Enter rise and run, or an angle, to get the pitch, slope and rafter factor. Add the building footprint for a roof-area estimate.
Pitch, angle and slope all describe the same thing in different ways. Slope is rise ÷ run. Pitch, the usual U.S. roofing term, states the rise for a 12-inch run, so it is 12 × rise ÷ run (a 6/12 pitch rises 6 in for every 12 in across). The angle is the arctangent of rise ÷ run, and slope percent is rise ÷ run × 100. Going from an angle back to pitch uses the tangent: pitch = 12 × tan(angle).
The rafter length factor is the length of the sloped surface for each unit of horizontal run, √(1 + (rise ÷ run)²), from the Pythagorean theorem. Multiply a horizontal run by it to get the sloped length. For a roof whose planes all share one pitch (a typical gable or hip roof), the surface area is the footprint area, including overhangs, times the same factor. U.S. roofers count area in "squares" of 100 sq ft.
| Pitch | Angle | Slope | Factor |
|---|---|---|---|
| 2/12 | 9.46° | 16.7% | 1.014 |
| 3/12 | 14.04° | 25.0% | 1.031 |
| 4/12 | 18.43° | 33.3% | 1.054 |
| 5/12 | 22.62° | 41.7% | 1.083 |
| 6/12 | 26.57° | 50.0% | 1.118 |
| 7/12 | 30.26° | 58.3% | 1.158 |
| 8/12 | 33.69° | 66.7% | 1.202 |
| 9/12 | 36.87° | 75.0% | 1.250 |
| 10/12 | 39.81° | 83.3% | 1.302 |
| 12/12 | 45.00° | 100.0% | 1.414 |
Example: a 30 × 40 ft house with 1 ft overhangs has a 32 × 42 ft footprint (1,344 sq ft). At 6/12 the factor is 1.118, so the roof surface is about 1,503 sq ft, or roughly 15 squares before waste for ridges, valleys and starter courses. A rafter with a 16 ft horizontal run would be about 17.89 ft long, before allowances for the ridge board and cuts.
Dormers, valleys and planes with different pitches each need their own calculation, and real rafter cutting includes adjustments for ridge thickness and seat cuts.
What is a "normal" roof pitch?
Many houses fall between about 4/12 and 9/12. Low-slope roofs (below roughly 3/12 to 4/12) usually need different roofing materials, so check the manufacturer's minimum slope for shingles or other products.
How do I measure pitch safely without climbing on the roof?
You can measure from the attic against a rafter, or on a gable end using a level and tape. A smartphone angle app or digital angle finder held on the rafter also works; enter the angle in From angle mode.
Is pitch the same as slope?
People often use them interchangeably, but strictly, slope is rise over run (6/12 = 0.5 or 50%), and in some trades "pitch" means rise over the full span. This calculator uses the common roofing meaning: rise per 12 of run.
Why does the roof area use a multiplier?
A sloped roof surface is longer than its flat footprint. Multiplying the footprint by the rafter factor converts flat area to sloped area for roofs where every plane has the same pitch.
What pitch is a 45 degree roof?
A 45° roof rises as much as it runs, so it is a 12/12 pitch, a 100% slope, with a rafter factor of about 1.414.