Roof pitch ratio:
reading 'x in 12' and converting it

What 'x in 12' really means

Roofers quote pitch as two numbers, such as 6 in 12 or 4/12. The second number is always 12 and stands for 12 units of horizontal run; the first is how many units the roof rises over that run. A 4 in 12 roof climbs 4 inches (or centimetres, or any unit as long as you are consistent) for every 12 across. Twelve is the convention because it is a neat divisor for the old foot-and-inch system, and the habit stuck even in places that use metric tape.

The same slope is also described by an angle in degrees or by a percentage, and designers move between all three as materials and codes demand.

The pitch formula

Run for a symmetrical gable roof is half of the building span, not the full span, because the ridge sits at the centre. Measuring the full span and the ridge height together gives half the pitch you expect, a very common mistake.

Worked example: 2 rise over 8 run

Because the ratio 0.25 is the same as a 25 % slope, the angle is arctan(0.25) = 14.04 degrees. The sloping rafter is √(8² + 2²) = √68 = 8.25 units long for every 8 of run.

From pitch to rafter length

A building spans 6 m, so the run is 3 m. At a 4 in 12 pitch the rise is 3 × 4 ÷ 12 = 1.0 m and the rafter is √(3² + 1²) = 3.16 m, before any overhang. A 6 in 12 pitch on the same building would rise 1.5 m and need a 3.35 m rafter.

Rafter length matters for ordering timber and for estimating sheeting: the roof's real surface area is larger than its footprint by the factor √(1 + (pitch ÷ 12)²), about 1.054 at 4 in 12 and 1.118 at 6 in 12.

Choosing a pitch

• Low pitches under about 3 in 12 are usually only suitable for specific membranes or sheets that are rated for them; check the manufacturer's minimum.
• Medium pitches of about 4 to 8 in 12 suit the widest range of tiles, shingles and metal sheets.
• Steeper pitches shed snow and rain quickly but cost more in material and need safer access for maintenance.
• Wind exposure, rainfall and local building codes set lower and upper limits, so confirm them before you finalise a design.

The roofing product's data sheet is the final authority on the minimum pitch it can be laid at, and an incorrect pitch can void a guarantee.

Pitch, slope percentage and angle side by side

Different trades prefer different notations, so it helps to move between them. Slope percentage is pitch ÷ 12 × 100, so a 6 in 12 roof is 50 %. Roofing manuals, drainage drawings and some software prefer degrees, while many national codes in metric countries quote angles such as 15, 22.5 or 30 degrees directly.

Going the other way, a roof drawn at 30 degrees has a pitch of tan(30°) × 12 = 0.5774 × 12 = 6.93, essentially 7 in 12. A 22.5 degree roof is 0.4142 × 12 = 4.97, very close to 5 in 12. A 15 degree roof gives 0.268 × 12 = 3.2, so it sits just above 3 in 12. Keep these three in mind and you can translate most plans by eye.

Pitch and the amount of material you buy

Footprint area underestimates what has to be covered. A building of 10 m × 6 m has a 60 m² footprint, but a roof at 6 in 12 has a sloping area of 60 × 1.118 = 67.1 m², and at 8 in 12 it is 60 × 1.202 = 72.1 m². Overhangs add more. So the same plan can need 20 % more material depending only on pitch.

This is also why allowance for waste differs between roof types. Hips and valleys make more cut offcuts than a simple gable, and tiles or sheets often need an extra 5 to 10 % for cuts and breakage. Always ask the supplier for the covering width and lap of the product, since they determine how many sheets or tiles each square metre of slope really takes.

A hip roof uses a slightly different geometry for the hip rafters, which run diagonally at the corners and are longer than the common rafters. The common rafter length you get from the formulas above still applies to the main planes; the hip length for a 4 in 12 roof is the plan diagonal of the run times the same sloping factor, but because it involves the plan diagonal it is best taken from a framing table or the roof designer's drawing.

For your own checking, write down the run, the pitch and the rafter length on the drawing next to each plane, and confirm that the rise at the ridge matches on both sides. A difference of even 2 or 3 cm between the two sides is a sign that a dimension has been transcribed wrongly.

Measuring an existing roof

1. 1Lay a level on a rafter or the roof surface, or place a straight board with a level on top.
2. 2Mark 12 units (inches or centimetres) along the level from the point where it touches the roof.
3. 3Measure straight down from the 12-unit mark to the roof surface, giving the rise per 12.
4. 4Read it as pitch = that measured rise in 12.

A slope calculation from two points is handy when you have rise and run in plan drawings, and a roofing sheets estimate then takes the sloping surface, not the footprint, as input.