Convert between X:12 ratio, degrees and percentage — plus rise, run & rafter length
Founder & CEO, Toolraxy
Faiq Ur Rahman is a web designer, digital product developer, and founder of Toolraxy, a growing platform of web-based calculators and utility tools. He specializes in building structured, user-friendly tools focused on health, finance, productivity, and everyday problem-solving.
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Ask three trades to describe the same roof and you will get three different answers. The framing carpenter speaks in 6:12; the engineer writes 26.57° on the drawings; the building inspector refers to a 50 percent slope. All three describe the identical angle, but converting between the formats requires trigonometry that is easy to get wrong under pressure. This calculator was built around that gap. It treats any of the three as the input and produces the other two, so a drawing in degrees can be discussed with a supplier who thinks in ratios, and a percentage given verbally can be checked against a framing square in seconds. It also exposes the slope factor, the multiplier that converts a building footprint into an actual roof surface area which is the figure estimators need when pricing materials on a steep or shallow roof.
Pick one of the three pitch fields, degrees, percentage or X:12 ratio and type the value you have.
Watch the other two fields fill in automatically as you type.
Read the pitch multiplier and slope factor from the four-tile grid below the hero display.
Check the Roof category tile to see whether the pitch falls into flat, low-slope, shallow, standard, steep or very steep.
Review the Rain shedding and Snow shedding tiles for a plain-language performance summary.
If you want rafter figures, enter the Full run across the roof span.
Add an Overhang if the rafter extends past the wall.
Read rafter length, total rise, line length and cut length with overhang in the lower grid.
Every figure on the page derives from one angle, which itself comes from whichever pitch field you last edited. The conversions between the three formats are direct trigonometric relationships.
Formula: Pitch Ratio (X:12) = tan(θ) × 12
Formula: Pitch Percentage = tan(θ) × 100
Formula: Pitch Angle (θ) = atan(Ratio ÷ 12) = atan(Percentage ÷ 100)
Formula: Pitch Multiplier = √(1 + tan²θ)
Formula: Slope Factor = 1 ÷ cos(θ)
Formula: Rafter Line Length = Run ÷ cos(θ)
Formula: Total Rise = Run × tan(θ)
Formula: Rafter with Overhang = Line Length + Overhang ÷ cos(θ)
Pitch must be greater than 0° and less than 89°; outside that band the results panel replaces every tile with a placeholder. Rise and run must both be greater than zero when used as inputs, and the overhang is treated as zero if left blank. The rise field is automatically recalculated to match the current pitch whenever the run is changed, keeping the ratio consistent across all three views.
A designer is working from a drawing that specifies a 32° roof pitch and needs to discuss it with a framing carpenter who thinks only in X:12 ratios. The building’s roof run is 5.4 m with a 600 mm overhang.
Pitch ratio = tan(32°) × 12 = 0.6249 × 12 = 7.50:12
Pitch percentage = tan(32°) × 100 = 62.49%
Pitch multiplier = √(1 + 0.6249²) = 1.1792×
Slope factor = 1 ÷ cos(32°) = 1.1792×
Rafter line length = 5.4 ÷ cos(32°) = 5.4 ÷ 0.8480 = 6.37 m
Total rise = 5.4 × tan(32°) = 5.4 × 0.6249 = 3.37 m
Overhang along slope = 0.6 ÷ 0.8480 = 0.71 m
Total cut length = 6.37 + 0.71 = 7.08 m
The takeaway: a 32° pitch sits between 7:12 and 8:12 on the ratio scale, and the slope factor of 1.179 means the roof surface is roughly 18 percent larger than the footprint beneath it. On a 100 m² footprint that is an extra 18 m² of material, a difference worth catching before the quote goes out.
It means the roof rises 6 units vertically for every 12 units it runs horizontally. In degrees that is 26.57°, and as a percentage it is 50%. It is the most common pitch in North American residential construction.
Multiply the tangent of the angle by 12. A 30° pitch gives tan(30°) × 12 = 0.5774 × 12 = 6.93:12. The calculator does this automatically when you edit the degrees field.
It converts a horizontal measurement into its sloped equivalent. Multiplying a building’s footprint area by the pitch multiplier gives the roof surface area. Multiplying an eave overhang by the same figure gives the extra rafter length needed along the slope.
Most asphalt shingle manufacturers set a minimum pitch of 4:12 for standard installation and require a double underlayment below that. Some products are rated for pitches as low as 2:12 with special installation methods. Always check the manufacturer’s published data sheet.
100%. A 45° angle corresponds to a ratio of 12:12, and the tangent of 45° equals 1, which becomes 100% when multiplied by 100. This is the point at which rise and run are equal.
Divide the run by the cosine of the pitch angle. For a 6:12 pitch at 26.57° and a run of 4 m, rafter length is 4 ÷ 0.8944 = 4.47 m. Add the overhang projected along the slope for the total cut length.
Rain sheds more easily than snow at any given pitch because water has lower friction and lower mass. A roof that sheds rain adequately at 4:12 may still hold snow, which is why cold-climate regions often specify steeper pitches.
Yes. Enter the decimal rise value directly in the ratio field. A 6.5:12 pitch is entered as 6.5. The calculator converts it to degrees and percentage in the same way as a whole number.
Standing-seam metal roofs are usually rated for pitches as low as 1:12 or even 0.5:12 with certain profiles, while through-fastened metal panels typically require a minimum of 3:12. Always confirm against the specific product’s installation manual.
Roof area equals footprint area multiplied by the slope factor. A 6:12 pitch multiplies the footprint by 1.118; a 12:12 pitch by 1.414. The steeper the roof, the larger the surface area for the same building dimensions.
Yes. The geometry is identical regardless of building size or type. For a mono-pitch roof, the run is measured from the low eave to the high wall, and the same formulas apply.
If the pitch is zero, negative or 89 degrees or higher, the calculator clears the results rather than producing a nonsensical figure. A pitch of 89° would be essentially a vertical wall, and zero would be a flat surface, neither of which is a roof in any useful sense.
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