Free roof pitch calculator: enter rise and run to get pitch as X/12, angle in degrees, slope percent, rafter length and pitch multiplier instantly.
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Roof pitch describes how steep a roof is, written as X/12: the inches a roof rises for every 12 inches of horizontal run. The calculator models the roof as a right triangle, with rise as the vertical leg and run as the horizontal leg. Pitch is rise divided by run, scaled to a 12 inch run. The angle is the arctangent of rise over run converted to degrees, and slope percent is the same ratio times 100. Rafter length is the hypotenuse of the triangle. These four numbers drive framing, shingle selection and material estimates.
Roof pitch is the ratio of vertical rise to horizontal run, and in the United States it is almost always written as X/12, meaning inches of rise per 12 inches of run. A 6/12 roof climbs 6 inches for every foot of level distance. Builders prefer this ratio over degrees because it can be checked directly with a tape measure and a level, and because the numbers feed straight into rafter math and material ordering. Pitch, slope percent and angle are three formats for the same steepness: pitch is rise per 12, slope percent is rise divided by run times 100, and angle is the arctangent of rise over run in degrees.
The safest method is from the attic: hold a level horizontally against the underside of a straight rafter, mark 12 inches along the level, then measure vertically from that mark to the rafter. That vertical reading is the X in X/12. On the roof itself, lay a level on a straight board touching the shingles and measure from the board down to the surface. From the ground, a phone inclinometer app or a photo of the gable end gives a rough angle you can convert back to pitch. Always measure run as level horizontal distance, never the sloped rafter length, and keep rise and run in the same units.
To convert X/12 to degrees, take the arctangent of X divided by 12 and multiply by 180 over pi. To convert degrees to X/12, multiply the tangent of the angle by 12. Slope percent is simply X divided by 12 times 100. Common reference points: 4/12 is about 18.43 degrees and 33.3 percent, 6/12 is about 26.57 degrees and 50 percent, 8/12 is about 33.69 degrees and 66.7 percent, and 12/12 is exactly 45 degrees and 100 percent. The 1/12 to 12/12 range covers nearly all residential roofs; anything above 9/12 is generally treated as steep work.
The pitch multiplier converts flat footprint area into true sloped roof area: multiply the horizontal footprint square footage by sqrt(1 plus (rise/run) squared) to get the roof surface you actually have to cover. For a 6/12 roof the multiplier is 1.118, so a 1,500 sq ft footprint is about 1,677 sq ft of roof. The hip/valley factor does the same job for hip and valley lines where two planes meet, and equals sqrt(pitch squared plus 288) divided by 12. Under-ordering shingles because footprint area was used instead of sloped area is one of the most common and expensive estimating mistakes.
Rafter length from the wall plate to the ridge is the hypotenuse of the rise/run triangle: the square root of rise squared plus run squared. This is the theoretical lumber line; add tail length for eaves, subtract for the birdsmouth seat cut, and account for ridge board thickness before ordering lumber. The roof angle doubles as the plumb cut angle at the top of the rafter, and the complementary angle (90 degrees minus roof angle) is the seat cut angle at the birdsmouth. Steeper pitches mean longer rafters for the same span, more roof area, and higher wind exposure.
The most common error is measuring run along the sloped rafter instead of horizontally, which understates pitch. Next is mixing units, like inches for rise and feet for run, without converting. Confusing slope percent with degrees is another classic: a 6/12 roof is 50 percent slope but only 26.57 degrees. Treating footprint area as roof area under-orders material on every pitched roof. Finally, low-slope roofs below 4/12 need special underlayment or membrane systems, and anything above about 7/12 should be treated as steep work with proper fall protection and staging.
Use this conversion chart to jump between the three ways roofers talk about slope: the X/12 pitch, the angle in degrees, and the slope as a percentage. Common conversions: 2/12 = 9.46 degrees = 16.67 percent; 4/12 = 18.43 degrees = 33.33 percent; 6/12 = 26.57 degrees = 50 percent; 8/12 = 33.69 degrees = 66.67 percent; 10/12 = 39.81 degrees = 83.33 percent; 12/12 = 45 degrees = 100 percent. To convert any X/12 pitch yourself: angle in degrees = arctan(X / 12), and slope percentage = (X / 12) × 100. Roof pitch conversion charts are a staple of framing references, and this calculator computes the exact conversion for any rise and run instead of only the standard whole-number pitches.
Measure the vertical rise and the horizontal run in the same units, then divide rise by run and multiply by 12. That gives the pitch as X/12. For example, 6 inches of rise over 12 inches of run is (6/12) × 12 = 6/12 pitch, with an angle of atan(6/12) = 26.57 degrees and a slope of 50 percent.
Most US homes fall between 4/12 and 9/12, and 6/12 is a very common middle value. It sheds water well with shingles, is walkable for most roofers, and looks proportional on most house styles. Four-twelve is the economical lower end, while 8/12 and above start to feel steep.
People use the words loosely, but they are formats for the same steepness. Pitch is written as X/12 (rise per 12 inches of run), slope percent is rise divided by run times 100, and roof angle is the arctangent of rise over run in degrees. A 6/12 pitch equals 50 percent slope equals 26.57 degrees.
A 6/12 pitch is atan(6/12) = 26.57 degrees. Other common conversions: 4/12 is 18.43 degrees, 8/12 is 33.69 degrees, 9/12 is 36.87 degrees, and 12/12 is exactly 45 degrees. To convert any X/12 to degrees use angle = atan(X/12) × 180/pi.
The pitch multiplier converts horizontal footprint area into true sloped roof area. It equals sqrt(1 + (rise/run)²⁾. Multiply a flat footprint square footage by the multiplier to get the roof surface area before waste. For 6/12 the multiplier is 1.118, so 1,500 sq ft of footprint becomes about 1,677 sq ft of roof. It also converts horizontal run into rafter length per unit run.
Pitches of 9/12 (36.87 degrees) and above are generally considered steep, and anything above 12/12 (45 degrees) is very steep. For asphalt shingles, 4/12 is the standard minimum in many product specs; pitches between 2/12 and 4/12 usually require special low-slope application with double underlayment. Below 2/12, membrane or built-up roofing is recommended.
Thirty degrees corresponds to a slope of tan(30) = 0.577, so in X/12 notation that is 12 × 0.577 = 6.93, or about 7/12. To convert any angle to X/12, multiply the tangent of the angle by 12.