Case 1
- Rise (vertical)
- 6
- Run (horizontal)
- 12
26.57°
Open with these valuesRoof Pitch Calculator
26.57°
Result: 26.57 °One slope, three names: 6:12 in the carpenter's notation, 50 % as a grade, 26.57° as an angle. This calculator turns rise and run into the angle. Use the same unit for both — they cancel in the ratio, so only their proportion counts, never the slanted rafter.
Worked examples
Case 2
- Rise (vertical)
- 3
- Run (horizontal)
- 12
14.04°
Open with these valuesCase 3
- Rise (vertical)
- 12
- Run (horizontal)
- 12
45.00°
Open with these valuesHow it's calculated
angle = arctan(rise ÷ run), in degrees
- StepMeasure the vertical rise and the horizontal run in the same unit.
- StepThe run is the flat distance across the ground, never the slanted rafter.
- StepThe angle is the arctangent of rise ÷ run; the grade is that ratio × 100.
- ResultFor the x:12 notation, enter 12 as the run and the first number as the rise.
Reference table
| Rise, run | Grade | Angle (°) |
|---|---|---|
| 0, 12 | 0 %, a flat roof | 0.00 |
| 3, 12 | 25 % | 14.04 |
| 6, 12 | 50 % | 26.57 |
| 9, 12 | 75 % | 36.87 |
| 12, 12 | 100 % | 45.00 |
| 10, 10 | 100 %, the same slope | 45.00 |
Questions
How do I calculate roof pitch?
Divide the rise by the run and take the arctangent for the angle. A 6:12 roof gives arctan(0.5) = 26.57°, which is the same slope as a grade of 50 %.
What does a pitch like 6:12 mean?
It states the rise for every 12 units of run. A 6:12 roof climbs 6 for every 12 across, about 26.57° and a 50 % grade, while 12:12 climbs 12 for 12 — a full 45° and 100 %.
Why is a 45° roof 100 % and not 50 %?
Because the grade is rise ÷ run × 100, not a share of a right angle. At 45° the rise equals the run, so the grade is exactly 100 %, and it climbs towards infinity as the roof approaches vertical.
What is the difference between rise and run?
The rise is the vertical height gained; the run is the horizontal distance covered, measured flat along the ground. Using the slanted rafter instead overstates the run and makes the roof look shallower than it is.
Which units should I use?
The same one for both. They cancel in the ratio, so centimetres, inches and metres all give the same angle — but mixing them, rise in inches against run in feet, does not.
Sources and last check
Information, not professional advice.