What roof pitch means
Roof pitch says how steep a roof is by comparing how much it rises with how far it runs. In the US it is usually written as the rise in inches for every 12 inches of level run. A 6/12 roof climbs 6 inches for each foot it goes across, and you may also see it written as 6:12 or "6 in 12". Because pitch is a ratio, the unit does not matter: 3 feet of rise over 6 feet of run is the same 6/12.
The same steepness can be given as an angle in degrees, measured from level, or as a percent slope, which is the rise divided by the run times 100. This roof pitch calculator takes any of the three and works out the other two, plus the pitch multiplier used for rafters and roof area.
Going the other way, a roof angle turns into a pitch with 12 × tan(angle). A 30 degree roof is 12 × 0.577 = 6.93, just under 7/12. To the nearest eighth that is 6 7/8 in 12, and the calculator shows both the exact value and the nearest common fraction.
Common roof pitches in degrees and percent
The table lists common pitches with their angle, percent slope and multiplier. A 12/12 roof is exactly 45 degrees, where the rise equals the run.
| Pitch | Angle | Slope | Multiplier |
|---|---|---|---|
| 1/12 | 4.76° | 8.33% | 1.003 |
| 2/12 | 9.46° | 16.67% | 1.014 |
| 3/12 | 14.04° | 25% | 1.031 |
| 4/12 | 18.43° | 33.33% | 1.054 |
| 5/12 | 22.62° | 41.67% | 1.083 |
| 6/12 | 26.57° | 50% | 1.118 |
| 7/12 | 30.26° | 58.33% | 1.158 |
| 8/12 | 33.69° | 66.67% | 1.202 |
| 9/12 | 36.87° | 75% | 1.250 |
| 10/12 | 39.81° | 83.33% | 1.302 |
| 11/12 | 42.51° | 91.67% | 1.357 |
| 12/12 | 45° | 100% | 1.414 |
| 14/12 | 49.4° | 116.67% | 1.537 |
| 16/12 | 53.13° | 133.33% | 1.667 |
| 18/12 | 56.31° | 150% | 1.803 |
| 24/12 | 63.43° | 200% | 2.236 |
Rafter length
On a simple gable roof each rafter runs from the top of a long wall up to the ridge in the middle, so its run is half the building width. Add the eave overhang, measured level from the wall to the end of the rafter tail, and multiply by the pitch multiplier. The result is the length along the slope.
Example: a building 24 ft wide with a 6/12 roof and a 1 ft overhang. The run is 12 ft, plus 1 ft of overhang makes 13 ft. Times 1.118 gives 14.53 ft, or about 14 ft 6 7/16 in. The ridge sits 6 ft above the top of the walls.
This is a line length, the kind you would measure along the top edge of the rafter. It does not include the extra length you need for the plumb cut at the ridge, the bird's mouth where the rafter sits on the wall or a tail cut, so buy lumber long enough to cover them. If a ridge board sits between the rafters, each rafter's run gets shorter by half the thickness of that board. Follow your framing plan for the exact cuts, and the lumber calculator helps price the boards.
Roof area and roofing squares
Seen from above, a gable roof covers the building plus its overhangs. The sloped surface is bigger than that footprint by exactly the pitch multiplier, because every foot of run carries more than a foot of roof. So the roof area is the footprint with overhangs, times the multiplier. The example building, 24 by 40 ft with 1 ft overhangs on every side, covers 1,092 square feet from above. At 6/12 the roof itself is about 1,221 square feet.
A roofing square is 100 square feet of roof surface, so the example roof is about 12.2 squares. That is the plain surface: add what the product instructions call for in starter rows, ridge caps and cutting waste. Hips, valleys, dormers and roofs with different pitches on each side need each plane worked out on its own, and the square footage calculator can add up several areas.
How to measure an existing roof
- From the attic: hold a level against the underside of a rafter, mark 12 inches along the level, and measure straight up from that mark to the rafter. That number is the rise per 12.
- From the gable end: measure the height of the ridge above the top of the walls and half the building width. Enter them as the rise and the run.
- With a phone or an angle finder: lay it along the roof surface or a rafter and enter the angle in degrees.
Stay off the roof when you can. Measuring in the attic or at the gable wall gives the same pitch with far less risk. Before you choose a roofing material, check its installation instructions and your local building code for the lowest slope it may be used on.
How to use the roof pitch calculator
- 1Choose how you know the slope: rise and run, an angle in degrees or a percent slope, and enter it. Or tap one of the common pitches.
- 2Read the pitch as x/12, the angle, the percent slope and the multiplier. The diagram shows the shape of the roof.
- 3For rafters and roofing, enter the building width and length and the overhangs, in feet or meters.
- 4Read the rafter length, the ridge height and the roof area in square feet and squares, then copy the result or a link.
Frequently asked questions
How do I convert roof pitch to degrees?
Divide the rise by the run and take the arctangent. For a 6/12 roof, 6 ÷ 12 = 0.5, and arctan(0.5) is 26.57 degrees. A 4/12 roof is 18.43 degrees. The other way round, the rise per 12 inches is 12 × tan(angle), so a 30 degree roof is about 6.93/12.
What angle is a 12/12 roof pitch?
Exactly 45 degrees. The rise equals the run, so the slope is 100 percent and the pitch multiplier is 1.414, the square root of 2. Every foot of run needs about 1.414 feet of rafter.
What is the pitch multiplier?
It is the length of the sloped roof for each unit of level run: the square root of 1 + (rise ÷ run)². For 6/12 it is 1.118. Multiply a run by it to get the rafter length, or multiply the area of the roof seen from above by it to get the sloped roof area.
How do I calculate rafter length?
Take the run, which is half the building width for a simple gable, add the overhang measured level, and multiply by the pitch multiplier. A 24 ft wide building with a 6/12 roof and a 1 ft overhang has a 12 ft run, so (12 + 1) × 1.118 = 14.53 ft, about 14 ft 6 7/16 in. That is the length along the slope before you allow for the ridge board and the cuts.
Is roof slope the same as roof pitch?
They describe the same steepness in different ways. Pitch is usually written as inches of rise per 12 inches of run, like 6/12 or 6:12. Percent slope is rise ÷ run × 100, so 6/12 is a 50 percent slope and 12/12 is 100 percent. The angle in degrees is a third way to say it.
How can I measure the pitch of my roof?
Hold a level against the underside of a rafter in the attic, mark 12 inches along the level from the point where it touches, and measure straight up from that mark to the rafter. That distance is the rise per 12. From the ground, you can also measure the gable wall: the ridge height above the top of the walls is the rise, and half the building width is the run.
How many squares of roofing do I need?
A roofing square is 100 square feet of roof surface. Divide the sloped roof area by 100. The example building above, 24 by 40 ft with 1 ft overhangs and a 6/12 roof, has about 1,221 square feet of roof, which is 12.2 squares before any waste for cuts, starter rows or ridge caps.