Use this Roof Pitch Calculator to calculate roof pitch, roof angle, rise, run, and slope quickly and accurately. Enter any two known measurements to determine the other roof dimensions.
A roof’s pitch is important when planning a new roof, replacing roofing materials, estimating roof surface area, calculating rafter dimensions, checking drainage, and determining whether certain roofing materials are suitable.
Roof Pitch Calculator
The calculator can determine:
- Roof pitch
- Roof angle in degrees
- Rise
- Run
- Roof slope
- Rafter length
- Pitch ratio
For a standard roof, pitch is usually expressed as a ratio such as 4:12, 6:12, or 8:12.
A 6:12 roof pitch, for example, means the roof rises 6 inches vertically for every 12 inches of horizontal run.
What Is Roof Pitch?
Roof pitch describes how steep a roof is.
It is commonly expressed as:
Rise : Run
For example:
6:12
means the roof rises 6 inches for every 12 inches of horizontal distance.
Roof pitch can also be expressed as an angle in degrees or as a percentage slope.
Common Ways to Express Roof Pitch
| Format | Example |
|---|---|
| Pitch ratio | 6:12 |
| Rise per 12 inches | 6 inches |
| Angle | 26.57° |
| Percentage slope | 50% |
These describe the same basic roof slope in different ways.
Roof Pitch Formula
The basic pitch formula is:
Pitch = Rise ÷ Run
For a roof with a 6-inch rise and a 12-inch run:
6 ÷ 12 = 0.5
The roof pitch is therefore:
6:12
or a 50% slope.
How to Calculate Roof Pitch
If you know the rise and run, calculating pitch is straightforward.
Example
Suppose the roof rises 8 inches over a horizontal run of 12 inches.
Pitch = 8 ÷ 12
Pitch = 0.667
Therefore, the roof pitch is:
8:12
The corresponding roof angle is approximately 33.69°.
How to Calculate Roof Angle
Roof pitch can be converted to an angle using the arctangent function:
Angle = arctan(Rise ÷ Run)
For a 6:12 roof:
Angle = arctan(6 ÷ 12)
Angle ≈ 26.57°
This means a 6:12 roof has an angle of approximately 26.6 degrees.
Roof Pitch to Angle Chart
The following table shows common roof pitches and their approximate angles.
| Roof Pitch | Angle |
| 1:12 | 4.76° |
| 2:12 | 9.46° |
| 3:12 | 14.04° |
| 4:12 | 18.43° |
| 5:12 | 22.62° |
| 6:12 | 26.57° |
| 7:12 | 30.26° |
| 8:12 | 33.69° |
| 9:12 | 36.87° |
| 10:12 | 39.81° |
| 11:12 | 42.51° |
| 12:12 | 45.00° |
A 12:12 roof has a 45-degree angle because its rise and run are equal.
Roof Pitch to Percentage
Roof slope can also be expressed as a percentage.
The formula is:
Slope % = Rise ÷ Run × 100
For a 6:12 roof:
6 ÷ 12 × 100 = 50%
Therefore:
6:12 = 50% slope
For an 8:12 roof:
8 ÷ 12 × 100 = 66.67%
Roof Pitch to Degrees
To convert a pitch ratio into degrees:
Angle = arctan(Rise ÷ Run)
For example:
4:12 Roof
arctan(4 ÷ 12) ≈ 18.43°
6:12 Roof
arctan(6 ÷ 12) ≈ 26.57°
8:12 Roof
arctan(8 ÷ 12) ≈ 33.69°
12:12 Roof
arctan(12 ÷ 12) = 45°
How to Measure Roof Pitch
You do not necessarily need to climb onto the roof to measure its pitch.
One practical method is to measure the rise and run from the underside of the roof structure, attic, or another accessible location.
Method 1: Measure From the Attic
If the roof structure is accessible:
- Place a level horizontally.
- Measure 12 inches along the level.
- Measure the vertical distance from the 12-inch point to the roof surface.
- The vertical measurement is the rise.
- Express the result as a pitch ratio.
For example, if the roof rises 7 inches over a 12-inch run:
Roof pitch = 7:12
Method 2: Use a Rafter
If you can safely access an exposed rafter, measure the horizontal run and vertical rise.
Avoid walking on a roof simply to measure pitch. Roof surfaces can be slippery and dangerous.
Roof Pitch Calculator Using Rise and Run
If you know both rise and run, the calculator can determine the pitch and angle.
For example:
- Rise = 9 inches
- Run = 12 inches
Pitch:
9:12
Angle:
arctan(9 ÷ 12) ≈ 36.87°
Slope:
9 ÷ 12 × 100 = 75%
Roof Pitch Calculator Using Rafter Length
If you know the rafter length and horizontal run, you can calculate the rise using the Pythagorean theorem.
