Roof Pitch Calculator
Roof pitch is the third length (hypotenuse) of a right-angle triangle. The pitch is quite often expressed as a ratio between the rise and run of a roof.
- Rise. Roof height measured from the top of the walls to the roof peak.
- Run. Distance from the exterior wall measured horizontally to the roof peak.
The pitch remains constant regardless of the unit of measurement–feet, inches, meters, or yards. It is usually written with the rise first and then the run. 4/12 or 4:12–either slash or hyphen is acceptable. Grade school math–Pythagoras Theorem–provides the length of the slope.
- Rise squared + run squared = hypotenuse squared.
- Rise divided by run = pitch (expressed as a percentage)
- Pitch = tan (angle) Roof pitch angle expressed in degrees.
Knowing the roof pitch gives the rafter lengths needed for constructing the roof. Trusses are also built according to the pitch and extra length can be added to provide a variety of overhang sizes.
A roof pitch is the measure of the slope or incline of a roof, indicating the vertical rise in relation to the horizontal run.
Calculating roof pitch is necessary to determine the amount of roofing materials required. Contractors use roof pitch and rafter lengths to figure out sheathing needs. Knowing the pitch in advance helps decide how to position materials on the roof and if it is walkable. (4/12 pitch and lower is comfortable to walk on. 6/12 less comfortable. Anything steeper is dangerous or unwalkable.)
How to Calculate Roof Pitch?
Roof Pitch Calculator
Enter the rise and run of the roof to calculate the pitch:
Roof pitch is determined using the Pythagorean theorem, with equations like rafter² = rise² + run². The slope is expressed as a percentage (rise/run), or in degrees using the tangent of the angle.
Example:
- Measure the run length – it is the horizontal distance between the roof ridge and the wall of the building. Let’s assume it is equal to 5 meters.
- Measure the rise of your roof. Let’s say it is equal to 1.5 meters.
- Calculate the rafter length, substituting these values into the following formula:
rafter² = rise² + run² = 1.5² + 5² = 2.25 + 25 = 27.25
rafter = √27.25 = 5.218 meters
- Calculate the roof pitch as the proportion of rise and run:
pitch = rise / run = 1.5 / 5 = 0.3
- Recalculate this value into an angle:
angle = arctan(pitch) * 180 / pi = arctan(0.3) * 180 / pi = 16.7°
- Finally, you can find the roof pitch in the form of x:12.
x = pitch * 12 = 0.3 * 12 = 3.6
The pitch of your roof is 3.6:12. It can also be written down as 30% or 16.7°.
Categories of Roofs
Roofs are loosely divided into four categories. All of them have a roof pitch to allow for water drainage.
- Flat Roofs. Flat roofs are not totally flat. The slope usually ranges from ½/12 to a 2/12 pitch. (½ /12 means half a foot in 12 feet. Not half of 12 feet.) Those numbers translate to 4.2 % – 16.7%. Flat roof rafters are installed level. The slope is added with the sheathing or insulation material.
- Low-Pitched Roofs. Low-pitched roof slopes are less than a 4/12 pitch. Shingles need to be wider and require different installation techniques to prevent leaks and wind damage.
- Conventional-Pitched Roofs. Conventional roof pitches range from 4/12 to 9/12 slopes (33.3% – 75%). They are usually easier to build and the lower range pitches are fairly safe to walk on.
- High-Pitched Roofs. High-pitched roofs can reach slopes up to 21/12 (175%). They are impossible to walk on, difficult and expensive to build, and require extra care to keep the roofing material in place.
What is the Standard Roof Pitch?
There is no universal standard for roof pitches. They vary depending on location, climate, and culture among other considerations. The roof designs used in different locations have evolved over time to take into consideration building materials, snow loads, the volume of rain, and personal preferences.
A standard roof pitch in the USA is between 4/12 and 9/12. UK roof slopes tend to be between 40 and 50 degrees (10/12 – 14/12). Many hot dry climates opt for flat roofs. There is very little moisture to shed and the roof often takes the place of a patio or deck.
| Roof Pitch | Pitch Angle | Description |
|---|---|---|
| 4/12 | 18.43° | Common roof pitch in the USA, also known as a "Steeper Slope" roof. |
| 5/12 | 22.62° | Slightly steeper than 4/12, and commonly used for residential homes. |
| 6/12 | 26.57° | A 6/12 pitch roof is a common choice for many homes because it strikes a good balance between aesthetics and function. |
| 7/12 | 30.26° | A steeper pitch than 6/12, this pitch is often used to create more space in the attic or for homes with vaulted ceilings. |
| 8/12 | 33.69° | A popular choice for homes with an aesthetic preference for steep roofs, as well as for areas with heavy snow loads. |
| 9/12 | 36.87° | Considered a "steeper slope" roof, this pitch is a good choice for areas with heavy snow loads. |
| 10/12 | 39.81° | Known as a "very steep" roof, this pitch is commonly used for Gothic and Tudor style homes. |
| 11/12 | 42.51° | This pitch is often used for homes with a very steep roofline, and can be seen on many European-style homes. |
| 12/12 | 45° | A roof with a 12/12 pitch is also known as a "full" or "100% slope" roof, and is commonly found on A-frame homes. |
| 14/12 | 54.46° | A very steep roof pitch, this is often used on larger buildings or homes with an aesthetic preference for steep roofs. |
| 16/12 | 63.43° | This pitch is used for specialized designs, such as octagonal or hexagonal buildings. |
| 18/12 | 72.47° | The pitch of a traditional thatched roof, this pitch is used for specialty homes or buildings. |