What is a 4/12 roof pitch?

A 4:12 pitch means that the roof rises 4 inches for every 12 inches of horizontal distance, which is equivalent to an angle of about 18.4 degrees and a slope ratio of 33.3%. This is a mild, walkable pitch that falls between flat and moderately steep roofs, with good drainage and suitable for standard asphalt or composite shingles. It may be slightly too shallow for snowy areas.

How do you convert a roof pitch to degrees?

Divide the rise by 12 to get the ratio of vertical change to horizontal change and then take the arctangent (inverse tangent) of that ratio. The slope of 6 over 12 is 0.5, and the arctangent of 0.5 is about 26.6 degrees. Conversely, you can take the tangent of an angle and multiply by 12 to get x for the ratio x:12. This calculator allows you to do calculations in both directions.

What is a standard or optimal roof pitch?

There is no single standard pitch. It depends on the climate, design and materials used. In the United States most houses have a slope between 4:12 and 9:12. Roofs with slopes of about 6:12 or steeper are better for shedding snow and are common in cold regions. A moderate slope offers good performance in high winds. Flatter commercial roofs often use waterproof membranes and shed water by slight runoff rather than actual roof pitch.

What roof pitch is walkable?

Generally speaking, roofs with a pitch of 6:12 (roughly 26.6 degrees) or flatter are relatively easy to walk on as long as you take care. A pitch of 7:12 is also doable but requires caution. At 8:12 to 10:12, walking is possible with extreme caution and appropriate footwear. Roofs steeper than roughly 10:12 are considered non-walkable and require scaffolding, ropes, or specialized roof racks. Falls from the roof can be serious, so always take this seriously.

What is the multiple of roof pitch?

The roof pitch multiplier is also called the roof pitch factor and is a value that is multiplied by the area of the roof to obtain the actual surface area of the sloped surface. It is calculated by squaring the ratio of rise over run length, then adding 1 before taking the square root. The multiplier for a 4:12 pitched roof is about 1.054, meaning that the actual area is about 5% larger than the area of the covered floor space. This helps avoid material shortages.

Roof Pitch Calculator

Roof slope

Describe the roof any way you like — two measurements, an angle, an x:12 pitch, or a grade. Every other form is worked out for you.

What do you know about the roof?

Pick what you know. Enter the two roof measurements, or an angle, an x:12 pitch, or a grade percentage — the calculator fills in all the other forms.

Rise and run

Angle (degrees)

Pitch (x:12)

Grade (%)

Rise is the vertical height from the top of the wall to the ridge; run is the horizontal distance from the wall to the point under the ridge. On a symmetric roof the run is half the span.

Rise

Run

Roof area and material (optional)

Turn the slope into a roofing quantity: the actual surface area, the number of squares, and a material cost.

Estimate roof surface area and cost

Multiply your roof footprint by the pitch multiplier to get the true sloped surface area, the number of roofing squares, and a material cost.

Your roof pitch

Roof angle

Roof pitch

: 12

Rafter length

That is a 4 in 12 pitch, an angle of 18.4349 deg (°), and a 33.33 percent grade. Multiply a roof footprint by 1.0541 to get its true sloped area.

Conventional roof. The 4:12 to 9:12 range is the common, walkable band that most shingles and roofing materials are designed for, and it sheds rain and light snow well.

Roof angle

deg (°)

Pitch (x:12)
Grade
Pitch multiplier

Rafter length: ft

Roof triangle

The roof pitch is the steepness of a roof or how much it rises. It's the only value that determines what materials can be used, how effectively rain and snow will shed, whether you can walk on it, and what area actually needs to be covered. This calculator allows you to determine the pitch from various inputs: enter two measurements of your roof, an angle, the x:12 ratio or the percent grade, and you'll be able to freely convert between them.

What is roof pitch?

The pitch is the steepness created by the rafters, and there are several common ways of expressing it. The rise is the vertical height that the roof rises while the run is the horizontal distance that the roof covers. In a typical gable roof, the run will be half the span of the entire building and is measured from the outside wall to the point directly below the ridge.

In the United States, builders usually express slope as a ratio in the form of x:12. This gives the rise (in inches) per horizontal run (12 inches). A roof with a ratio of 4:12 rises 4 inches for every 1 foot of horizontal travel. The same slope can also be expressed as an angle (in degrees), or as a percent grade, by dividing the rise by the run and multiplying by 100.

How to calculate roof pitch?

Since the rise dimension, horizontal span and rafter form a right triangle all calculations are based on the same geometric principles as any other right triangle. All calculations can be done with three formulas.

\text{rafter}^2 = \text{rise}^2 + \text{run}^2

\text{grade} = \frac{\text{rise}}{\text{run}} \times 100\%

\text{angle} = \arctan\!\left(\frac{\text{rise}}{\text{run}}\right)

Firstly there is the Pythagorean theorem which is used to calculate the length of rafters. Secondly it converts the ratio of rise and run into a percentage. Thirdly it converts the same ratio into the angle that the roof makes with the horizontal. To get the US form x:12, multiply the ratio of rise/run by 12.

Example calculation:

Suppose the horizontal span is 6 meters and the rise is 1.5 meters. We first calculate the length of the rafter using the Pythagorean theorem.

\text{rafter} = \sqrt{1.5^2 + 6^2} = \sqrt{38.25} \approx 6.18\ \text{m}

The next thing is the percent grade which is the result of dividing the rise by the horizontal span. If you divide 1.5 by 6, you get 0.25, which is equal to 25%. This ratio is then put into the arctangent function to obtain the angle.

\text{angle} = \arctan(0.25) \approx 14^{\circ}

The slope of x:12 is the result of multiplying the ratio by 12. So if you multiply .25 by 12, you get 3. This means that a slope of 3:12 would be the same angle as 25% or about 14 degrees. All three numbers describe the exact same roof pitch.