The formula is:
Rise = √(Rafter Length² − Run²)
For example, if:
- Rafter length = 15 feet
- Run = 12 feet
Then:
Rise = √(15² − 12²)
Rise = √81
Rise = 9 feet
The roof therefore has a rise-to-run ratio of:
9:12
which is equivalent to a 3:4 slope.
Roof Pitch and Rafter Length
Roof pitch is also useful when calculating rafter length.
The basic relationship is:
Rafter² = Rise² + Run²
Therefore:
Rafter Length = √(Rise² + Run²)
For a 6:12 roof with a 12-foot horizontal run:
- Rise = 6 feet
- Run = 12 feet
Rafter length:
√(6² + 12²) ≈ 13.42 feet
This is the theoretical slope length before accounting for details such as overhangs, birdsmouth cuts, ridge-board dimensions, or other framing considerations.
Common Roof Pitches
Different roof pitches are suited to different architectural designs, climates, materials, and structural requirements.
2:12 Roof Pitch
A 2:12 roof is relatively low-slope.
It is often associated with low-slope roof systems, but the appropriate roofing material depends on the manufacturer’s requirements and local building standards.
3:12 Roof Pitch
A 3:12 roof has a moderate-low slope and is commonly found on certain residential roof designs.
4:12 Roof Pitch
A 4:12 roof is a relatively moderate slope and is common in residential construction.
5:12 Roof Pitch
A 5:12 roof provides a noticeably steeper appearance while remaining less steep than many high-pitch roofs.
6:12 Roof Pitch
A 6:12 roof is a common residential pitch and has an angle of approximately 26.6°.
8:12 Roof Pitch
An 8:12 roof is significantly steeper and produces a more pronounced roof profile.
10:12 Roof Pitch
A 10:12 roof is steep and can make installation and maintenance more challenging.
12:12 Roof Pitch
A 12:12 roof rises 12 inches for every 12 inches of run and has a 45° angle.
Low-Slope vs. Steep-Slope Roofs
Roofing classifications can vary depending on the standard or organization being used.
Generally, a low-slope roof has relatively little vertical rise compared with its horizontal run, while a steep-slope roof has a much greater rise.
The distinction matters because different roofing systems may have different minimum slope requirements.
Always check the roofing manufacturer’s installation specifications and applicable local building requirements before selecting a material.
Why Roof Pitch Matters
Roof pitch affects several aspects of a roofing project.
Water Drainage
Steeper roofs generally allow water to move off the roof more quickly, while low-slope roofs require appropriate drainage design.
Roofing Material
Some roofing materials have minimum pitch requirements.
Roof Area
A steeper roof has more surface area than a flat horizontal projection with the same footprint.
Attic Space
A steeper roof can create more usable space within the roof structure.
Construction Cost
Steep roofs can increase labor, safety requirements, material handling difficulty, and installation complexity.
Snow and Weather
Roof geometry can influence how precipitation accumulates and drains, but structural design and local conditions must be considered.
Roof Pitch and Roofing Materials
Different roofing systems have different minimum slope requirements.
For example, asphalt shingles, metal roofing, tile, slate, and low-slope membrane systems may have different installation requirements.
Never assume that a roofing material can be installed on every pitch.
Always check:
- Manufacturer specifications
- Local building codes
- Required underlayment
- Flashing requirements
- Installation instructions
- Climate and exposure conditions
Roof Pitch and Roof Area
Roof pitch can be used to determine the actual sloped roof area from the horizontal footprint.
For a simple gable roof, the roof surface area can be calculated by determining the slope length and multiplying it by the roof length.
For one roof side:
Roof Area = Slope Length × Roof Length
For a two-sided gable roof:
Total Roof Area = 2 × Slope Length × Roof Length
Complex roofs require separate calculations for each roof section.
Roof Pitch Factor
A roof pitch factor can simplify roof-area calculations.
For a roof with rise R and run 12, the slope factor is:
√(12² + R²) ÷ 12
Some common approximate factors are:
| Pitch | Approximate Factor |
| 1:12 | 1.003 |
| 2:12 | 1.014 |
| 3:12 | 1.031 |
| 4:12 | 1.054 |
| 5:12 | 1.083 |
| 6:12 | 1.118 |
| 7:12 | 1.158 |
| 8:12 | 1.202 |
| 9:12 | 1.250 |
| 10:12 | 1.302 |
| 11:12 | 1.356 |
| 12:12 | 1.414 |
This factor can be multiplied by the horizontal roof footprint to estimate the sloped surface area for a simple roof section.
