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Before starting the calculation, we need to know some technical terms related to a pitched roof.

## Rafter Of Roof:

Rafter is the distance between the ridge or hip of the roof to the wall plate of the external wall.

## Span Of Roof:

Span is the clear distance between the supports of an arch, beam or roof truss.

## Rise Of Roof:

It is the vertical distance between the wall and the top of the ridges.

## Pitch Of Roof:

The pitch of a roof is its vertical rise over its horizontal span. The angle, or pitch of a roof, is calculated by the number of inches it rises vertically for every 12 inches it extends horizontally. For example, a roof that rises 6 inches for every 12 inches of horizontal run has a 6/12 pitch.

There is no standard, universal pitch of roof. It varies depending on culture, climate, style, and available materials. The most common roof pitch is designed with a pitch ranging from 4/12 to 9/12.

**Pitch = Rise/Run**

## Run Of Roof:

In roof framing, the run is the distance from the outside of the wall’s top plate to a point directly below the center of the ridge. In simple words, the run is the half distance of span.

**Run = Span/2**

## Exmple 1:

Given,

Span = 30 ft.

Pitch = 5/12

Run = Span/2 = 30/2 = 15 ft.

Rafter length =??

According to Pythagoras theorem, **a** **²** ** + b** **²** ** = c** **²**

Run **²** + Rise **²** = Rafter **²**

**Rafter = √ (Run** **²** ** + rise** **²** **)**

Pitch = 5/12

Rise/Run = 5/12

∴ Rise = Run x 5/12 = 15 x 5/12 = 6.25 ft.

Rafter **²** = Run **²** + Rise **²** = 15 **²** + 6.25 **²** =264.0625

∴ Rafter = **√** 264.0625 = 16.25 ft.

## Example 2:

## Calculate Rafter Length Using Angle:

Given,

Length of roof = 30 ft.

Rise = 6 ft.

Angle = 20°

We know,

Sinθ = Opposite/Hypotenuse

Cosθ = Adjacent/Hypotenuse

tanθ = Opposite/Adjacent

In the above triangle,

a = Opposite = Run

b = Adjacent = Rise

c = Hypotenuse = Rafter

Cosθ = Adjacent/Hypotenuse = b/c

c = b/Cosθ = 6/Cos20° = 6.38 ft.

∴ Rafter length = 6.38 ft.

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