Roof Pitch Calculator

What roof pitch actually is

Roof pitch is the steepness of a roof plane, and in the American trades it is written as a ratio of vertical rise to a fixed horizontal run of twelve inches. A roof that climbs six inches for every twelve inches you travel horizontally is a “six in twelve,” written 6/12 and spoken as “six twelve.” The run is always twelve. That is the whole convention, and it is why you will never hear a roofer say “a one-half pitch” even though 6/12 is arithmetically a one-half slope.

Three other people will describe the same roof three other ways. An architect or a solar installer will give you degrees — the angle between the roof plane and level ground. A civil engineer or a drainage plan will give you percent slope, which is rise divided by run times one hundred. And an estimator will care about only one number, the pitch multiplier, because that is the number that turns a floor plan into a materials order.

The percent-slope convention trips up more people than any other. A 45-degree roof is a 12/12 pitch and a 100 percent slope, not fifty percent. Percent slope has no upper bound; it runs to infinity as the roof approaches vertical. If someone hands you a number over 100 and calls it a slope, they are almost certainly using this convention.

Given a rise R over a run of 12 inches:

  pitch          =  R / 12          (written "R in 12")
  angle          =  arctan(R / 12)  degrees
  percent slope  =  (R / 12) x 100  percent
  multiplier     =  sqrt(R^2 + 12^2) / 12

Going the other way:

  R from angle   =  tan(angle) x 12
  R from percent =  (percent / 100) x 12

Why the pitch multiplier exists

A roof plane is the hypotenuse of a right triangle. Its two legs are the rise and the run, so the plane is always longer than the horizontal distance it covers — it is longer than its own shadow. Pythagoras gives the exact ratio: the sloped length over the horizontal length is sqrt(rise² + run²) / run. Because the roof only stretches in one direction — along the slope, not across it — that same single ratio scales area as well as length. Multiply the footprint area by it and you have the real roof area.

This is genuinely useful because a footprint is easy to measure and a roof is not. You can pace off a house, or pull the dimensions from a county property record or a satellite image, and get the footprint in a couple of minutes with your feet on the ground. The multiplier does the rest. On a simple gable or a simple hip, the answer is exact, not an approximation.

Roof pitch multiplier chart

Every value below is computed from the formulas above, not copied from another chart. The roof multiplier column converts footprint area to roof area. The hip / valley column is the length factor for the diagonal members, which climb across the plan rather than straight up it, and so run longer than a common rafter at the same pitch.

Shaded rows are the conventional-slope range, 4/12 through 8/12, where most American houses land and where no steep-pitch labor surcharge applies. For half pitches such as 4.5/12 or 7.5/12, use the calculator above — the formula takes decimals.

Worked example

A ranch house measures 40 ft by 30 ft at the eaves. In the attic, a 12-inch level held against the bottom of a rafter reads 6 inches of rise at its far end. Here is every number that follows from those three measurements.

Pitch          = 6 in 12  ->  6/12

Angle          = arctan(6 / 12)
               = arctan(0.5)
               = 26.57 degrees

Percent slope  = (6 / 12) x 100
               = 50 %

Multiplier     = sqrt(6^2 + 12^2) / 12
               = sqrt(36 + 144) / 12
               = sqrt(180) / 12
               = 13.4164 / 12
               = 1.1180

Footprint      = 40 ft x 30 ft
               = 1,200 sq ft

Roof area      = 1,200 sq ft x 1.1180
               = 1,341.6 sq ft
               = 13.42 squares  (before waste)

Hip / valley   = sqrt(6^2 + 2 x 12^2) / 12
               = sqrt(36 + 288) / 12
               = sqrt(324) / 12
               = 18 / 12
               = 1.5000

Note the sanity check built into that last line: 6/12 is one of the pitches where the hip factor comes out to a clean 1.5, because 324 is a perfect square. If you were framing this roof, a hip rafter would run exactly one and a half feet of length for every foot of horizontal travel across the plan. Two other pitches give clean numbers worth memorizing: 5/12 has a roof multiplier of exactly 13/12, or 1.0833, and 9/12 comes out to exactly 1.25.

Three ways to measure roof pitch

What your pitch changes about the job

• ●Whether shingles are even allowed. Below 2/12, asphalt shingle manufacturers do not approve their product at all and a shingle roof there will leak and void its warranty. That is membrane territory — see the flat roof guide.
• ●How the underlayment is detailed. From 2/12 to just under 4/12, shingles are permitted but require a low-slope application — two plies of underlayment cemented together, or a self-adhering membrane. Crews skip this more often than homeowners realize, and it is invisible once the shingles are on.
• ●Labor cost. Above roughly 8/12 a crew can no longer simply walk the roof. Roof jacks, planks and staging go up, production slows, and most contractors add a steep-pitch surcharge. The same square footage can cost meaningfully more purely because of the angle.
• ●How much material you buy. A 12/12 roof has 41 percent more surface than its own footprint. Quote a job off the footprint and you are short by that entire margin before you have counted a single valley.
• ●Ventilation and snow behavior. Steeper roofs shed snow and water faster and drive attic airflow harder; low-slope roofs hold both, which is why ice dams and ponding are low-slope problems. Size the airflow with the ventilation calculator.

Common mistakes

• ●Confusing percent slope with the ratio. A 6/12 roof is a 50 percent slope, and a 12/12 roof is 100 percent. People routinely read “50 percent” as half of 12/12 and call it a 6/12 — which happens to be right — then read “100 percent” as a flat roof, which is badly wrong.
• ●Using the multiplier as a length factor for hips. The roof multiplier scales common rafters and area. Hips and valleys travel diagonally across the plan and need the larger hip/valley factor. Ordering hip cap off the wrong column leaves you short on the last hip of the day.
• ●Assuming the whole roof is one pitch. Porches, additions, shed dormers and garages are frequently framed shallower than the main house. Measure each section and total them separately.
• ●Measuring over the shingles at a course line. If the level lands on a shingle butt, the step adds phantom rise. Slide the level so both contact points sit on the same course.
• ●Rounding the multiplier to two decimals early. Rounding 1.1180 to 1.12 is harmless on a small roof and costs you most of a bundle on a large one. Carry four decimals through the calculation and round at the end.

Roof pitch questions

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