Roof Pitch Multiplier
One pitch, four useful numbers. Enter rise per 12 inches of run and get the slope factor (the multiplier that turns plan length into sloped length — the rafter multiplier), the roof angle in degrees for saw setups and spec sheets, the grade as a percent, and inches of rafter per foot of run. This is pure trigonometry — the same slope factor that drives the roof area calculator — so the results are exact for the pitch you enter. Free, no login.
Pitch
Conversions
Slope factor = √(rise² + 12²) / 12. Multiply plan length by the slope factor to get sloped length.
How this calculator works
Pitch defines a right triangle — rise over a 12" run — and everything here falls out of that triangle:
slope factor = √(rise² + 12²) ÷ 12 · angle = atan(rise ÷ 12) · grade % = rise ÷ 12 × 100
The slope factor is the workhorse: multiply any plan (horizontal) dimension by it to get the true sloped dimension. A 14 ft horizontal run at 6/12 needs 14 × 1.1180 = 15.65 ft of rafter (plus overhang and less the ridge deduction); a 1,000 ft² footprint carries 1,118 ft² of roof surface. No code table is involved and none is cited — pitch-to-angle is definitional math.
Worked example
A 6/12 pitch:
- Slope factor: √(36 + 144) ÷ 12 = 1.1180 — every plan foot is 13.416 inches of slope.
- Angle: atan(6/12) = 26.57°; grade: 6 ÷ 12 = 50%.
- Applied: a 12 ft plan run needs 12 × 1.1180 = 13.42 ft of rafter length before overhang and ridge adjustments.
Enter 6 above to reproduce it.
Reference: the pitch ladder
Every standard pitch from 1/12 to 12/12, computed by the same engine as the calculator.
| Pitch | Slope factor | Angle | Grade | Rafter per ft of run |
|---|---|---|---|---|
| 1/12 | 1.0035 | 4.76° | 8.3% | 12.042 in |
| 2/12 | 1.0138 | 9.46° | 16.7% | 12.166 in |
| 3/12 | 1.0308 | 14.04° | 25% | 12.369 in |
| 4/12 | 1.0541 | 18.43° | 33.3% | 12.649 in |
| 5/12 | 1.0833 | 22.62° | 41.7% | 13 in |
| 6/12 | 1.1180 | 26.57° | 50% | 13.416 in |
| 7/12 | 1.1577 | 30.26° | 58.3% | 13.892 in |
| 8/12 | 1.2019 | 33.69° | 66.7% | 14.422 in |
| 9/12 | 1.2500 | 36.87° | 75% | 15 in |
| 10/12 | 1.3017 | 39.81° | 83.3% | 15.62 in |
| 11/12 | 1.3566 | 42.51° | 91.7% | 16.279 in |
| 12/12 | 1.4142 | 45.00° | 100% | 16.971 in |
Frequently asked questions
What is a roof pitch multiplier and how is it calculated?
The pitch multiplier (slope factor) converts flat, plan-view measurements to true sloped measurements: multiplier = √(1 + (rise/12)²). Enter the pitch here and the calculator returns it to four decimals — 4:12 gives 1.0541, 6:12 gives 1.1180, 12:12 gives 1.4142. Multiply a plan length by it to get the sloped length, or a footprint area by it to get roof surface area.
How do I convert roof pitch to degrees?
Angle = arctan(rise ÷ 12). A 4:12 pitch is 18.43°, 6:12 is 26.57°, 8:12 is 33.69°, and 12:12 is exactly 45°. Note the relationship isn't linear — doubling the pitch doesn't double the angle — which is why the calculator does the trig instead of a proportion.
What does rafter length per foot of run mean?
It's the slope factor expressed in inches: how many inches of rafter you need for every 12 inches of horizontal run. At 6:12 that's 13.416 inches per foot of run, so a 14-foot run needs 14 × 13.416 ≈ 187.8 inches (15.65 ft) of rafter to the ridge line. That figure is the framing-square number — in practice you still add the eave overhang and deduct half the ridge-board thickness when cutting.
How do I measure the pitch of an existing roof?
Hold a level horizontally with one end touching the roof (or the underside of a rafter in the attic), measure out 12 inches along the level, then measure straight down from that point to the surface — that vertical distance in inches is your rise per 12. Measuring on a rafter avoids shingle buildup throwing off the number. A speed square with a pivot or a phone inclinometer app gives you degrees, which you can convert back here.
What pitch is too low for shingles?
The IRC (R905.2.2) sets 2:12 as the minimum slope for asphalt shingles, and between 2:12 and 4:12 the underlayment requirements are stricter — commonly a doubled or fully self-adhered membrane per the adopted code and the shingle manufacturer's instructions. Below 2:12 you're into low-slope systems (membrane, rolled, or standing seam rated for low slope). Manufacturers can be stricter than code, so check the wrapper before shingling anything under 4:12.
What is the difference between pitch, slope, and grade percent?
In the field they're used interchangeably; this calculator treats pitch as rise in inches per 12 inches of run (6:12, '6 pitch'). Grade percent is rise ÷ run × 100 — a 6:12 is a 50% grade — which is how excavation and civil drawings express the same geometry. Historically 'pitch' meant rise over full span (a fraction like 1/4 pitch), so on old drawings confirm which convention is in play before cutting rafters.
Method: slope factor = √(rise² + 144) ÷ 12, angle = atan(rise/12), grade = rise/12 as a percent, rafter-per-foot = slope factor × 12 inches. Pure trigonometry with no code citation. The slope factor converts plan dimensions to sloped dimensions only — actual rafter stock length adds the overhang and subtracts half the ridge thickness, and framing member sizing is a span-table question, not a pitch question. Walkability, underlayment requirements, and shingle low-slope limits are separate product/code rules tied to pitch but not computed here.
Pair with the Roof Area & Pitch Calculator to apply the factor to a footprint, the Shingle & Bundle Calculator for the material order, or the Metal Roofing Panel Calculator where panel length is the sloped (rafter) length this multiplier produces.