roofing

Roof Pitch Calculator

Calculate roof pitch, slope angle, rafter length, rise, run, and slope percentage for roofing projects.

Calculator How to Calculate Formulas & Examples FAQs

Determine roof pitch, angle, rise, run, and rafter length.

Calculation Results

Awaiting inputs

Enter roof specifications and click Calculate to estimate pitch, slope, angle, and rafter length.

Formula Details

Roof Pitch Formula

Pitch Rise (X) = (Rise / Run) × 12

Roof pitch is standardly represented as a ratio of rise in inches per 12 inches of run (X:12). If rise and run are in the same unit, dividing rise by run gives the slope fraction, which is then scaled by 12 to find the rise ratio.

Variables Explained

Rise
Vertical Rise:The vertical height of the roof slope from the wall plate to the ridge.
Run
Horizontal Run:The horizontal distance covered by the slope (typically half of the span for a gable roof).

Roof Angle Formula

Angle (θ) = arctan(Rise / Run) × (180 / π)

The roof slope angle in degrees is derived by taking the inverse tangent (arctangent) of the slope ratio (Rise/Run) and converting the result from radians to degrees.

Variables Explained

Rise / Run
Slope Ratio:The vertical elevation divided by the horizontal span.
180 / π
Radian Conversion:Converts radians to standard degrees (approximately 57.2958).

Rafter Length Formula

Rafter Length = √ (Rise² + Run²)

Uses the Pythagorean theorem to calculate the diagonal rafter length (hypotenuse) from the rise (height) and run (width) of the roof slope. Note: Add overhang length to get the total board cut length.

Variables Explained

Rise
Vertical Rise:The vertical height of the slope.
Run
Horizontal Run:The horizontal run of the slope.

Roof Slope Percentage Formula

Slope % = (Rise / Run) × 100

Converts the slope ratio into a percentage. A flat roof has a 0% slope, while a 45-degree roof (12:12 pitch) has a 100% slope, since the rise equals the run.

Variables Explained

Rise / Run
Slope Ratio:The vertical elevation divided by the horizontal span.

Calculation Example

Worked Example

Scenario

Determine the roof pitch, angle, rafter length, and slope percentage for a residential house with a Gable roof span of 24 feet and a vertical rise of 6 feet.

Calculation Steps

1.Identify the horizontal run. The run is half the total building span.
Run = 24 ft / 2 = 12 ft
2.Calculate the slope ratio and scale it to a 12-inch run to find the pitch.
Slope = 6 ft / 12 ft = 0.5 Pitch Rise (X) = 0.5 × 12 = 6 Pitch Ratio = 6:12
3.Calculate the roof slope angle in degrees.
θ = arctan(0.5) × (180 / π) = 26.57°
4.Calculate the rafter length (diagonal span).
Rafter Length = √(6² + 12²) = √(36 + 144) = √180 = 13.42 ft
5.Calculate the roof slope percentage.
Slope % = (6 / 12) × 100 = 50.0%

Final Quantity NeededPitch is 6:12, Slope Angle is 26.57°, Rafter Length is 13.42 ft, and Slope is 50%.

Worked Example

Scenario

Calculate the vertical rise, slope angle, rafter length, and slope percentage for a garage roof with an 8:12 pitch and a horizontal run of 10 feet.

Calculation Steps

1.Determine the rise value from the pitch ratio (8:12 means 8 inches rise per 12 inches run).
Slope = 8 / 12 = 0.6667 Rise = Run × Slope = 10 ft × 0.6667 = 6.67 ft
2.Calculate the slope angle in degrees.
θ = arctan(8 / 12) × (180 / π) = 33.69°
3.Calculate the rafter length.
Rafter Length = √(6.67² + 10²) = √(44.49 + 100) = √144.49 = 12.02 ft
4.Calculate the slope percentage.
Slope % = (8 / 12) × 100 = 66.7%

Final Quantity NeededRise is 6.67 ft, Slope Angle is 33.69°, Rafter Length is 12.02 ft, and Slope is 66.7%.

Worked Example

Scenario

Calculate the vertical rise, pitch ratio, rafter length, and slope percentage for a garden shed in metric units. The roof has an angle of 18.43 degrees and a run of 3 meters.

