How to use it
- Choose Pitch given as and type the rise and the run, the angle, or the percent slope from your drawing.
- Type the Building width, across the ridge and the Building length, along the ridge from your plan.
- Enter the Overhang at the eaves and the gables, or 0 for none.
- Read the angle, the percent and the rafter length. Use Common pitches to compare with a standard roof.
How the pitch is converted
A roof pitch is a slope, the rise divided by the run. The angle is the arctangent of that slope, the percent is the slope times 100, and the x:12 ratio is the slope times 12, which is how a roof is written in the imperial system. A slope of 1 is 45°, which is 100 %, and 12:12.
The rafter runs from the ridge to the outside of the eave. Half the building width plus the overhang is its horizontal length; the slope adds the factor √(1 + slope²). A gable roof has two such slopes over the footprint.
slope = rise ÷ run = tan(angle) = percent ÷ 100
angle = arctan(slope)
x:12 = slope × 12
rafter = (span ÷ 2 + overhang) × √(1 + slope²)
roof area = 2 × rafter × (length + 2 × overhang)What this calculator does not include
- Hips, valleys, dormers and a roof that is not a simple gable, for which the area differs.
- The rafter's cut, the ridge board, the birdsmouth and the material for the boards and battens.
- Snow and wind loads, and the minimum pitch the roof covering needs; check the tile or sheet maker's rules.
Worked example: a 4:12 roof on a building 8 m wide and 12 m long
The slope is 4 ÷ 12 = 0.333. The angle is arctan(0.333) = 18.43°, and the percent is 33.3 %.
The rafter is (8 ÷ 2 + 0.5) × √(1 + 0.333²) = 4.5 × 1.054 = 4.74 m. The roof area is 2 × 4.74 × (12 + 2 × 0.5) = 123.33 m².
| Angle | Slope | Roof area | |
|---|---|---|---|
| 4:12 (this example) | 18.43° | 33.3 % | 123.33 m² |
| 6:12 | 26.57° | 50.0 % | about 131 m² |
Frequently asked questions
How do I convert a pitch of 6:12 to degrees?
Divide the rise by the run: 6 ÷ 12 = 0.5. The angle is the arctangent of 0.5, which is 26.57°, and the slope is 50 %.
What is the difference between a slope in percent and an angle?
They describe the same roof. A 100 % slope is 45°, but 50 % is not 50°: a percent is the rise per 100 units of run, and an angle is measured from the horizontal, so 50 % is 26.57°.
Why is the rafter longer than the half-width of the building?
The rafter is the sloping side of the roof, so it is longer than the horizontal half-width by the factor √(1 + slope²). The overhang adds to the horizontal length before that factor is applied.
How do I measure the rise and run of an existing roof?
Hold a spirit level or a straight board flat up the slope, then measure the vertical drop from its far end to the roof, and the horizontal length of the board. The two give the rise and the run.
Does the tool store what I enter?
No. The calculation runs in your browser and nothing you type is sent to us or stored.
Sources
Figures and text last checked on Tuesday, November 10, 2026.