The first table turns a pitch into degrees and a multiplier. Multiply a run by it to get the length along the slope. The second table has rafter line lengths for common runs, plate to ridge.
Pitch to angle and multiplier
| Pitch | Angle | Multiplier | Rafter per foot of run |
|---|---|---|---|
| 1/12 | 4.8° | 1.003 | 12 1/16" |
| 2/12 | 9.5° | 1.014 | 12 3/16" |
| 3/12 | 14.0° | 1.031 | 12 3/8" |
| 4/12 | 18.4° | 1.054 | 12 5/8" |
| 5/12 | 22.6° | 1.083 | 13" |
| 6/12 | 26.6° | 1.118 | 13 7/16" |
| 7/12 | 30.3° | 1.158 | 13 7/8" |
| 8/12 | 33.7° | 1.202 | 14 7/16" |
| 9/12 | 36.9° | 1.250 | 15" |
| 10/12 | 39.8° | 1.302 | 15 5/8" |
| 11/12 | 42.5° | 1.357 | 16 1/4" |
| 12/12 | 45.0° | 1.414 | 17" |
Rafter line length
| Pitch | 6 ft run | 8 ft run | 10 ft run | 12 ft run |
|---|---|---|---|---|
| 3/12 | 6' 2 3/16" | 8' 2 15/16" | 10' 3 11/16" | 12' 4 7/16" |
| 4/12 | 6' 3 7/8" | 8' 5 3/16" | 10' 6 1/2" | 12' 7 13/16" |
| 5/12 | 6' 6" | 8' 8" | 10' 10" | 13' |
| 6/12 | 6' 8 1/2" | 8' 11 5/16" | 11' 2 3/16" | 13' 5" |
| 7/12 | 6' 11 3/8" | 9' 3 1/8" | 11' 6 15/16" | 13' 10 11/16" |
| 8/12 | 7' 2 9/16" | 9' 7 3/8" | 12' 1/4" | 14' 5 1/16" |
| 9/12 | 7' 6" | 10' | 12' 6" | 15' |
| 10/12 | 7' 9 3/4" | 10' 4 15/16" | 13' 3/16" | 15' 7 7/16" |
| 12/12 | 8' 5 13/16" | 11' 3 3/4" | 14' 1 11/16" | 16' 11 5/8" |
How this is worked out
Pitch is how many inches the roof rises for every 12 inches it runs. A 6/12 roof climbs 6 inches each foot.
The angle is the arctangent of rise over run. It's also the plumb cut you set a rafter square to. The seat cut is 90 degrees minus that.
The multiplier is the slope's length for each foot of run. Square the pitch, add 144, take the square root and divide by 12. A 12/12 roof comes out at the square root of 2, about 1.414. Roofers use the same number to turn a footprint into roof area.
Rafter line length is the long side of the triangle. Handyman Calc works it out to a thousandth of an inch and rounds to the nearest sixteenth once, at the end. Nothing comes off for the ridge board, since its thickness varies. Take off half of it at the top.
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The chart is on one page in the printable PDF, US Letter size.
More charts: how many bags of concrete a slab takes, how many sheets of drywall a room takes, a fraction to decimal chart for inches, how much paint a room takes, how much mulch a bed takes, how many steps a rise takes, the diagonal that squares a frame and board feet for common lumber.
To work out your own sizes, there's a material estimator spreadsheet, and more on the Handyman Calc page.