Roof Pitch Calculator Example
Consider a simple gable roof with:
- Building width: 30 feet
- Roof pitch: 6:12
- Building length: 40 feet
For a symmetrical gable roof, the horizontal run for each side is:
30 ÷ 2 = 15 feet
At a 6:12 pitch, the rise is:
15 × 6 ÷ 12 = 7.5 feet
The slope length is:
√(15² + 7.5²) ≈ 16.77 feet
One roof side has an approximate area of:
16.77 × 40 = 670.8 square feet
Both sides:
670.8 × 2 = 1,341.6 square feet
This is a simplified calculation and does not include overhangs, dormers, valleys, hips, or other roof features.
Roof Pitch Calculator for a Shed
For a simple shed roof, the pitch can be calculated using the rise and run.
For example:
- Horizontal run = 10 feet
- Rise = 3 feet
Pitch:
3 ÷ 10 = 0.30
The equivalent angle is:
arctan(0.30) ≈ 16.70°
The roof has a 30% slope.
If expressed using the common 12-inch run convention:
0.30 × 12 = 3.6
So the approximate pitch is 3.6:12.
Roof Pitch Calculator for a Gable Roof
A gable roof has two sloping sides that meet at a ridge.
For a symmetrical gable:
Run = Building Width ÷ 2
Then:
Rise = Run × Pitch ÷ 12
Once rise and run are known, the rafter length can be calculated using:
Rafter = √(Rise² + Run²)
This provides the basic geometric rafter length before framing allowances.
Roof Pitch Calculator for a Hip Roof
Hip roofs have multiple sloping roof sections, so calculating the complete roof area is more complicated.
A basic pitch calculation still uses:
Rise ÷ Run
However, a complete roof-area estimate must account for the individual roof planes, hips, valleys, ridges, and overhangs.
For material ordering, detailed roof measurements are preferable to relying only on the building footprint.
Roof Pitch vs. Roof Slope
The terms roof pitch and roof slope are sometimes used interchangeably, but technically they can be expressed differently.
Roof pitch is commonly written as a ratio such as:
6:12
Roof slope is often represented as:
0.5
or:
50%
The two measurements describe the same geometric relationship when the same rise and run are being used.
Roof Pitch vs. Roof Angle
Roof pitch and roof angle are not the same measurement.
For example:
6:12 pitch = 26.57°
The pitch describes rise relative to run, while the angle describes the inclination of the roof surface relative to the horizontal.
Both can be useful depending on the application.
Frequently Asked Questions
What is a roof pitch calculator?
A roof pitch calculator determines roof pitch and can also calculate related measurements such as roof angle, slope percentage, rise, run, and rafter length.
What does a 6:12 roof pitch mean?
A 6:12 roof rises 6 inches vertically for every 12 inches of horizontal run. Its angle is approximately 26.57 degrees.
What is the most common roof pitch?
There is no single pitch used on every home. Common residential roof pitches include 4:12, 5:12, 6:12, and 8:12, depending on architectural design, climate, roofing material, and local construction requirements.
What is a 4:12 roof pitch in degrees?
A 4:12 roof pitch has an angle of approximately 18.43 degrees.
What is a 6:12 roof pitch in degrees?
A 6:12 roof pitch has an angle of approximately 26.57 degrees.
What is an 8:12 roof pitch in degrees?
An 8:12 roof pitch has an angle of approximately 33.69 degrees.
What is a 12:12 roof pitch?
A 12:12 roof rises 12 inches for every 12 inches of horizontal run. It has a 45-degree angle.
How do I calculate roof pitch from rise and run?
Divide the rise by the run. If using the standard 12-inch run, express the result as rise:12.
Can I calculate roof pitch without climbing onto the roof?
Yes. You can often measure the rise and run from an accessible attic, rafter, gable end, or another safe location.
Does roof pitch affect roofing cost?
Yes. A steeper roof can increase installation complexity, labor requirements, safety requirements, and material-handling difficulty.
Does roof pitch affect roof area?
Yes. As roof pitch increases, the sloped roof surface becomes larger relative to the horizontal footprint.
Can roof pitch determine rafter length?
Yes. Once the rise and horizontal run are known, the basic rafter length can be calculated using the Pythagorean theorem.
Is a steeper roof always better?
No. The appropriate roof pitch depends on the building design, roofing system, climate, drainage requirements, structural design, cost, and local regulations.
Final Thoughts
A Roof Pitch Calculator makes it easy to convert between roof pitch, rise, run, angle, slope percentage, and basic rafter dimensions.
For a standard roof, remember the fundamental relationship:
Roof Pitch = Rise ÷ Run
A roof with a 6:12 pitch rises 6 inches for every 12 inches of horizontal run and has an angle of approximately 26.57°.
For roofing material selection, structural framing, or construction work, treat calculator results as geometric estimates and verify the final design against manufacturer requirements, local building codes, and qualified professional guidance.