# How to calculate the roof pitch | pitch formula for roof

To calculate the roof pitch, you’ll need to determine the angle of incline of the roof. The roof pitch is typically expressed as a ratio, like 4:12 or 6:12, which represents the vertical rise in inches for every 12 inches of horizontal run. Here’s how you can calculate it:

1. Measure the vertical rise (the height) from the base of the roof to the peak.

2. Measure the horizontal run (the length) from the base of the roof to the point where you measured the vertical rise.

3. Divide the vertical rise by the horizontal run.

4. Express the ratio in the form of X:12, where X is the result of the division. For example, if you have a vertical rise of 4 feet and a horizontal run of 12 feet, the roof pitch would be 4:12.

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.

One may ask, how to calculate the roof pitch?, to determine the roof pitch or pitch of roof you need Pitch formula for roof calculator, by means you can easily calculate value of roof pitch in fraction, in ratio and angles in degrees, you can also calculate length of rafter, rise height per foot run, roof height and span.

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.

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.

## How to calculate the roof pitch

Regarding this “how to calculate pitch on roof/ or how to determine the roof pitch?”, generally roof pitch is calculated from the Pythagorus 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 pitch formula and equation for roof to calculate the length of rafter and to determine pitch of roof.

### Pitch formula for roof

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

● rafter = rise/ sinθ

● rafter = run/ cosθ

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

● Pitch = tan (angle), where angle is pitch of roof expressed in degree.

● rise of pitch = tan (angle) × 12

● roof height = √ (Rafter^2 _ total run^2)

● roof pitch to degrees = tan-1(pitch)

● degrees to roof pitch = tan (angle) × 12, this will give you X in the ratio X/12.

### How to determine the roof pitch

● 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 4 meters

● measure the vertical height of rise of your roof, assuming it is 1 meters.

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

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

● to calculate pitch on roof 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%.

### How to calculate length of rafter

● 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.

● to determine the rafter length by using this formula, 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.

### How to calculate rise of roof pitch

If you have given the roof’s angle in degrees, you can find the pitch of roof by converting the angle in degrees to a slope, then determining the rise by multiplying the slope by 12 or by using this formula, rise of pitch = tan (angle) × 12

● First, determine the slope by finding the tangent of the degrees, assume rafter is inclined to run by 20°, then slope = tan(degrees), so slope = tan 20° = 0.3639

● Then, secondly multiply the slope by 12 to get the rise such as rise per foot of run = 0.3639 ×12 = 4.36″, it means slope of roof 4.36″ vertical rises per foot or 12″ of horizontal run.

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### Roof pitch to angle in degrees

Roof pitch formula help you to convert roof of pitch ratio or fraction of slope in angle 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 angle in 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 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 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.

### Angle in degrees to roof pitch

Angle in degrees to roof pitch formula 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.

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### How to calculate the height of a pitched roof

If you have given the roof’s angle in degrees and span, to determine the finished height of the ridge beam by by converting the angle in degrees to a slope, then determining the vertical roof height by multiplying the slope by horizontal run (run= span/2) or by using this formula, roof height = √ (Rafter^2 _ total run^2).

● first calculate slope by converting the angle in degrees to a slope, assume roofs angle in degrees is 30°, then slope = tan 30° = 0.577

● then secondly, multiplying the slope by horizontal run (run= span/2), this will give you roof vertical height, such as assume horizontal span = 30 ft, then run = 30/2 = 15 feet, so height of pitched roof = 0.577×15 = 8.65 feet, thus 8.65 feet will be height of pitched roof.

● if horizontal run and rafter length is given, then recalculate the roof height by using a right angle triangle formula Pythagorus theorem as roof height = √ (Rafter^2 _ total run^2)

● assume length of rafter for roof pitch is 5 meters and horizontal run is 4 meters, then roofs vertical height = √ (5)^2 _ (4)^2 = 3 meters, thus 3 meters is height of pitched roof.