Roofing
Pitch is a ratio, not an angle, and almost every number you need downstream of it is a different transformation of that ratio. Here is every common pitch converted four ways, plus the two slope thresholds the building code actually enforces.
Rise is per 12 inches of run. The slope factor converts footprint area to sloped roof area; the hip/valley factor does the same for a rafter running diagonally into a corner.
| Pitch | Angle | Slope | Slope factor | Hip / valley | Asphalt |
|---|---|---|---|---|---|
| 0:12 | 0.00° | 0.0% | 1.0000 | 1.4142 | not permitted |
| 1:12 | 4.76° | 8.3% | 1.0035 | 1.4167 | not permitted |
| 2:12 | 9.46° | 16.7% | 1.0138 | 1.4240 | double underlayment |
| 3:12 | 14.04° | 25.0% | 1.0308 | 1.4361 | double underlayment |
| 4:12 | 18.43° | 33.3% | 1.0541 | 1.4530 | double underlayment |
| 5:12 | 22.62° | 41.7% | 1.0833 | 1.4743 | standard |
| 6:12 | 26.57° | 50.0% | 1.1180 | 1.5000 | standard |
| 7:12 | 30.26° | 58.3% | 1.1577 | 1.5298 | standard |
| 8:12 | 33.69° | 66.7% | 1.2019 | 1.5635 | standard |
| 9:12 | 36.87° | 75.0% | 1.2500 | 1.6008 | standard |
| 10:12 | 39.81° | 83.3% | 1.3017 | 1.6415 | standard |
| 11:12 | 42.51° | 91.7% | 1.3566 | 1.6853 | standard |
| 12:12 | 45.00° | 100.0% | 1.4142 | 1.7321 | standard |
| 14:12 | 49.40° | 116.7% | 1.5366 | 1.8333 | standard |
| 16:12 | 53.13° | 133.3% | 1.6667 | 1.9437 | standard |
| 18:12 | 56.31° | 150.0% | 1.8028 | 2.0616 | standard |
| 24:12 | 63.43° | 200.0% | 2.2361 | 2.4495 | standard |
For a pitch that is not on this list, or to work from a measured angle instead of a ratio, the roof pitch calculator computes the same four values for any rise and run.
Most roof pitch charts present the slope factor as a table of magic numbers, which leaves you unable to check a value or handle a pitch that is not listed. It is Pythagoras. A roof rising R inches over a 12 inch run has a rafter length of √(R² + 12²) for every 12 inches of horizontal run, so:
slope factor = √(rise² + run²) ÷ run
Two rows are worth memorising because they come out exact. At 12:12 the factor is √2 = 1.4142 — a 45° roof is 41% larger than the ground it covers. At 6:12 it is 1.1180. Everything else falls between, and the growth is slower than people expect: a 4:12 roof is only 5.4% bigger than its footprint.
That non-linearity is the practical point. Doubling the pitch does not double the area, so estimating "add about 20% for the slope" is wrong at both ends of the range. Applied to a 1,800 sq ft footprint:
| Pitch | Factor | Sloped area | Added |
|---|---|---|---|
| 4:12 | 1.0541 | 1,897 sq ft | 97 sq ft |
| 8:12 | 1.2019 | 2,163 sq ft | 363 sq ft |
| 12:12 | 1.4142 | 2,546 sq ft | 746 sq ft |
A common rafter runs straight up the slope. A hip or valley rafter runs into a corner at 45° in plan, so before you account for any rise at all it is already travelling further horizontally — 12√2, about 16.97 inches, for every 12 inches of common run. The rise then gets added to that longer base:
hip / valley factor = √(rise² + 2 × run²) ÷ run
At 6:12 that lands on exactly 1.5, one of the few genuinely round numbers in roof geometry. On a dead flat roof it is still √2 = 1.4142, because the diagonal does not disappear just because the roof stopped rising.
