How to calculate roof pitch
Roof pitch describes how steep a roof is. It can be written in four ways that all mean the same thing. Rise and run is the vertical rise over a horizontal distance. The US x:12 notation gives the rise for 12 units of run, so 6:12 rises 6 inches per foot. Percent slope is rise divided by run times 100, common on European drawings and for flat roofs. Degrees is the angle between the roof surface and the horizontal, the form used by most tile manufacturers and in BIM software.
The calculator converts everything through the slope s = rise ÷ run. From it, the angle is the arctangent, the x:12 pitch is 12 × s and the percent is 100 × s. The pitch multiplier, √(1 + s²), turns any horizontal length into the length along the slope.
angle = atan(s) · x:12 = 12 × s · percent = 100 × s
multiplier m = √(1 + s²)
rafter = (span ÷ 2 + overhang) × m
roof surface = (length + 2 × gable overhang) × (span + 2 × eave overhang) × m
Worked example
A house is 8 m wide and 10 m long, with a 30° gable roof and 0.5 m overhangs on all sides. The slope is tan 30° = 0.577, which is 57.7% or 6.93:12, and the multiplier is 1.1547. The rafter runs 4 m to the ridge plus 0.5 m of overhang, so 4.5 × 1.1547 = 5.20 m along the slope. The ridge sits 4 × 0.577 = 2.31 m above the wall plate. The roof covers 11 × 9 = 99 m² on plan, and the real surface is 99 × 1.1547 = 114.3 m² — about 15% more than the plan area, which is why tiles are always ordered from the sloped area.
Common roof pitches
| x:12 | Degrees | Percent | Multiplier | Typical use |
|---|---|---|---|---|
| 1:12 | 4.8° | 8.3% | 1.003 | Metal, membrane, low slope |
| 2:12 | 9.5° | 16.7% | 1.014 | Sheds, standing seam |
| 3:12 | 14.0° | 25.0% | 1.031 | Low pitch tiles (check product) |
| 4:12 | 18.4° | 33.3% | 1.054 | Shingles, many interlocking tiles |
| 6:12 | 26.6° | 50.0% | 1.118 | Typical residential |
| 8:12 | 33.7° | 66.7% | 1.202 | Steeper residential, usable attic |
| 9:12 | 36.9° | 75.0% | 1.250 | Plain tiles, slate |
| 12:12 | 45.0° | 100% | 1.414 | Steep roofs, alpine regions |
Choosing a pitch
The covering sets the lower limit: every tile, shingle or sheet product has a minimum pitch in its data sheet, and going below it voids the warranty and invites leaks. Snow load, wind exposure, local planning rules and the attic you want set the rest. Steeper roofs give more usable attic space and shed water and snow faster, but they need longer rafters and more material. If you model roofs in Revit, our RoofBeam plugin places rafters and beams along the slope automatically.
Frequently asked questions
How do I convert roof pitch to degrees?
Divide the rise by the run and take the arctangent. A 6:12 pitch is atan(6/12) = 26.57 degrees, a 12:12 pitch is 45 degrees.
What does a 4/12 roof pitch mean?
The roof rises 4 units for every 12 units of horizontal run. That is a slope of 33.3% and an angle of about 18.4 degrees.
What is a pitch multiplier?
The pitch multiplier is the ratio between the sloped length and the horizontal length, the square root of 1 plus slope squared. Multiply the plan area of a roof by it to get the real roof surface.
How do I calculate rafter length?
For a symmetrical gable, take half the building span, add the horizontal overhang and multiply by the pitch multiplier. This gives the length along the top of the rafter, before ridge and plumb cut allowances.
What is the minimum roof pitch for tiles?
It depends on the tile and the manufacturer. Many interlocking concrete and clay tiles are rated from about 15 to 22 degrees, plain tiles often need 35 degrees or more. Metal and membrane roofs can go much lower. Always follow the product data sheet.
Is roof pitch the same as slope in percent?
They describe the same thing in different units. Percent is rise divided by run times 100, so 6:12 is 50% and 12:12 is 100%. Degrees is the angle itself.