How to use the roof pitch calculator
Roof pitch drives a surprising amount of a design: which roofing materials you can use, how the roof sheds rain and snow, the height of the ridge against planning limits, whether the loft is usable and how much material to order. This calculator converts between the ways pitch is written and turns it into the dimensions you need for drawings and estimates.
- Enter the pitch the way you have it. Use x/12 for US drawings, degrees for most metric projects, percent grade for low-slope roofs, or a measured rise and run from site or an existing drawing (use the same unit for both).
- Add the building span, measured wall to wall across the roof, and the building length along the ridge.
- Add the eave overhang measured horizontally from the wall face, so the rafter length and roof area include it.
The results show the pitch in all three formats, the slope factor, the rafter length from wall plate to ridge plus overhang, the ridge height above the wall plate, the area of a simple gable roof and the number of roofing squares. A note tells you which roofing materials usually suit that pitch.
Roof pitch formulas
Pitch (x/12) = Rise ÷ Run × 12
Angle = atan(Rise ÷ Run) · Grade % = Rise ÷ Run × 100
Slope factor = √(1 + (Rise ÷ Run)²)
Rafter length = (Span ÷ 2 + Overhang) × Slope factor
Ridge height = Span ÷ 2 × Rise ÷ Run
Gable roof area = 2 × Rafter length × Building length
The slope factor is the number to remember. Multiply any horizontal measurement by it to get the true length along the roof surface, and multiply any plan area by it to get the true roof area. For a hip roof of a single pitch, the plan-area method still works: roof area is the plan area including overhangs times the slope factor.
| Pitch | Angle | Grade | Slope factor |
|---|---|---|---|
| 2/12 | 9.46° | 16.7% | 1.014 |
| 4/12 | 18.43° | 33.3% | 1.054 |
| 6/12 | 26.57° | 50% | 1.118 |
| 8/12 | 33.69° | 66.7% | 1.202 |
| 10/12 | 39.81° | 83.3% | 1.302 |
| 12/12 | 45° | 100% | 1.414 |
Worked examples
A US gable roof at 6/12
The house is 30 ft wide and 40 ft long with a 1 ft overhang. The run to the ridge is 15 ft, so the rafter covers 15 + 1 = 16 ft horizontally. With a slope factor of 1.118, each rafter is about 17.89 ft long. The ridge sits 15 × 6 ÷ 12 = 7.5 ft above the wall plate, and the roof surface is 2 × 17.89 × 40 ≈ 1,431 ft², or about 14.3 squares before waste.
A metric roof at 35°
An 8 m wide, 12 m long house with a 0.5 m overhang. tan 35° = 0.700, so the pitch is about 8.4/12 or a 70% grade. The rafter is 4.5 m ÷ cos 35° ≈ 5.49 m, the ridge is 4 × 0.700 = 2.80 m above the plate and the roof area is 2 × 5.49 × 12 ≈ 131.8 m².
Measuring an existing roof
Holding a level 24 inches long against the rafter in the attic, you measure 9 inches from the level up to the rafter. 9 ÷ 24 × 12 = 4.5, so the roof is 4.5/12, about 20.6° or a 37.5% grade.
Who this calculator helps
- Architects setting roof pitches in early massing, checking ridge heights against planning limits and coordinating sections.
- Architecture students converting between degrees and x/12 on international projects and getting roof sections right.
- Roofers and contractors estimating squares, rafter lengths and material quantities for quotes.
- Carpenters and framers checking rafter lengths before cutting.
- Solar installers converting pitch to the tilt angle used for panel output estimates.
- Homeowners comparing roofing quotes, planning a loft conversion or checking whether a material suits their roof.
Choosing a pitch: practical tips
- Check the material minimum first. Under the IRC, asphalt shingles need at least 2/12 (with double underlayment up to 4/12), clay and concrete tile 2.5/12, wood shingles 3/12, and slate and wood shakes 4/12. Manufacturers' instructions can be stricter.
- Steeper roofs shed snow and rain faster and create usable attic space, but they add roof area, cost and ridge height.
- Rafter lengths here are line lengths. Allow for the ridge board, birdsmouth and tail cuts, and order material in standard lengths.
- Add 10–15% waste to the roof area for a gable roof and more for hips, valleys and dormers.
- Get the floor area under the roof with the square footage calculator, draw the section to scale with the architectural scale converter, and size the loft stair with the stair calculator.
Want to compare a steeper roof, new tiles or a different colour on the actual house? Upload a photo and try it with Exterior Redesign.
