Roof Pitch Calculator
Free roof pitch calculator. Convert roof rise and run into pitch (x/12), angle degrees, grade %, and slope factor for area estimates.
A roof pitch calculator converts a roof’s rise and run into four linked figures: the pitch in “x per 12” form, the angle in degrees, the grade as a percentage, and the slope factor used to turn floor area into actual roof area.
What the four outputs mean
- Pitch is the standard roofer’s format: rise per 12 inches of run. It comes from
pitch = (rise ÷ run) × 12. - Angle is the slope’s arctangent, converted to degrees:
atan(rise ÷ run) × 180 ÷ π. - Grade is the same slope as a percentage:
(rise ÷ run) × 100. - Slope factor is the hypotenuse ratio,
√(1 + (rise ÷ run)²). Multiply a footprint area by it to get sloped surface area.
Worked example: a 6/12 roof
Defaults: rise 6 in, run 12 in.
| Output | Calculation | Result |
|---|---|---|
| Ratio | 6 ÷ 12 | 0.5 |
| Pitch | 0.5 × 12 | 6.0/12 |
| Angle | atan(0.5) in degrees | 26.6° |
| Grade | 0.5 × 100 | 50.0% |
| Slope factor | √(1 + 0.25) | 1.118 |
To price materials, take the building footprint and multiply by the slope factor. A 1,500 ft² footprint on a 6/12 roof is 1,500 × 1.118 = 1,677 ft² of actual surface — the number a roofer quotes against, not the footprint.
Reference: pitch conversions
| Pitch | Angle | Grade | Slope factor |
|---|---|---|---|
| 1/12 | 4.8° | 8.3% | 1.003 |
| 2/12 | 9.5° | 16.7% | 1.014 |
| 3/12 | 14.0° | 25.0% | 1.031 |
| 4/12 | 18.4° | 33.3% | 1.054 |
| 5/12 | 22.6° | 41.7% | 1.083 |
| 6/12 | 26.6° | 50.0% | 1.118 |
| 7/12 | 30.3° | 58.3% | 1.158 |
| 8/12 | 33.7° | 66.7% | 1.202 |
| 9/12 | 36.9° | 75.0% | 1.250 |
| 10/12 | 39.8° | 83.3% | 1.302 |
| 12/12 | 45.0° | 100.0% | 1.414 |
Run is the horizontal distance from the wall to the ridge, which for a simple gable is half the span, not the full building width. Getting that wrong doubles the apparent pitch.
From pitch to rafter length
The slope factor is the same ratio used to find rafter length. For a horizontal run of R feet, the rafter measured along the slope is R × slope factor. At 6/12 a 12-foot run needs a rafter about 13.4 feet long before you add the ridge and overhang. That is why steeper roofs consume more lumber for the same building footprint.
| Pitch | Slope factor | Rafter for a 12 ft run |
|---|---|---|
| 3/12 | 1.031 | 12.4 ft |
| 4/12 | 1.054 | 12.6 ft |
| 6/12 | 1.118 | 13.4 ft |
| 8/12 | 1.202 | 14.4 ft |
| 12/12 | 1.414 | 17.0 ft |
Pitch also drives material choice. Very low pitches drain slowly and need a continuous membrane or a specific underlayment, while steep pitches shed water quickly but cost more to walk and to roof.
Typical pitch ranges
Residential roofs commonly sit between 4/12 and 8/12. Below about 3/12, drainage slows and most shingle makers require a double underlayment or a low-slope membrane. Above 9/12 the roof is steep enough that walking it needs fall protection, and labour rates climb with it. Flat or near-flat roofs use a membrane system rather than shingles. Knowing where a quoted pitch falls in these ranges tells you a lot about the likely material and labour cost.
Common mistakes
- Using pitch as the angle. A 4/12 roof is 18.4°, not 4°. They are different scales entirely.
- Forgetting the slope factor. Roofing materials price against sloped surface. Using footprint area underprices the job.
- Measuring run as the full width. Run is horizontal distance to the ridge, typically half the span for a gable.
- Mixing rise and run. Rise is vertical, run is horizontal. Swapping them gives the wrong angle and the wrong factor.
What does a 4/12 roof pitch mean?
The roof rises 4 inches for every 12 inches of horizontal run. That is about 18.4°, with a slope factor of 1.054, so the actual roof surface is roughly 5% larger than the footprint.
How do I convert footprint area to roof area?
Multiply the footprint by the slope factor. At 6/12 the factor is 1.118, so a 1,500 ft² footprint becomes 1,677 ft² of roof.
What pitch is walkable?
Low-slope and moderate pitches are generally considered walkable for maintenance, while steeper roofs need fall protection and cost more to work on. The angle output lets you compare a quoted pitch against a safe working range.
The sloped area this produces feeds directly into the roofing cost calculator, and the rafter length is the same right-triangle relationship as the Pythagorean calculator.