# How to calculate length of roof rafters and pitch of roof

To calculate the length of roof rafters and the pitch of the roof, you’ll need some key measurements. Here’s a basic overview:

1. Roof Pitch: The roof pitch is the slope or steepness of the roof. It is usually represented as a ratio of vertical rise to horizontal run. For example, a 6:12 pitch means that for every 12 inches of horizontal run, the roof rises 6 inches.
You can measure the pitch using a level and a ruler. Place the level horizontally on the roof surface and measure the vertical distance it rises over a 12-inch horizontal span.

2. Run and Rise: The run is the horizontal distance from the outside edge of the wall to the center of the house. The rise is the vertical distance from the top of the wall plate to the highest point of the roof.

3. Rafter Length: Once you have the pitch, run, and rise, you can use the Pythagorean theorem to calculate the rafter length. The formula is:Rafter length = √(rise² + run²). This formula accounts for the horizontal run and vertical rise to find the diagonal rafter length.

Hi guys in this article you know about length of rafters, span of roof, rise of roof, run of roof and pitch of roof and also know about maximum and minimum length of roof rafters.

Everybody need a new house with a classical appearance, roof is the one of the most important part of any building structure that prevents the the other structure of building and inhabitant from adverse climatic weather condition and also ensure the privacy for the inhabitants. In earlier time from the beginning of civilization peoples are always looking for or house which built by timber covered with roof to prevent from heavy rainfall and snowfall conditions.

Design and construction of roof is depending on many factors but one of the most common important factor is climatic and weather condition of your surrounding areas, in your cities and countries. The area which has heavy rainfall and snowfall require good drainage for roof, roof drainage depending on slope of the roof provided, based on slope of roof it is categorised into two types flat roof and pitched roof or sloping roof. These are two types of roof structure based on slop.

Flat roof is type of roof in which slope is generally less than 10°, which only enable to ensure adequate drainage of rainwater in low to moderate rainfall regions. Pitched roof is type of roof comprising sloping surface or surface with an angle of usually over 20°, generally it slopes downward in one two or more parts depending on design and construction.

A rafter is a structural component build of wood or steel that is used as part of a roof construction. Rafter runs from the ridge or hip of the roof to the wall plate of the external wall. Rafters are generally provide in series, side by side, providing a plateform to support roof decks and roof coverings.

Length of roof rafters depending on climatic condition, style, slope and type of structure. It is used over brick external wall, wall plate, over two support and over top of beam.

The first step for deciding to figure out length of roof rafters in conventional roof framing is to layout and cut a common rafter pattern. The length of rise and run of the common rafter will determine the height of the ridge board as well as the length of any hip / valley rafters that may be involved with a conventionally framed roof.

Conventional framing of roof rafters falls under the heading of rough framing carpentry. Anyone who has ever tried framing a roof can tell you it is a fine tuned skill that can only be acquired with experience.

Let us now discuss some common terms are used in figure out length of roof rafters.

● 1) Rafters of roof :- distance between the top ridge on roof or hip of the roof to the wall plate of external wall.

● 2) span of roof :- span of roof is the clear distance between the two supporting arc,beam, external brick wall or beam truss.

● 3) Run of roof :- in rafter roof framing Run of roof is horizontal distance from external wall outside plate to the point which are directly below centre of Ridge. In general term run of root is half of span of roof. Run of roof = span of roof/2.

● 4) Rise of roof :- it is vertical distance between top of ridge to the centre of clear span between two support.

● 5) pitch of roof :- it is the inclined angle formed between Rafters of roof and run of roof. Which of roof is calculated by number of inches it Rises vertically for every 12 inches in extend horizontally. for example a roof that Rises 6 inches vertically for every 12 inches of horizontal run. So pitch of roof is equal to = rise/run = 6/12.

There is no standard value of pitch of roof, its value is depending on varying condition like climatic condition sloping areas height of a structure, location, style and culture climate.

Rise is define as vertical change in height per unit of horizontal length or run. For example a pitch of 4/12 represents 4″ vertical height or rise for every 1 foot or 12 inches of horizontal distance or run. General value of rise for pitch roof is range between 4″ to 9″ for every 12 inches of run. These are good and standard height of rise generally used for conventional structure such as garage, residential building, shed, godowns etc.

Run is defined as the distance from the outside of wall top plate to a point directly below the centre of the Ridge or hip. It is a horizontal distance for pitch and Rafter is a structural component used as part of roof construction that it runs from the ridge of roof or hip of roof to the wall plate of external wall.

The most common pitch of roof ranging between 4/12 to 8/12 feet.

