Roof pitch is quoted three different ways and the three are not interchangeable in conversation. Trades in some places say a ratio — four in twelve — meaning four units of rise for twelve of horizontal run. Architects say degrees. The rafter itself is neither, because it is the hypotenuse and it is longer than the run. This gives you all three from two measurements, and tells you what the pitch means for what you can put on the roof, because below a certain angle most tiles and slates stop shedding water and start relying on the felt underneath.
Span, rise and length
Pitch is a ratio, an angle and a rafter length. All three get used, and they disagree.
Wall plate to wall plate, horizontally.
From the wall plate up to the ridge.
Result
Three ways to say the same thing
A roof's steepness is a single geometric fact expressed in three conventions, and confusing them causes real problems. The ratio — rise over run, quoted as so many inches per foot or per twelve — is the language of the trade in North America and of most carpentry. Degrees are the language of drawings and of anything involving mathematics. Percentage is the language of drainage and of flat roofing. And the rafter length is what you actually cut.
They are all derived from the same right-angled triangle. Half the span is the horizontal run, the rise is the vertical, and the rafter is the hypotenuse. Given any two, the rest follows: the angle is the arctangent of rise over run, the ratio is rise over run scaled to twelve, and the rafter is the square root of the sum of the squares. None of them is more correct than the others, but only one of them is what you order timber for.
Why the angle decides the covering
Every roofing material has a minimum pitch below which it stops working. Water gets between the laps by capillary action and by wind driving it uphill, and below the minimum, the laps are no longer shedding — the underlay is. Interlocking concrete tiles are typically rated to about 22.5 degrees, plain tiles to 35, and natural slate to around 20 depending on the size and the lap.
Below those figures, the system changes rather than the material: a lower-pitch installation uses a breather membrane with sealed laps, battens, and often every course mechanically fixed, and the tiles become a weathering layer rather than the waterproof one. Going below the minimum without changing the system is the most common cause of a leaking roof that looks perfect from the ground.
An old roof has usually moved. The ridge settles, the plates spread, and the pitch you measure on site is rarely the pitch on the original drawing.
Measure the span at the wall plates and the rise to the top of the ridge board, and take the measurement from the existing timber rather than from the ceiling below.
What the pitch does to everything else
Pitch sets the roof area, which sets the material quantity and the cost. A 6 m span at a 1.8 m rise has a rafter of 3.5 m against a run of 3 m, so the roof is 17 percent larger than the footprint it covers — and that is before the overhangs, the ridge and the hips. On a hipped roof the geometry compounds, because every hip is a diagonal rafter and every hip adds waste.
It also sets how the roof behaves. A steep roof sheds water and snow fast and is easier to waterproof, but it presents more surface to the wind and it is more dangerous to work on. A shallow roof is cheaper per square metre of building covered, holds snow, and is far more sensitive to any defect in the covering.
| Degrees | Ratio :12 | Percent | Typical use |
|---|---|---|---|
| 5° | 1:12 | 9% | Flat roof minimum fall |
| 15° | 3.2:12 | 27% | Standing seam and low-pitch systems |
| 22.5° | 5:12 | 41% | Minimum for most interlocking tiles |
| 30° | 6.9:12 | 58% | Typical domestic gable |
| 35° | 8.4:12 | 70% | Plain tiles; comfortable |
| 45° | 12:12 | 100% | Steep; period properties, snow country |
| 60° | 20.8:12 | 173% | Very steep; decorative |
A worked example
- RunHalf of a 6 m span is 3.0 m of horizontal run.
- AngleA 1.8 m rise over that run is arctan(0.6), which is 31.0 degrees.
- RatioScaled to twelve, that is 7.2 in twelve — the figure a supplier wants.
- RafterThe hypotenuse of 3.0 and 1.8 is 3.50 m, not 3.0 m.
- Roof areaTwo slopes of 3.5 m over an 8 m building is 55.98 m² of roof, against a 48 m² footprint.
Fifty-six square metres against forty-eight is a sixteen percent difference, and it is the sort of thing that turns a correct-looking order into a short one. The rafter is always longer than the run, and the roof is always bigger than the building.
Measuring a roof you cannot get inside
From outside, measure the gable end: the horizontal distance between the eaves and the vertical distance from eaves to ridge. That gives the pitch directly without any access. From inside a loft, measure horizontally along a ceiling joist from the wall plate to a point directly under the ridge, then up to the ridge — the two measurements of the same triangle.
A smartphone with a level app is accurate to about half a degree, which is good enough for a pitch check but not for setting out. For setting out, use a length of timber and a level, or a pitch template, because a half-degree error over a six-metre span is fifty millimetres at the ridge.
Whether the roof is being re-covered or the structure is being altered, the renovation timeline is where the sequencing gets planned, and the labour hours figure is where the roof area turns into days. Where the space under the pitch is being used, the room volume figure handles the usable space rather than the structure.
Do
- Measure the span at the plates and the rise to the ridge board.
- Quote the pitch in the unit the supplier works in — usually the ratio.
- Check the covering's minimum pitch before choosing it.
- Remember the rafter is longer than the run, and the roof bigger than the footprint.
- Use the gable end if you cannot get into the loft.
Avoid
- Ordering tiles by the footprint area rather than the roof area.
- Assuming a ratio and the equivalent angle are close enough at steep pitches.
- Fitting a tile below its minimum pitch without changing the system.
- Trusting the original drawing on a roof that has moved.
- Setting out from a phone level, which is not accurate to the millimetre.
Where the numbers stop being true
This treats the roof as two flat planes meeting at a point. A hipped roof has four planes and two diagonal hip rafters, a gambrel or mansard has breaks in the slope, and any roof with a dormer has intersections where water is directed sideways rather than down. None of those change the pitch, but all of them change the area substantially.
The rafter length is the length of the slope from plate to ridge, with no allowance for the overhang at the eaves, for the ridge board, or for the birdsmouth cut where the rafter sits on the plate. Add for all three when ordering timber — typically another 300 to 500 millimetres per rafter.
Nothing here accounts for deflection. A ridge that has sagged reads as a shallower pitch at the ridge and a steeper one near the eaves, and a roof that is visibly wavy needs a structural look before it needs a calculator.
How the figures are produced
Half the span is the horizontal run. The angle is the arctangent of rise over run, converted from radians to degrees. The ratio is rise over run multiplied by twelve. The rafter is the square root of run squared plus rise squared, and the roof area is two rafter lengths times the length of the building. The gauge runs to sixty degrees, which covers everything from a flat roof to a steep period property.
Questions people ask
Is 7 in 12 the same as 30 degrees?
Close but not the same. Seven in twelve is 30.3 degrees. The two only coincide exactly at 6.9:12.
What is the shallowest pitch I can tile?
About 22.5 degrees for most interlocking tiles, and about 35 for plain tiles. Below that, the system has to change rather than the tile.
Why is the rafter longer than the run?
Because it is the hypotenuse of the triangle. Over a 3 m run with a 1.8 m rise it is 3.5 m.
How do I measure pitch without a loft hatch?
Measure the gable end: horizontal eaves to eaves, vertical eaves to ridge. Same triangle, no access needed.
Does a steeper roof cost more?
Yes, in area and in labour. More square metres of covering, more time per square metre, and it is slower and riskier to work on.
What about snow and wind?
Steep sheds snow and catches wind. Shallow holds snow and is more sensitive to defects. Both matter more in an exposed location than the pitch itself does.