Roof Pitch Chart: Degrees, Percent Grade, Slope Factor and Hip/Valley Factor

Roofing math · Reference tables · Updated 2026-09-27

This page is the reference sheet, not the explanation. Everything below is a lookup table you can read one-handed standing at an eave: pitch to degrees and percent grade, degrees back to pitch, a flat footprint to the actual roof surface above it, and rafter length per foot of run. The prose between the tables is only here to tell you which column you want and when the column is not good enough.

Every figure was computed from four formulas and rounded once, at the end. Angle is arctan of rise over run. Percent grade is rise over run times 100. Slope factor is 1 divided by the cosine of the angle, which is also the square root of 144 plus x squared, all over 12. Hip and valley factor is the square root of 288 plus x squared, all over 12. Degrees and grade are given to two decimals, the two factors to four, because a factor rounded early moves money.

If you want the reasoning rather than the numbers, roof pitch to degrees covers the conversion in both directions and roof slope factor covers what the multiplier is actually doing. If you need the angle in the first place, that is what Roof Pitch Gauge is for.

How to read the master table

• Pitch is rise in inches over 12 in of run. 6/12 means the roof climbs 6 in vertically for every 12 in of horizontal run. The same pitch is sometimes written 6:12 on drawings, and it means exactly the same thing.
• Degrees is that same steepness expressed as an angle up from horizontal. It is what a digital level, a smart level, an inclinometer or a phone gauge reads out, and what a truss plant or an engineer will ask you for.
• % grade is rise divided by run times 100. A 12/12 roof is 100 % grade because the rise equals the run. Grade turns up on civil and site drawings and in some metal roofing literature.
• Slope factor is the multiplier that takes a flat footprint to the sloped surface over it, and a horizontal run to the common rafter along it. It is the same number for both jobs.
• Hip/valley factor does that job for a member running diagonally across a square corner, which climbs while it also travels sideways. It is always larger than the slope factor on the same roof, and it never drops below 1.4142 even on a dead flat corner.

Degrees back to a pitch

Instruments speak degrees and materials speak x/12, so you will convert one to the other constantly. The table below runs the other direction, from whole degrees to the equivalent pitch, computed as 12 times the tangent of the angle. Notice that the x/12 column almost never lands on a whole number, which is the useful part: a roof you measured at 25 degrees is 5.60/12, not 5/12 and not 6/12. The last column gives the nearest standard whole pitch with its true angle in brackets, so you can see how far the roof is from the pitch you were about to write on the order.

Rafter length per foot of run

The slope factor and the common rafter length per foot of run are the same number, because they come out of the same right triangle. A foot of run at 6/12 is 1.1180 ft of rafter, and a square foot of footprint under a 6/12 roof is 1.1180 square feet of roof. So the fourth column of the master table is already a rafter table and the fifth column is already a hip and valley table; the table below just does the multiplication for a 12 ft run so you can see the shape of it. The mistake that costs real money here is the input, not the factor: run is half the span on a simple symmetrical gable, so a 24 ft wide building has a 12 ft run. Multiply the factor by the run, never by the span. These are theoretical line lengths, before you take off half the ridge thickness and add the tail for the overhang, which rafter length calculator works through with the deductions.

Footprint to actual roof surface

Roof area is the flat footprint under the roof times the slope factor. Measure the building at ground level or scale it off a plan, including the overhangs, and you have the footprint; the factor turns it into the surface somebody has to cover. A roofing square is 100 square feet, so divide by 100 at the end. The worked check: a 2,400 sq ft footprint on a 6/12 roof is 2,400 x 1.1180 = 2,683 sq ft of roof, which is 26.83 squares. Two cautions on the table below. The columns are computed from unrounded factors, so a hand check off the four-decimal column can land a square foot away on some rows. And none of it includes waste, starter, hip and ridge, or the extra courses a valley eats, which how to calculate roof area covers.

The reading comes before the lookup. Every column on this page starts with an angle, and Roof Pitch Gauge & Factor is how you get the angle: lay the phone flat on the deck or run its long edge along a rake board and it reads out degrees, x/12 and % grade together, with the slope factor and an arrow down the fall line. It snaps to the nearest standard whole pitch when the reading is within half a degree of one, and tells you it snapped and what it actually measured. Learn more about Roof Pitch Gauge & Factor.

When the pitch falls between rows

1. Write down the degrees, not the fraction: A reading of 20.6 degrees is not 4/12 and it is not 5/12. Record 20.6 degrees and carry it. Rounding to a whole pitch at the start is how a quarter of a square goes missing and how a rafter comes up short.
2. Run the one formula if you can: Slope factor is 1 divided by the cosine of the angle. At 20.56 degrees that is 1.0680, which is a 4.5/12 roof with a hip/valley factor of 1.4631. Every number on this page comes out of that line and its two siblings, so a calculator beats any chart for an odd pitch.
3. Interpolate only as a field shortcut: Halfway between the 4/12 and 5/12 slope factors is 1.0687 against a true 1.0680 at 4.5/12, about 7 parts in 10,000, or about 2 sq ft on a 30 square roof. The degrees column behaves the same way: halfway between 18.43 and 22.62 is 20.53 against a true 20.56. Close enough to order from, not close enough to cut from.
4. Treat a gap of more than one row as a bad reading: If two readings on the same plane land more than a row apart, the plane is not the problem, the measurement is. Zero the gauge on a known-flat surface, keep the phone still, and take it again in the same posture before you trust either number.

