Home Improvement
Pitch multiplier table
The geometric factor that turns a flat measurement into a sloped one.
The Formula
multiplier = sqrt(1 + (rise / 12)^2)
The geometric factor that turns a flat measurement into a sloped one.
| Symbol | Meaning | Unit | Notes |
|---|---|---|---|
| multiplier | Pitch factor | unitless | 1.0541 at 4/12, 1.118 at 6/12, 1.4142 at 12/12. |
| rise | Pitch rise | inches | The first number in the pitch, such as the 6 in 6/12. |
What Each Symbol Means
multiplierunitless
Pitch factor
1.0541 at 4/12, 1.118 at 6/12, 1.4142 at 12/12.
riseinches
Pitch rise
The first number in the pitch, such as the 6 in 6/12.
See It Worked With Real Numbers
A formula on its own does not tell you which number goes where. The how to calculate shingles needed page applies this equation to a concrete case, shows every intermediate step, and names the mistakes that produce a wrong answer even when the algebra is right.
Where This Formula Appears
This equation is the working core of How To Calculate Shingles Needed, filed under Everyday Life. Every number the guide produces comes from substituting into this one line.