## How to calculate length of roof rafters & pitch for roof

One may ask, how to figure out pitch on a roof?, to determine the length of rafter and pitch for roof you need Pitch of roof calculator, by means you can easily calculate degrees to roof pitch and roof pitch to degrees, or you can also used roof pitch calculator degrees and degrees to roof pitch calculator to solve this.

If pitch of roof is measured in fraction fall under the range of 4/12 to 9/12 or “4 in 12” to “9 in 12” slope, measured in ratio in the range of 4:12 to 9:12, measured in percentage in the range of 25% to 75% and measured in degree in the range of 18° to 37°.

Pitch for roof or slope means you how many inches the roof vertical rises for every 12 inches or 1 foot in horizontal distance run. An Example of a pitch for roof would be a 5/12 or “5 in 12” slope means that the roof vertical rises 5 inch for every 1 foot or 12 inches of horizontal distance run. There are two types of suggested ways to measure a roof pitch either in percentage or in degrees. Let us know about some definition of rafter, rise and run which help in better understanding while calculating the pitch of roof.

Regarding this “how to calculate roof pitch/ or how to figure out pitch on a roof?”, generally roof pitch is calculated from the Pythagoras theorem of right angle formula in which hypotenuse of right angle triangle is length of rafter, their height is rise and base is run and you can use following formula and equation to calculate the length of rafter and figure out pitch on a roof or slop.

● Rafter^2 = rise^2 + run^2 (by Pythagoras theorem of right angle formula)

● Pitch = rise/run (where pitch in express in percentage

● Pitch = tan (angle), where angle is pitch of roof expressed in degree. How to calculate the roof pitch | pitch formula for roof

Calculation for Pitch of roof

● take the measurement of horizontal run length:- it is horizontal distance out side of walls top plate to a point directly below the centre of the Ridge or hip of roof, assuming it is 10 meters

● measure the vertical height of rise of your roof, assuming it is 2.5 meters.

● Calculate the rafter length, as Rafter^2 = rise^2 + run^2, Rafter^2 = 2.5^2 + 10^2, Rafter^2 = 6.25+100, rafter = √106.25, Rafter = 10.31 meters, hence rafter for pitched roof will be 10.31 meters.

● Calculate the roof pitch as the proportion of rise and run as pitch = rise/ run, pitch = 2.5/10 = 1/4, which is equal as 25%, hence pitch for roof will be 25%.

● Recalculate the value of pitch in angle, as pitch = tan (angle), so angle = arctan (pitch) = arctan (0.25) = 14°, hence pitch for roof will be 14 degrees.

● find the roof pitch is in the form of X:12, as pitch = X/12, so X = pitch × 12 = 0.25 ×12 = 3, hence pitch of your roof will be 3:12, and it can be also express in fraction as 3/12, or “3 in 12”, or in percentage as 25%.

Convert Roof pitch into degrees

Roof pitch calculator degrees help you to convert pitch ratio or fraction of slope in degrees in following two steps:- 1) divide the first part of the ratio by 12 to figure out the pitch and 2) find the inverse tangent of pitch to find the angle in degrees.

For 2/12 roof pitch into degrees:- 1) pitch = rise/run such as 2/12 = 0.1666, 2) tan inverse of pitch = tan-1(0.1666) = 9.46°, thus a roof pitch of fraction 2/12, or “2 in 12” slope, or in ratio 2:12 is equivalent to 9.46 degrees.

For 3/12 roof pitch into degrees:- 1) pitch = rise/run such as 3/12 = 0.25, 2) tan inverse of pitch = tan-1(0.25) = 14.04°, thus a roof pitch of fraction 3/12, or “3 in 12” slope, or in ratio 3:12 is equivalent to 14.04 degrees.

For 4/12 roof pitch into degrees:- 1) pitch = rise/run such as 4/12 = 0.33, 2) tan inverse of pitch = tan-1(0.33) = 18.43°, thus a roof pitch of fraction 4/12, or “4 in 12” slope, or in ratio 4:12 is equivalent to 18.43 degrees.

For 5/12 roof pitch into degrees:- 1) pitch = rise/run such as 5/12 = 0.416, 2) tan inverse of pitch = tan-1(0.416) = 22.62°, thus a roof pitch of fraction 5/12, or “5 in 12” slope, or in ratio 5:12 is equivalent to 22.62 degrees.

For 6/12 roof pitch into degrees:- 1) pitch = rise/run such as 6/12 = 0.5, 2) tan inverse of pitch = tan-1(0.5) = 26.57°, thus a roof pitch of fraction 6/12, or “6 in 12” slope, or in ratio 6:12 is equivalent to 26.57 degrees.