Cutting a hip to the common rafter length is a classic and expensive mistake. Over a 14 ft run:
| Pitch | Common rafter | Hip / valley rafter |
|---|---|---|
| 4:12 | 14 ft 9 1/16 in | 20 ft 4 1/8 in |
| 6:12 | 15 ft 7 13/16 in | 21 ft |
| 8:12 | 16 ft 9 15/16 in | 21 ft 10 11/16 in |
| 12:12 | 19 ft 9 9/16 in | 24 ft 3 in |
These are theoretical lengths along the slope, measured to the intersection of the centre lines. They do not include the ridge thickness deduction, the birdsmouth, or an overhang — those come off the layout, not off a chart.
Most of a pitch chart is geometry, and geometry has no opinion. Two thresholds are not geometry, and both are in the last column of the table above.
2:12 is the floor for asphalt shingles. IRC R905.2.2 permits them only at 2:12 or steeper. Below that the water moves too slowly and wind-driven rain gets under the laps regardless of how carefully it is installed. There is no underlayment that buys you a 1:12 shingle roof — that slope needs a different covering.
2:12 through 4:12 needs double underlayment. IRC Table R905.1.1(2) requires two layers across that band. It is a genuine cost line on a low-slope roof and it is routinely missed at estimate stage, because the shingle count does not change — only the felt does.
Above 4:12 you are in standard single-underlayment territory as far as slope is concerned. Ice barrier requirements are separate and depend on your climate rather than your pitch.
From inside the attic is easiest and safest. Hold a level horizontally against the underside of a rafter, mark 12 inches along it, then measure straight up from that mark to the rafter. That vertical distance is your rise per 12, and it is your pitch directly.
A phone inclinometer works too, but it gives you degrees rather than a ratio, and the two are not interchangeable. Convert with tan: a reading of 26.6° is 6.0:12. Rest the phone on a rafter or a flat board on the roof plane — held against shingles it reads the shingle surface, which is not quite the plane you want.
Whatever you measure, check it against a second rafter. Old roofs sag, additions get framed to a different pitch than the original, and a single measurement on a house that has been added to twice is a good way to order the wrong quantity of everything.
Pitch is an input, not an answer. The slope factor turns your footprint into real roof area, which is what every material on the roof is ordered against — and getting it wrong compounds through the shingles, the underlayment, the starter and the cap all at once.
The roofing shingles calculator applies the factor and converts to bundles at published coverage, and the bundles-and-squares guide explains why three bundles usually cover 98.4 sq ft rather than a full square. One warning that applies to all of it: a footprint × factor calculation assumes a single pitch. A main gable at 8:12 with a porch at 3:12 is two takeoffs added together, and running the whole footprint at either pitch is wrong in both directions.
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Between 4:12 and 9:12 on most American houses. 6:12 is the one people picture: 26.57°, a 50% slope, and an area multiplier of 1.1180. Below 2:12 asphalt shingles are not permitted at all, and above about 9:12 a roof usually needs staging rather than being walked.
26.57 degrees. Pitch and angle are not the same thing — pitch is a ratio of rise to run, and the angle is its arctangent. That is why the numbers do not scale evenly: 12:12 is not double 6:12, it is 45° against 26.57°.
Divide rise by run and multiply by 100. A 6:12 pitch is a 50% slope, and 12:12 is 100%. Percentage slope is how the IRC words some of its thresholds, and it is not interchangeable with the angle in degrees.
The number you multiply a flat footprint by to get real sloped area: √(rise² + run²) ÷ run. At 6:12 it is 1.1180, so 1,000 sq ft of footprint is 1,118 sq ft of roof. It is often printed as a mystery table, but it is Pythagoras and you can check every row.
A hip or valley rafter runs at 45° in plan, so for every 12 inches of common run it travels 12√2 ≈ 16.97 inches horizontally before the rise is added. The factor is √(rise² + 2·run²) ÷ run — always larger. At 6:12 the common factor is 1.1180 and the hip factor is exactly 1.5.
IRC R905.2.2 permits asphalt shingles only on slopes of 2:12 or steeper. From 2:12 up to and including 4:12, IRC Table R905.1.1(2) requires double underlayment. Below 2:12 you need a different roof covering entirely, not a workaround.
