Roof Pitch Explained: Rise Over Run, Degrees, and Rafter Length

Roof pitch is one of those numbers that sounds simple until three different trades each write it a different way. The framer says 6/12. The architect's drawing says 26.57 degrees. The shingle spec sheet says 50 percent. They are all describing the exact same slope, and the only reason it feels confusing is that nobody told you they are three labels for one thing. Once you can move between them, a roof drawing stops being a translation puzzle.

This guide walks through what pitch actually measures, how to turn it into degrees and a slope factor, and how to get a real rafter length you can cut to. If you want the arithmetic done for you, the roof pitch calculator converts all three notations and the rafter length the moment you type a number.

What rise over run really means

A pitch written as x-in-12 means the roof rises x inches for every 12 inches of horizontal run. The second number is the run, and in US framing it is almost always 12, because a framing square is marked in twelfths. So 6/12 means six inches of vertical rise across twelve inches of horizontal travel. Walk a foot toward the ridge and you have climbed half a foot.

The reason 12 stays fixed is practical, not mathematical. You can lay a framing square flat on a rafter, mark 12 along one leg and 6 along the other, snap a line between the marks, and you have the exact angle without touching a calculator. The notation was built for the tool. That is also why a 4/12 and an 8/12 are instantly comparable on site: the run is the same, so the first number alone tells you which is steeper.

Slope as a percentage is the same ratio expressed differently. Percent slope is rise divided by run, times 100. A 6/12 is 6 ÷ 12 = 0.5, so 50 percent. Drainage specs and grading plans tend to speak in percent, which is why a flat-ish commercial roof might be quoted as a 2 percent slope rather than a fraction.

Converting pitch to an angle in degrees

The angle a roof line makes with the horizontal is the arctangent of rise over run:

angle = arctan(rise ÷ run)

That is the single formula behind every pitch-to-degrees conversion. For 6/12 you take arctan(6 ÷ 12) = arctan(0.5), which is about 26.57 degrees. A 4/12 roof works out to arctan(4 ÷ 12) ≈ 18.43 degrees, and a 12/12 roof — where rise equals run — lands on exactly 45 degrees, because the tangent of 45 degrees is 1.

Here is the trap worth burning into memory: percent and degrees are not the same scale. A 50 percent slope is about 26.57 degrees, not 50 degrees. A 100 percent slope is 45 degrees, not 90. Percent keeps climbing without bound as the roof gets steeper, while degrees can only ever reach 90 for a vertical wall. If you set a saw to 50 degrees because the drainage plan said 50 percent, you have just cut a roof nearly twice as steep as the design.

A worked example: the 6/12 roof

Let me run one all the way through, because the abstract formulas land better with real numbers behind them.

Say the plans call for a 6/12 main roof on a house that is 8 metres wide. First, the angle: arctan(6 ÷ 12) is about 26.57 degrees. That is what your miter saw and rafter layout want.

Next, the slope factor, also called the rafter multiplier. It is the length of the sloped line per unit of horizontal run:

multiplier = √(rise² + run²) ÷ run

For 6/12 that is √(6² + 12²) ÷ 12 = √(36 + 144) ÷ 12 = √180 ÷ 12 ≈ 13.416 ÷ 12 ≈ 1.118.

Now the rafter length. A simple symmetric gable rafter only runs from the ridge to the wall, which is half the building width — so the run is 4 metres, not 8. Multiply: 4 × 1.118 ≈ 4.47 metres of structural line length, ridge to outside wall, before any eave overhang. That is the number you cut to.

The first time I framed a small shed roof I skipped the multiplier and cut my rafters to the flat 4-metre run. Every single one came up short by about half a metre once I tried to set it on the wall, because a 6/12 rafter is roughly 11.8 percent longer than its horizontal projection. The multiplier is not optional trim — it is the difference between lumber that fits and a pile of expensive offcuts.

Why the multiplier matters more than it looks

The slope factor catches people because the horizontal run is the number you can measure on the ground or read off a plan, so it feels like the real length. It is not. The rafter follows the hypotenuse of a right triangle whose legs are the rise and the run, and the hypotenuse is always longer than either leg.

That is also why ordering lumber from the building span alone goes wrong twice over. Feed the full 8-metre width instead of the 4-metre half-span and you double every rafter. Then forget the multiplier on top of that and you are short by another twelve percent. The fix is the same two-step every time: take half the span for a gable, then multiply by √(rise² + run²) ÷ run. If you would rather not chase the square root by hand, the roof pitch calculator returns the multiplier and the finished rafter length once you enter the run.

The same hypotenuse-versus-leg logic shows up in any sloped run, which is exactly why a stair calculator treats stringer length the same way pitch treats rafter length — rise and run set the angle, and the diagonal is what you actually cut.

How pitch drives materials and drainage

Pitch is not just a geometry exercise; it decides what you are allowed to put on the roof. Most asphalt shingle products draw a line around 4/12, roughly 18.4 degrees. Below that, the manufacturer typically requires a double layer of underlayment because a low slope sheds water slowly enough that wind-driven rain can creep back up under the courses. A 3/12 roof — 25 percent, about 14 degrees — sits in low-slope territory, and a single-layer install there can void the warranty.

Steeper roofs shed water and snow faster, which is why cold-climate and high-rainfall regions favour bigger pitches, while arid flat-roof regions get away with almost nothing. Drainage codes usually state a minimum in percent, so being able to read your 3/12 as 25 percent lets you check it against the spec directly instead of guessing. The practical habit is to confirm which scale a spec is quoting — rise over run, percent, or degrees — before you commit, because the same roof reads as 6/12, 50 percent, or 26.57 degrees depending on who wrote the document.

Putting it together

The whole skill comes down to three moves. Read the pitch as rise over run and you can lay it out with a framing square. Take the arctangent of rise over run and you have the angle for a saw or a drawing. Apply √(rise² + run²) ÷ run and you have a rafter length that fits the wall. Get those three down and a roof plan stops being a wall of unfamiliar numbers and becomes one slope you can describe in any language the job needs.

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Made by Toolora · Updated 2026-06-13