How do you calculate roof pitch in metric units?
Short answer. In metric, roof pitch is usually given in degrees, calculated as the arctangent of rise divided by run, both in millimetres. You can also express it as millimetres of rise per metre of run or as a percentage. A US 6/12 pitch equals 500 mm per metre, 50 percent, or 26.6 degrees.
The formula
Pitch angle in degrees = arctan(rise ÷ run). Measure rise and run in the same unit, millimetres being easiest.
Example: a rise of 1,800 mm over a run of 4,000 mm: 1,800 ÷ 4,000 = 0.45, and arctan(0.45) = 24.2 degrees.
Converting from the US x/12 system
- Millimetres of rise per metre = (x ÷ 12) × 1,000.
- Percent = (x ÷ 12) × 100.
- Degrees = arctan(x ÷ 12).
Common values
- 3/12: 250 mm per metre, 25 percent, 14.0 degrees
- 4/12: 333 mm per metre, 33 percent, 18.4 degrees
- 6/12: 500 mm per metre, 50 percent, 26.6 degrees
- 8/12: 667 mm per metre, 67 percent, 33.7 degrees
- 10/12: 833 mm per metre, 83 percent, 39.8 degrees
- 12/12: 1,000 mm per metre, 100 percent, 45.0 degrees
Going from degrees back to x/12
Rise per 12 = 12 × tan(angle). A 30 degree roof is 12 × 0.577 = 6.9, about 7/12. A 22.5 degree roof is about 5/12.
Area in square metres
Multiply the flat plan area by the slope factor, which is 1 ÷ cos(angle). For 30 degrees that is 1.155, so 100 square metres of plan becomes about 115.5 square metres of roof.
Product minimums in the US are written in x/12, so convert before checking a material's lowest allowed slope. See how roofers measure a roof.