For 7/12 roof pitch into degrees:- 1) pitch = rise/run such as 7/12 = 0.583, 2) tan inverse of pitch = tan-1(0.583) = 30.26°, thus a roof pitch of fraction 7/12, or “7 in 12” slope, or in ratio 7:12 is equivalent to 30.26 degrees.

For 8/12 roof pitch into degrees:- 1) pitch = rise/run such as 8/12 = 0.666, 2) tan inverse of pitch = tan-1(0.666) = 33.69°, thus a roof pitch of fraction 8/12, or “8 in 12” slope, or in ratio 8:12 is equivalent to 33.69 degrees.

For 9/12 roof pitch into degrees:- 1) pitch = rise/run such as 9/12 = 0.75, 2) tan inverse of pitch = tan-1(0.75) = 36.87°, thus a roof pitch of fraction 9/12, or “9 in 12” slope, or in ratio 9:12 is equivalent to 36.87 degrees.

Convert degrees to roof pitch

Degrees to roof pitch calculator help you to convert from degrees to roof pitch ratio in following two ways:- 1) calculate the tangent of the angle and 2) multiply the pitch by 12 to find the X in the ratio X/12.

For 10 degrees to roof pitch:- 1) tan of 10 degrees as tan 10° = 0.176, this will give you the pitch of the roof, 2) multiply the pitch by 12 to find the X in the ratio X/12 such as 0.176 ×12 = 2, thus, a 10 degrees angle of roof pitch is same as 2/12 or “2 in 12” slope, or pitch ratio 2:12.

For 20 degrees to roof pitch:- 1) tan of 20 degrees as tan 20° = 0.3639, this will give you the pitch of the roof, 2) multiply the pitch by 12 to find the X in the ratio X/12 such as 0.3639 ×12 = 4.36, thus, a 20 degrees angle of roof pitch is same as 4/12 or “4 in 12” slope, or pitch ratio 4:12.

For 15 degrees to roof pitch:- 1) tan of 15 degrees as tan 15° = 0.2679, this will give you the pitch of the roof, 2) multiply the pitch by 12 to find the X in the ratio X/12 such as 0.2679 ×12 = 3.2, thus, a 15 degrees angle of roof pitch is same as 3/12 or “3 in 12” slope, or pitch ratio 3:12.

For 30 degrees to roof pitch:- 1) tan of 30 degrees as tan 30° = 0.577, this will give you the pitch of the roof, 2) multiply the pitch by 12 to find the X in the ratio X/12 such as 0.577 ×12 = 6.9, thus, a 30 degrees angle of roof pitch is same as 7/12 or “7 in 12” slope, or pitch ratio 7:12.

For 40 degrees to roof pitch:- 1) tan of 40 degrees as tan 40° = 0.839, this will give you the pitch of the roof, 2) multiply the pitch by 12 to find the X in the ratio X/12 such as 0.839 ×12 = 10, thus, a 40 degrees angle of roof pitch is same as 10/12 or “10 in 12” slope, or pitch ratio 10:12.

Calculate length of rafter

● take the measurements of span of roof, assume span of roof = 30 feet, slope of roof = 5/12, so Run of roof is equal to half of span = span/2 = 30/2= 15 feet.

● calculate rise of roof:- as you know that slope = Rise/ Run = 5/12 = Rise/ Run, hence Rise = (Run ×5)/12 = 15×5/12 = 6.25 feet, so Rise of roof = 6.25 feet.

● to figure out the length of roof rafters, by Pythagoras theorem we know that c2 = a2 + b2, c = √ a2 + b2, we have a = Run = 15 feet, Rise = b = 6.25 feet and c = roof rafters =?,

Now Rafters = √ 15^2 + 6.25^2

Rafters length = √ 264.0625 = 16.25 feet
hance length of roof rafters = 16.25 feet.

### Calculate Roof Rafters length using angle

Look at the given picture, we have Rise = 6 ft ,angle of pitch = 20° and length of roof = 30 feet.

In right angle triangle we have c = rafters = hypotenuse, a = opposite side = Run and b = adjacent side = Rise

We know sinθ = opposite/ hypotenuse

Cosθ = b/c , c = b/Cosθ = 6/Cosθ = 6.38 feet

hance length of Roof Rafters = 6.38 feet.

How to calculate height of rise for pitch roof

If you know about the pitch roof’s angle in degrees, you can find the roof pitch by converting the angle in degrees to a slope, then finding the rise by multiplying the slope by 12.

● slope can be figure out by finding the tangent of the degrees, assume roofs angle is 20°, such as slope = tan (degrees), so slope = tan 20° = 0.3639

● then multiply the slope by 12 to get the rise such as 0.3639 ×12 = 4.36″