Roof pitch describes how steep a roof is, but it can be written in more than one way. In the United States, builders commonly express pitch as inches of vertical rise for every 12 inches of horizontal run. To convert roof pitch to degrees, use a simple trigonometric formula. The result helps homeowners compare roof slopes, estimate roof area, and communicate more clearly with contractors. A conversion chart and worked examples make the calculation easier, while a few important cautions help prevent confusion between pitch, angle, and percent slope.
What Roof Pitch Means
Roof pitch is the relationship between a roof’s vertical rise and its horizontal run. A roof with a 6:12 pitch rises 6 inches for every 12 inches of horizontal distance. The first number represents rise; the second represents run. In common U.S. roofing practice, the run is usually standardized to 12 inches, even when the roof’s actual dimensions are larger.
Roof pitch is a ratio, not an angle. A 6:12 roof pitch is therefore not a 6-degree angle. The angle is approximately 26.6 degrees. The distinction matters because roof plans, estimating tools, building documents, and measurement apps may use different formats.
The word “slope” can also refer to a ratio, an angle, or a percentage. These describe the same incline in different ways, but the numbers are not interchangeable without conversion. When comparing measurements, confirm which format is being used.
How To Convert Roof Pitch To Degrees
For a roof pitch written as rise:run, calculate the angle with the inverse tangent function:
Roof angle in degrees = arctan(rise ÷ run) × 180 ÷ π
For a standard U.S. pitch written as x:12, the calculation becomes:
Roof angle in degrees = arctan(x ÷ 12) × 180 ÷ π
Here, arctan means inverse tangent, often displayed as tan⁻¹ on a calculator. The calculator must be set to degrees if it displays the answer in degrees. For example, a 6:12 roof has a rise-to-run ratio of 6 ÷ 12, or 0.5. The inverse tangent of 0.5 is about 26.565 degrees, which rounds to 26.6 degrees.
The formula applies to any rise and run measured in the same units. A roof rising 4 feet over a 10-foot horizontal run has the same angle as one rising 4 inches over a 10-inch run: arctan(0.4), or about 21.8 degrees.
Roof Pitch To Degrees Conversion Chart
The following chart converts common U.S. roof pitches into approximate angles. Values are rounded to one decimal place. The pitch ratio is rise per 12 inches of horizontal run.
| Roof Pitch | Rise Per 12-Inch Run | Approximate Angle |
|---|---|---|
| 1:12 | 1 inch | 4.8° |
| 2:12 | 2 inches | 9.5° |
| 3:12 | 3 inches | 14.0° |
| 4:12 | 4 inches | 18.4° |
| 5:12 | 5 inches | 22.6° |
| 6:12 | 6 inches | 26.6° |
| 7:12 | 7 inches | 30.3° |
| 8:12 | 8 inches | 33.7° |
| 9:12 | 9 inches | 36.9° |
| 10:12 | 10 inches | 39.8° |
| 11:12 | 11 inches | 42.5° |
| 12:12 | 12 inches | 45.0° |
| 14:12 | 14 inches | 49.4° |
| 16:12 | 16 inches | 53.1° |
These are mathematical conversions, not recommendations for a particular roofing material or climate. Manufacturer requirements and local building codes determine whether a specific roof covering is suitable for a given pitch.
Worked Roof Pitch Conversion Examples
Convert a 4:12 roof pitch to degrees
Divide the rise by the run: 4 ÷ 12 = 0.3333. Then calculate arctan(0.3333). The roof angle is approximately 18.4 degrees.
Convert a 9:12 roof pitch to degrees
Divide 9 by 12 to get 0.75. The inverse tangent of 0.75 is approximately 36.9 degrees. This describes a substantially steeper roof than a 4:12 slope.
Convert an angle to roof pitch
The conversion can be reversed. For an angle in degrees, use:
Rise per 12-inch run = 12 × tan(angle)
For a 30-degree roof, tan(30°) is about 0.577. Multiplying 0.577 by 12 gives a rise of roughly 6.9 inches per 12 inches of run. The closest commonly stated pitch is about 7:12.
Using a Calculator, Spreadsheet, or Phone
A scientific calculator can convert pitch directly if it includes an inverse tangent function. For a 7:12 pitch, enter arctan(7 ÷ 12) while the calculator is in degree mode. Depending on the device, the function may appear as “atan,” “tan⁻¹,” or be accessed through a secondary key.
In a spreadsheet, the formula can be entered as =DEGREES(ATAN(rise/run)). For a pitch represented by a single rise value, such as 7 for 7:12, use =DEGREES(ATAN(7/12)). Spreadsheet functions and separators can vary by software and locale.
