, and through that page it is inside every sheet and bundle count later in the cluster.

Now enter twelve instead and watch the factor. At 12-in-12 the rafter outruns its run by a margin most people find surprisingly large — the reason footprint-only estimates come in short on steep roofs, and the reason this conversion sits first in the cluster.

What each input represents

Assumptions and limits

• The pitch is uniform: one triangle describes the whole plane. A roof that changes pitch partway needs each pitch converted separately, and the pack carries a dedicated gambrel layout for the classic two-pitch case.
• Rise and run are measured plumb and level respectively. A tape run along the rafter itself measures the hypotenuse, not the rise, and produces a pitch that is too shallow.
• The conversion is pure geometry. Nothing here knows what is structurally sensible, what a covering product is rated for, or what local practice expects.
• Degrees are reported in decimal form, matching how inclinometers read, rather than in minutes and seconds.

What the guards protect against

• The rise is bounded between zero and twenty-four. The cap is not a fact about geometry — the triangle would happily compute — it is a tripwire for the commonest mistake this calculator can meet: an angle in degrees typed where a rise belongs. A plausible measured angle lands above twenty-four and is refused rather than converted into a pitch no building has.
• Zero is admitted, because dead-flat is a real quantity a take-off may pass through, but a negative rise is refused: a roof that falls as it runs is the same triangle described from the other eave, and accepting the sign would let two descriptions of one roof disagree.
• Beyond the declared range the engine refuses rather than extrapolates. A refusal here is cheap; the same wrong pitch carried silently into the rafter, sheathing and shingle arithmetic downstream surfaces only when the material order is already wrong.

Provenance

Standard roof-framing trigonometry (rise-per-12-of-run convention)

Degrees from the arctangent of rise over run, percent slope from the same ratio scaled to a hundred, and the slope factor from the Pythagorean hypotenuse of the pitch triangle per unit of run; the declared reverse workflow solves the angle relation for rise.

Geometry and quantity reference to be checked against the construction documents and the professionals responsible for the roof — not a structural determination. The signed pack carries its own citation, and the page reports the verification state of the release it mounted.