Reference
Roof pitch chart
Pitch is rise over a 12 inch run: 4:12 is 18.43 degrees, a 33.33 percent grade and a slope factor of 1.054, so a 4:12 roof covers 5.4 percent more surface than its footprint.
Written by Gary Thompson · Steel Building Research EditorSteel Building Research EditorReviewed by Find Steel Buildings Editorial Team
- 1:12
- 4.76° · 8.33% · ×1.003
- 3:12
- 14.04° · 25% · ×1.031
- 4:12
- 18.43° · 33.33% · ×1.054
- 12:12
- 45° · 100% · ×1.414
Conversion chart
Pitch, degrees, percentage and slope factor
Computed on every page load: degrees = arctan(rise ÷ 12), slope factor = √(1 + (rise ÷ 12)²)
| Pitch | Degrees | Percentage grade | Slope factor | Roof area multiplier |
|---|---|---|---|---|
| 1:12 | 4.76° | 8.33% | 1.003 | × 1.003 |
| 2:12 | 9.46° | 16.67% | 1.014 | × 1.014 |
| 3:12 | 14.04° | 25% | 1.031 | × 1.031 |
| 4:12 | 18.43° | 33.33% | 1.054 | × 1.054 |
| 5:12 | 22.62° | 41.67% | 1.083 | × 1.083 |
| 6:12 | 26.57° | 50% | 1.118 | × 1.118 |
| 7:12 | 30.26° | 58.33% | 1.158 | × 1.158 |
| 8:12 | 33.69° | 66.67% | 1.202 | × 1.202 |
| 9:12 | 36.87° | 75% | 1.250 | × 1.250 |
| 10:12 | 39.81° | 83.33% | 1.302 | × 1.302 |
| 11:12 | 42.51° | 91.67% | 1.357 | × 1.357 |
| 12:12 | 45° | 100% | 1.414 | × 1.414 |
Slope factor and roof area multiplier are the same number: multiply the footprint area by it to get the sloped roof surface.
Worked example
Slope factor applied to real footprints
Roof surface area = footprint area × slope factor (no overhang)
| Footprint | Floor area | Roof area at 3:12 | Roof area at 4:12 | Roof area at 6:12 |
|---|---|---|---|---|
| 30 × 40 | 1,200 sq ft | 1,237 sq ft | 1,265 sq ft | 1,342 sq ft |
| 40 × 60 | 2,400 sq ft | 2,474 sq ft | 2,530 sq ft | 2,683 sq ft |
| 50 × 100 | 5,000 sq ft | 5,154 sq ft | 5,270 sq ft | 5,590 sq ft |
Geometry
What pitch does to ridge height
Ridge rise above the eave line = (span ÷ 2) × (rise ÷ 12)
| Clear span | Ridge above eave at 1:12 | at 3:12 | at 4:12 | at 6:12 |
|---|---|---|---|---|
| 24′ | 1′ | 3′ | 4′ | 6′ |
| 30′ | 1.25′ | 3.75′ | 5′ | 7.5′ |
| 40′ | 1.67′ | 5′ | 6.67′ | 10′ |
| 60′ | 2.5′ | 7.5′ | 10′ | 15′ |
Add your eave height to read the total ridge height. On a 60 ft span, moving from 1:12 to 4:12 adds 7.5 ft of ridge.
Context
Pitch on steel buildings
Steel buildings are commonly ordered at low pitches — 1:12 and 3:12 appear far more often than the 6:12 and above familiar from shingled roofs. A low pitch keeps the ridge down, which keeps wall panel and end-wall area down, and it changes the roof area very little: 1:12 adds 0.3 percent to the footprint area, while 6:12 adds 11.8 percent.
At 1:12 the slope factor is 1.003 and the angle is 4.76°. At 6:12 it is 1.118 and 26.57°. Every figure on this page is recalculated from arctan and the Pythagorean slope factor when the page renders.
Planning
What a low slope changes
Stated planning input
Evidence
Where these numbers come from
Evidence record
- Platform calculation
Roof pitch in degrees = arctan(rise / run)
Computed on this page
- Platform calculation
Slope factor = sqrt(1 + (rise/run)^2); roof area = footprint x slope factor
Computed on this page
- Platform calculation
Ridge height = eave height + (span / 2) x (rise / 12)
Computed on this page
Computed values are recalculated whenever this page renders. Published figures link to the source document. Planning inputs are shown as inputs so you can substitute your own.
Keep planning
Next step
Answers
Common questions
18.43 degrees. Pitch converts to an angle with arctan(rise ÷ run), so 4:12 is arctan(4 ÷ 12).
16.67 percent. Percentage grade is simply rise divided by run, expressed as a percentage.
It converts floor area to roof surface area. A 40 x 60 footprint is 2,400 sq ft of floor and 2,530 sq ft of roof at 4:12, because the slope factor is 1.054.
A lower pitch keeps the ridge down, which keeps end-wall and wall-panel area down. It also barely changes roof area: 1:12 adds 0.3 percent over the footprint where 6:12 adds 11.8 percent.
Continue your research
Related planning topics
Background reading on the questions this page raises. None of these pages sells anything.
Planning a building?
Working out a building, not just a pitch?
Pitch changes ridge height and roof area. See how both land on a real span.
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