Different ways of representing a general slope.

Here are some common slopes used in everyday life with their angles, percentages and multiples. The multiples will be explained more fully below.

Pitch (x:12)	Angle	Grade	Multiplier
1:12	4.8 deg	8.3%	1.003
2:12	9.5 deg	16.7%	1.014
3:12	14.0 deg	25.0%	1.031
4:12	18.4 deg	33.3%	1.054
6:12	26.6 deg	50.0%	1.118
8:12	33.7 deg	66.7%	1.202
9:12	36.9 deg	75.0%	1.250
12:12	45.0 deg	100.0%	1.414

Flat roof, low pitched roof, typical roof, steep pitched roof.

Roofs can be roughly classified by their pitch with this classification determining the choice of materials and construction.

A flat roof is not actually completely flat. It has a slight slope of about 0.5:12 to 2:12 due to the need for water runoff and uses a tight waterproof membrane instead of tiles.
A low-slope roof has a pitch of less than 4:12. While shingles can be used on these roofs, it is necessary to use additional underlayment and take care in the installation of the flashing.
The usual roof pitches are between 4/12 and 9/12. This range is the easiest to build, offers safe walkability, and most materials are made for this range.
Steep roofs have a pitch of 9:12 or more and can be as steep as 21:12. They provide excellent water and snow shedding, but usually require additional fasteners and scaffolding during installation.

In regions with a lot of snow, pitches from about 6:12 to 7:12 or steeper will allow the snow to slide off before it accumulates. In areas with very high winds, a moderate pitch of 4:12 to 6:12 is often the safer choice.

The multiple of the roof inclination.

The surface area of a sloped roof is larger than the area of the plane on which it sits. Therefore, the materials required are always greater than that expected from the ground area. The multiple of the roof pitch sometimes referred to as the roof pitch factor represents the value that relates these two quantities.

\text{multiplier} = \sqrt{\left(\frac{\text{rise}}{\text{run}}\right)^2 + 1}

When you multiply that factor by the area of the plane surface covered by the roof, it gives you the actual area to be covered on the sloped surface. The factor for a 4:12 roof is about 1.054 so a building with a footprint of 2,000 square feet will actually have a roof area of about 2,108 square feet. You can do this calculation and check the roof areas and material costs by opening the Area Calculation feature of this tool.

How to use this tool:

Choose how the roof is represented. You can choose between rise and run, angle, ratio of x:12, or percent slope.
Enter the values that the tool requires. You can change the units for length or angle in each field.
Check results to show pitch, angle, percent grade, rafter length and multiple.
Open up the surface area calculator to find out how much material you need. Enter in your roof's footprint and cost per square foot.

If you are measuring an existing roof, the safest way to do this is from inside the attic. Place a level on one of the rafters and measure 12 inches along the level. Then measure vertically from that end to the rafter. The value obtained by dividing that change in distance by 12 is the pitch of the roof.

This calculator is for planning purposes only. Working on a roof is dangerous because it's at height. Have the measurements, materials and load classes checked by a qualified roofer before beginning work or climbing onto the roof.

Frequently asked questions

What is a 4/12 roof pitch?: A 4:12 pitch means that the roof rises 4 inches for every 12 inches of horizontal distance, which is equivalent to an angle of about 18.4 degrees and a slope ratio of 33.3%. This is a mild, walkable pitch that falls between flat and moderately steep roofs, with good drainage and suitable for standard asphalt or composite shingles. It may be slightly too shallow for snowy areas.
How do you convert a roof pitch to degrees?: Divide the rise by 12 to get the ratio of vertical change to horizontal change and then take the arctangent (inverse tangent) of that ratio. The slope of 6 over 12 is 0.5, and the arctangent of 0.5 is about 26.6 degrees. Conversely, you can take the tangent of an angle and multiply by 12 to get x for the ratio x:12. This calculator allows you to do calculations in both directions.
What is a standard or optimal roof pitch?: There is no single standard pitch. It depends on the climate, design and materials used. In the United States most houses have a slope between 4:12 and 9:12. Roofs with slopes of about 6:12 or steeper are better for shedding snow and are common in cold regions. A moderate slope offers good performance in high winds. Flatter commercial roofs often use waterproof membranes and shed water by slight runoff rather than actual roof pitch.
What roof pitch is walkable?: Generally speaking, roofs with a pitch of 6:12 (roughly 26.6 degrees) or flatter are relatively easy to walk on as long as you take care. A pitch of 7:12 is also doable but requires caution. At 8:12 to 10:12, walking is possible with extreme caution and appropriate footwear. Roofs steeper than roughly 10:12 are considered non-walkable and require scaffolding, ropes, or specialized roof racks. Falls from the roof can be serious, so always take this seriously.
What is the multiple of roof pitch?: The roof pitch multiplier is also called the roof pitch factor and is a value that is multiplied by the area of the roof to obtain the actual surface area of the sloped surface. It is calculated by squaring the ratio of rise over run length, then adding 1 before taking the square root. The multiplier for a 4:12 pitched roof is about 1.054, meaning that the actual area is about 5% larger than the area of the covered floor space. This helps avoid material shortages.

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Disclaimer: This calculator is provided for general informational and educational purposes only. Our calculators are under active development, and results may be inaccurate, incomplete, or unsuitable for your situation. Always verify the figures independently and seek advice from a qualified professional before relying on them. We make no warranties and accept no liability for any loss or decision arising from use of this tool.

References

Wikipedia - Roof pitch
Definitions of pitch, slope, and the standard ratio and angle conventions used for roofs.
NIST Special Publication 811: Guide for the Use of the International System of Units
The US national standard for SI units, unit names and symbols, and conversion factors.