Online roof pitch calculators can be convenient, but users should check what information the tool expects. Some request rise and run; others request pitch, angle, or a roof measurement in inches. Entering a pitch value into an angle field will produce an incorrect result.
Pitch, Degrees, Percent Slope, And Roof Ratio
These terms describe related measurements but use different scales. A pitch of 6:12 means 6 inches of rise for 12 inches of horizontal run. Its angle is about 26.6 degrees. Its percent slope is 50%, calculated as rise divided by run multiplied by 100. The 50% figure does not mean a 50-degree roof.
| Measurement | What It Describes | Example For 6:12 |
|---|---|---|
| Pitch ratio | Vertical rise compared with horizontal run | 6:12 |
| Angle | Incline measured from horizontal | About 26.6° |
| Percent slope | Rise divided by run, multiplied by 100 | 50% |
The angle is measured from a horizontal plane. Measuring from vertical instead would produce the complementary angle: 90 degrees minus the roof angle. That difference can explain conflicting readings from some tools or drawings.
Why Roof Pitch In Degrees Is Useful
Comparing roof steepness
Degrees can be easier to picture than a ratio, especially when comparing roof designs. A 3:12 pitch is about 14 degrees, while a 12:12 pitch is 45 degrees. However, the ratio remains the common format in many U.S. roofing plans and estimates, so both values may be useful.
Estimating roof surface area
A roof’s sloped surface is larger than its horizontal footprint. For a simple roof plane, the slope factor can be calculated as √(1 + (rise ÷ run)²). Multiply the horizontal plan area of that plane by this factor to estimate its sloped area, before accounting for overhangs, valleys, dormers, and waste.
For example, a 6:12 roof has a slope factor of about 1.118. A 1,000-square-foot horizontal roof footprint for one plane would correspond to roughly 1,118 square feet of sloped surface, assuming the footprint and roof plane are defined consistently. Real material orders require additional measurement and waste allowances.
Discussing plans and product requirements
Converting to degrees can help when interpreting diagrams or comparing specifications that use angular measurements. For actual product selection, the manufacturer’s installation instructions are more important than an informal conversion. Shingles, metal panels, membranes, and underlayment systems can have different minimum-slope requirements and installation details.
How To Measure Roof Pitch Safely
A pitch can often be determined from building plans or from a safely accessible attic rafter, rather than by climbing onto the roof. On an exposed rafter, measure a 12-inch horizontal distance and record the vertical rise over that distance. A level and tape measure can help establish the horizontal reference.
On a roof surface, a digital angle finder may report the angle directly, while a roof pitch gauge may display rise per 12 inches. Read the tool’s instructions and confirm whether it measures from horizontal or vertical. Measurements can vary if the tool is not seated properly or the surface is uneven.
Roof work can involve serious fall hazards. A conversion does not determine whether a roof is safe to walk on. Wet, icy, fragile, or steep surfaces and nearby overhead power lines increase risk. When access or measurement is unsafe, a qualified roofing professional can assess the roof with appropriate equipment.
Common Roof Pitch Conversion Mistakes
- Treating the pitch number as degrees: A 6:12 pitch is about 26.6°, not 6°.
- Using the wrong denominator: The standard ratio uses horizontal run, not the length of the sloped rafter.
- Mixing measurement units: Rise and run must use the same units before division.
- Using a calculator in radians: A correct ratio can still yield an unexpected result if the display mode is wrong.
- Confusing percent slope with degrees: A 50% slope corresponds to 6:12 and about 26.6°, not 50°.
- Rounding too early: Keep several decimal places during calculations, then round the final angle to the precision needed.
Roof Pitch, Materials, And Building Requirements
Pitch affects drainage, exposure to wind and weather, the amount of roofing material needed, and installation methods. A steeper roof may shed water and snow differently from a low-slope roof, but performance depends on the full roof assembly, climate, design, and maintenance—not angle alone.
There is no single pitch that is correct for every U.S. home. Local building codes, adopted code editions, structural design, and manufacturer instructions can all affect requirements. The International Residential Code includes provisions related to roof coverings and slope, but local jurisdictions may adopt amendments or different editions. Homeowners should verify requirements with the local building department and the product manufacturer.
For a reliable specification, record the roof pitch as a ratio and, when helpful, include the approximate degree measurement in parentheses. For example: 8:12 pitch (about 33.7°). This format preserves the familiar roofing convention while making the angle clear to anyone working from degree-based plans or tools.
Sources: The conversion formula follows standard trigonometry. For code-related decisions, consult the locally adopted building code and the applicable product installation instructions; the International Code Council publishes the International Residential Code, and individual jurisdictions determine which provisions apply.