The low slope end of the chart

The master table starts at 1/12 because that is the row just below the point where asphalt shingles stop being an option. Anything under 2/12 is normally called low slope and is a membrane job rather than a shingle job. Down here the slope factors are all within a couple of percent of 1.00, which is why nobody argues about slope factor on a flat commercial deck and everybody argues about drainage instead. The hip and valley column does not follow them down: a diagonal across a square corner is 1.4142 times the run even when the corner is dead flat. What each covering needs as a minimum is set by the International Residential Code as adopted in your jurisdiction and by the manufacturer installation instructions, and either one can be stricter than the other, so read both; minimum roof pitch by material lists the IRC figures covering by covering.

When a lookup is not enough

• The roof has more than one pitch. A porch, a dormer, a shed addition or a garage is very often framed flatter than the main roof. Each plane needs its own reading, its own factor and its own line on the estimate.
• The framing has moved. A chart gives you the pitch you typed into it. A sagged ridge, a cupped rafter or a wavy deck shows up only in a measurement, and it shows up differently at the eave than at the ridge, so take a reading in more than one place on a plane that looks off.
• The hip is not a 45 degree hip. The hip/valley column assumes the hip runs at 45 degrees in plan, which is the normal case on a square corner between two equal pitches. An unequal pitch hip has a different plan angle and needs its own layout, not this column.
• You need a number you can defend. A pitch guessed from the ground, from a photo or from a chart is not a measurement of the plane. Adjusters, truss plants and warranty claims ask what the slope is, and a reading taken on the plane and saved with the job is the answer to that question.
• You are close to a threshold. The 2/12 and 4/12 lines both change what a shingle roof requires, so a reading within a few tenths of a degree of 9.46 or 18.43 degrees is worth zeroing the gauge and taking again before you commit to an underlayment plan. Walkable roof pitch covers the other reason to care where a roof lands on this chart before you get on it.

Frequently asked questions

What is a 6/12 roof pitch in degrees?

A 6/12 pitch is 26.57 degrees. It is also 50 % grade, a slope factor of 1.1180 and a hip/valley factor of 1.5000. The conversion is arctan of 6 divided by 12, and it is the sixth row of the master table on this page.

What roof pitch is 30 degrees?

30 degrees is 6.93/12, which sits between the 6/12 and 7/12 rows and is closest to 7/12 at 30.26 degrees. The exact figure is 12 times the tangent of 30 degrees, or 6.9282. If the number is going on an order or a cut list, carry the 30 degrees and its slope factor of 1.1547 rather than rounding to a whole pitch first.

How do you convert roof pitch to percent grade?

Divide the rise by the run and multiply by 100, which for an x/12 pitch is just x divided by 12 times 100. A 6/12 roof is 50 % grade and a 12/12 roof is 100 % grade. Grade and degrees are not interchangeable: 100 % grade is 45 degrees, not 100 degrees, and the two scales only agree near zero.

What is the slope factor for a 4/12 roof?

1.0541. Multiply a flat footprint by 1.0541 to get the actual roof area above it, and multiply a horizontal run by 1.0541 to get the common rafter line length. A 1,000 sq ft footprint at 4/12 is 1,054 sq ft of roof, or 10.54 squares before any waste.

What is the hip and valley factor used for?

It turns a run into the length of a hip or valley rafter, which climbs and travels sideways at once and so is always longer than a common rafter on the same roof. At 6/12 the hip/valley factor is 1.5000 against a slope factor of 1.1180, so a 12 ft run gives an 18.00 ft hip line length against a 13.42 ft common rafter. The figure assumes the hip runs at 45 degrees in plan, which is the usual case on a square corner.

How many squares is a 2,400 square foot roof at 6/12?

26.83 squares. The 2,400 sq ft footprint times the 6/12 slope factor of 1.1180 is 2,683 sq ft of actual roof surface, and a roofing square is 100 square feet. That is surface area only, before waste, starter course, or hip and ridge.

Is 6:12 the same as 6/12?

Yes. 6:12 and 6/12 are two notations for the same thing, 6 in of rise over 12 in of run, and a drawing may show it instead as a small triangle with 6 and 12 on the legs. In strict traditional usage pitch once meant rise over the full span while slope meant rise over the run, but in the North American roofing trade x/12 today means rise over 12 in of run, and that is what every chart and every shingle wrapper means by it.

Keep reading

• Roof Pitch to Degrees: Converting Both Ways, With the Full Chart
• Roof Slope Factor: What It Is, the Full Table, and How Estimators Use It
• How to Calculate Roof Area: From Footprint to Roofing Squares