The roof pitch is essentially a measure of the steepness of your roof. Roofs that are roughly flat have a small pitch, while very steep roofs have larger pitches.

It is most common for roof pitch to be expressed as a slope. You might remember the mathematical formula for slope is

$$Slope = {rise \over run}$$

The *run* is the horizontal span of the roof measured from the roof ridge to the side of the building. The *rise* is the height of the roof from its lowest to highest points. One way to calculate the rise is to measure the height of the roof at its highest point (floor to ceiling) and then subtract the height at its lowest point (typically from the floor to the lowest point of the roof).

Usually, the slope is converted into an equivalent ratio in the form x/12. The idea is that the roof *rises *x inches for every 12 inches it *runs *(or *spans*) in the horizontal direction.

**So, how do you find x?**

Just *multiply* the ratio of rise to run by 12:

$$x = 12 × {rise \over run}$$

It is also common to see roof pitch described as an angle or characterized by a roof slope multiplier.

This is why the conversion chart can be extremely helpful.

## What is the roof pitch chart?

Roof Pitch | Angle | Roof Pitch Multiplier |
---|---|---|

1/12 | 4.76° | 1.0035 |

2/12 | 9.46° | 1.0138 |

3/12 | 14.04° | 1.0308 |

4/12 | 18.43° | 1.0541 |

5/12 | 22.62° | 1.0833 |

6/12 | 26.57° | 1.1180 |

7/12 | 30.26° | 1.1577 |

8/12 | 33.69° | 1.2019 |

9/12 | 36.37° | 1.2500 |

10/12 | 39.81° | 1.3017 |

11/12 | 42.51° | 1.3566 |

12/12 | 45.00° | 1.4142 |

It is important to think about the roof pitch when building your home because this will have a significant effect on what construction materials you need and the total cost.

While steep roofs may sometimes be desirable, they tend to cover more surface area and therefore require more building materials and result in a higher overall cost.

*The roof slope table shows all of the important information in one place. *

The roof pitch chart contains a diagram illustrating different roof shapes, and a table of associated values of the slope (with conversion to an angle) and multiplier.

The mathematical formulas are:

$$Pitch = {rise \over run}$$ in the form x/12

$$Angle = arctan {rise \over run} = arctan(pitch)$$

$$\text{Roof pitch multiplier} = {\sqrt{rise^2+run^2} \over run}$$

These formulas come from the properties of right triangles and the Pythagorean Theorem.

In order to get a handle on how much building materials you need and the associated cost, it is worthwhile figuring out some additional quantities such as rafter length and surface area. The roof pitch chart can help.

### Example 1: Calculating rafter length using the roof pitch chart

- Decide what roof pitch is most appropriate for your building. Deciding factors might be how much area you want the roof to cover, aesthetic reasons, or weather considerations. For this example, let’s assume that the pitch will be 5/12.
- From the table, a pitch of 5/12 corresponds to a multiplier of 1.08.
- Decide on the width of the building. Suppose the width is 50 feet across from wall to wall. Since two rafters are needed, we must divide this number by two.

Multiplying by the slope factor gives the rafter length:

$$\text{Rafter length = 0.5 × total width of building × roof pitch multiplier = 0.5 × 50 × 1.08 = 27 feet}$$

### Example 2: Calculating surface area using the roof pitch chart

- For this example, let’s continue to assume that the pitch will be 5/12. The multiplier is again 1.08.
- Multiply the area to be covered by the roof by the roof slope factor to find the total surface area of the roof. Let’s assume that the area is 600 square feet:

$$\text{Surface area of roof = area covered by roof × roof pitch multiplier = 600 × 1.08 = 648 square feet}$$