Formula
Pitch per 12 is the slope times 12. Degrees are the arctangent of the slope. Percent is the slope times 100. The multiplier is the hypotenuse of a unit run, which is how a rafter table turns run into line length.
slope = rise ÷ run
pitch = slope × 12
degrees = arctan(slope)
percent = slope × 100
multiplier = √(1 + slope²)
A 6/12 is slope 0.5, 26.565 degrees, 50%, multiplier √1.25 = 1.11803. The rafter calculator takes the rise-per-12 number, a span, an overhang, and a ridge thickness. This page does not lay out a hip or a valley.
Worked examples
6/12. 26.57°, 50%, multiplier 1.1180. On a 12 ft run the line length is 13.42 ft, which is the default rafter on the homepage.
A rise of 6 inches in a run of 12 inches. The same 6/12. Any rise and run with the ratio 1:2 lands there. Metric mode converts those two lengths together, so the ratio holds.
45 degrees. Slope 1, so 12/12, 100%, multiplier √2 = 1.4142.
Reference
Common pitches. Multiplier is line length per unit of horizontal run.
| Pitch | Degrees | Percent | Multiplier |
|---|---|---|---|
| 3/12 | 14.04 | 25% | 1.0308 |
| 4/12 | 18.43 | 33.33% | 1.0541 |
| 5/12 | 22.62 | 41.67% | 1.0833 |
| 6/12 | 26.57 | 50% | 1.118 |
| 7/12 | 30.26 | 58.33% | 1.1577 |
| 8/12 | 33.69 | 66.67% | 1.2019 |
| 9/12 | 36.87 | 75% | 1.25 |
| 12/12 | 45 | 100% | 1.4142 |
Questions
What is a 6/12 pitch in degrees?
26.57 degrees. The slope is 6/12 = 0.5, and arctan(0.5) is 26.565 degrees. That is a 50% grade. The rafter multiplier is √(1 + 0.5²) = 1.118.
How do I measure pitch?
Level a 12 inch run and read the rise, or enter any rise and run you measured. You can also enter the angle from a digital level, or a percent grade. All four describe the same slope.
What is the rafter multiplier?
The hypotenuse of a right triangle whose run is 1 and whose rise is the slope. Multiply a horizontal run by it to get the rafter line length. The rafter calculator does that for a whole span, including ridge and overhang.
Sources
- Pitch = (rise / run) × 12. Degrees = arctan(rise / run). Percent grade = (rise / run) × 100. Rafter multiplier = √(1 + slope²).