Calculation Steps

1.Calculate the slope ratio using tangent of the angle.
Slope = tan(18.43°) = 0.3333
2.Calculate the vertical rise.
Rise = Run × Slope = 3.00 m × 0.3333 = 1.00 m
3.Calculate the pitch rise ratio (X:12).
X = 0.3333 × 12 = 4 Pitch Ratio = 4:12
4.Calculate the rafter length.
Rafter Length = 3.00 / cos(18.43°) = 3.16 m
5.Calculate the slope percentage.
Slope % = 0.3333 × 100 = 33.3%

Final Quantity NeededRise is 1.00 m, Pitch is 4:12, Rafter Length is 3.16 m, and Slope is 33.3%.

How to Use

Determine roof slope, angle, pitch ratio, and rafter dimensions with these simple steps:

Choose your Calculation Method: Select from Rise and Run, Pitch Ratio (X:12), or Roof Angle (Degrees).
Choose Unit System: Toggle between Imperial (ft/in/yd) and Metric (m/cm/mm) in the top right to customize your inputs and results.
Enter Required Values:
- For Rise and Run, enter both vertical rise height and horizontal run length.
- For Pitch Ratio, select a standard ratio preset (or enter a custom value) and the horizontal run.
- For Roof Angle, enter the slope angle in degrees and the horizontal run.
Click Calculate: View all derived values (Pitch, Angle, Rise, Run, Rafter Length, and Slope Percentage) rendered together in the results section.
Toggle Units (Optional): If you want to see your results in the alternate unit system, toggle the unit buttons. Your inputs will be dynamically converted.

Roof Pitch Reference Chart

Common residential roof pitches, their corresponding angles, slope percentages, and typical classifications:

Pitch (Ratio)	Angle (Degrees)	Slope (Percent)	Classification & Usage
1:12	4.76°	8.3%	Low Slope / Sheds & covered patios
2:12	9.46°	16.7%	Low Slope / Minimum for shingled roofs (with double underlayment)
3:12	14.04°	25.0%	Low Slope / Traditional porch roofs
4:12	18.43°	33.3%	Standard Slope / Common, easy-to-walk-on residential roofs
6:12	26.57°	50.0%	Standard Slope / The most popular US residential pitch
8:12	33.69°	66.7%	Steep Slope / Requires safety anchors to walk on
12:12	45.00°	100.0%	Steep Slope / 45-degree angle; common in A-frames and snow regions

Frequently Asked Questions

What is roof pitch?

Roof pitch is the slope or steepness of a roof. It is expressed as a ratio of vertical rise to horizontal run, typically written in inches of rise per 12 inches of run (e.g., 6:12). A 6:12 pitch rises 6 inches for every 12 inches of horizontal run.

How is roof pitch measured?

Roof pitch is measured by finding the vertical rise over a horizontal distance (run). You can measure this on-site by holding a carpenter's level horizontally and measuring 12 inches along the level. Then, measure the vertical distance from the 12-inch mark down to the roof plane to find the rise.

What is the difference between pitch and roof angle?

Pitch is a ratio (e.g. 6:12), which is common in construction blueprints in North America. Roof angle is the actual slope measured in degrees (e.g. 26.57°), which is common in physics, engineering, and international standards. Both describe the exact same physical steepness.

What is a good roof pitch?

For standard shingled roofs, pitches between 4:12 (18.43°) and 9:12 (36.87°) are recommended. Pitches under 2:12 are considered low slope and require specialized watertight membranes instead of shingles. Pitches over 9:12 are very steep and require extreme caution during installation or maintenance.

How is rafter length calculated?

Rafter length is calculated using the Pythagorean theorem: Rafter Length = √(Rise² + Run²). This yields the straight-line diagonal distance from the eave line to the ridge beam. Make sure to add the eave overhang length to find the total board cut length.

Can I convert roof angle into roof pitch?

Yes. To convert a roof angle in degrees into a pitch ratio, take the tangent of the angle and multiply by 12. For example, if a roof has an angle of 30°, then tan(30°) × 12 ≈ 0.577 × 12 = 6.93. The roof pitch is approximately 6.93:12.

Need to calculate materials or costs?

Try our full Roofing Calculator to estimate shingles bundles, metal sheets, underlayment rolls, waste factors, and cost breakdowns for Gable, Hip, Shed, Flat, Gambrel, or Mansard structures.

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Disclaimer

Calculations are estimates based on the values you enter and standard engineering formulas. Results are intended for planning and estimation only. Always verify critical measurements, specifications, and local building requirements before purchasing materials or beginning construction.