Calculator
Example Data Table
| Pitch | Angle | Percent grade | Pitch factor | Common note |
|---|---|---|---|---|
| 3 in 12 | 14.0362° | 25% | 1.0308 | Low slope |
| 4 in 12 | 18.4349° | 33.333% | 1.0541 | Moderate slope |
| 6 in 12 | 26.5651° | 50% | 1.1180 | Common residential pitch |
| 9 in 12 | 36.8699° | 75% | 1.2500 | Steeper roof |
| 12 in 12 | 45° | 100% | 1.4142 | Very steep roof |
Formula Used
Slope decimal: rise ÷ run
Pitch: slope decimal × 12
Angle: arctan(rise ÷ run)
Percent grade: (rise ÷ run) × 100
Rafter length: square root of rise² + run²
Pitch factor: rafter length ÷ run
Roof area: effective rafter × roof length × roof faces
Total with waste: roof area × (1 + waste ÷ 100)
How To Use This Calculator
- Select the known measurement method.
- Enter the matching rise, pitch, angle, grade, or rafter value.
- Enter the horizontal run in one consistent unit.
- Add roof length, overhang, faces, and waste percentage.
- Press calculate to see pitch, angle, factor, and area.
- Use CSV or PDF buttons to save the result.
Roofing pitch math guide
Roof pitch is a small triangle placed on the roof. The run is the horizontal side. The rise is the vertical side. The slope angle is found from those two sides. This calculator lets you move between those values without redrawing the triangle.
Why angle conversion matters
A pitch such as 6 in 12 means six units of rise for twelve units of run. The same shape can also be written as an angle, a percent grade, or a pitch factor. Each form is useful. Designers often use degrees. Roofers often use pitch. Estimators often use the factor because it changes plan area into sloped area.
Good pitch math prevents waste. A small angle error can change rafter length, flashing length, and roof surface quantity. It also affects drainage. Low slopes need suitable covering systems. Steeper roofs may need extra safety planning, longer access time, and different cutting notes.
Choosing an input method
The calculator accepts several starting points. Use rise and run when you measured a real roof. Use pitch and run when a drawing gives a ratio. Use angle and run when an instrument gives degrees. Use percent grade when civil or layout notes use grade. Use rafter and run when an existing rafter length is known.
Area planning notes
The rafter length is the hypotenuse of the triangle. The pitch factor is rafter length divided by horizontal run. Multiplying flat plan area by this factor estimates sloped roof area for one face. Adding overhang and waste gives a safer material figure.
For complex roofs, split the surface into roof faces. Calculate each face separately. Then add the areas together. Hip and valley framing needs extra care. Dormers and skylights reduce or add material depending on trim. Use waste percentage to cover cuts, laps, starter courses, and mistakes.
Practical accuracy tips
Always keep units consistent. Do not mix feet with inches unless you convert first. The pitch value itself is dimensionless, so 6 in 12 means the same shape in inches, feet, meters, or centimeters.
Use the result as a planning guide. Field conditions may include sag, sheathing thickness, ridge details, valleys, hips, dormers, and local code rules. Confirm final measurements before ordering materials.
FAQs
What is roof pitch?
Roof pitch is the rise compared with horizontal run. A 6 in 12 pitch rises 6 units for every 12 horizontal units.
How do I convert pitch to angle?
Divide rise by run. Then take the arctangent of that value. The calculator returns the angle in degrees and radians.
What does pitch factor mean?
Pitch factor converts flat plan area into sloped roof area. Multiply plan area by the factor for a quick surface estimate.
Can I use inches and feet together?
Use one unit system for each calculation. Convert inches to feet, or feet to inches, before entering mixed measurements.
Why is my rafter length longer than run?
The rafter is the sloped side of the roof triangle. It must be longer than the horizontal run when rise is above zero.
Does this calculate both roof sides?
Yes. Enter the number of roof faces. Use 2 for a simple gable roof with two equal sloped sides.
Should I include overhang?
Include overhang when estimating roof surface or rafter extension. Leave it zero when only checking the basic pitch triangle.
Is the material estimate final?
No. It is a planning estimate. Confirm field dimensions, hips, valleys, openings, laps, and local requirements before buying materials.