Lean To Roof Slope Calculator
Get your lean-to roof slope from the rise and the run. The tool reports the industry standard X/12 pitch, the angle in degrees, the percent grade, the rafter length, and the rafter multiplier for material estimates, in feet, inches, or meters. A lean-to has a single sloping plane leaning off a taller wall, so one rise and one run describe the whole roof.
Lean-To Roof Slope Calculator
Pitch in X/12, angle, grade, rafter length and multiplier from one rise and run
Rise and run must use the same unit. Rafter length is the straight ridge-to-wall-plate run; add overhang and waste when ordering lumber.
Quick Answer
The short answer: a rise of 6 ft over a run of 12 ft gives a 6.00/12 pitch, an angle of 26.57 degrees, a 50.00% grade, a rafter length of 13.42 ft and a multiplier of 1.1180. Pitch is (rise ÷ run) × 12, the angle is arctan(rise ÷ run), and the rafter is √(rise² + run²).
How to use the lean-to roof slope calculator
Enter the rise, enter the run, pick the unit both were measured in, and press Calculate. The only hard rules are that the run must be greater than zero, because every output divides by it, and the rise cannot be negative. There is no upper limit: the tool will happily convert a rise of 100 over a run of 3 into a 400.00/12 pitch at 88.28 degrees, which is a wall, not a roof, so sanity-check steep results against your tape measurements before ordering anything.
Read the five outputs as a set. The X/12 pitch is what a roofer quotes and what material minimums are written in. The angle is what you set a saw or a speed square to. The percent grade is the drainage language used on plans. The rafter length is the straight slope length between ridge and wall plate. The multiplier is the shortcut that turns any other run, or the whole footprint area, into slope length or sloped area without redoing the triangle.
Worked example, checked against this exact tool
Rise 6 ft, run 12 ft. Slope = 6 ÷ 12 = 0.5. Pitch = 0.5 × 12 = 6.00/12. Angle = arctan(0.5) = 26.57 degrees. Grade = 0.5 × 100 = 50.00%. Rafter = √(6² + 12²) = √180 = 13.42 ft. Multiplier = √(1 + 0.5²) = 1.1180. Every figure matches the tool’s output line for line, including the formula block it prints under the result.
Two more checks worth keeping. The same slope in inches, rise 24 and run 48, returns the identical 6.00/12 pitch, angle, grade and multiplier, with a rafter length of 53.67 in, because pitch is a ratio and only the rafter label follows the unit. And a metric shed at rise 3 m over run 10 m gives a 3.60/12 pitch, 16.70 degrees, a 30.00% grade, a 10.44 m rafter and a 1.0440 multiplier. If your numbers ever disagree with these three cases, the inputs, not the math, are where to look.
Reading roof pitch: the X/12 notation
Roofers describe pitch as rise over a standard 12-unit run, because it can be checked on site with a level and a tape: hold a 12-inch level horizontal against the slope and measure the vertical drop at its end. A 6/12 roof climbs 6 units for every 12 units of level distance. The same slope can be stated four ways, and confusing them is the most common ordering mistake on a small build: 6/12 pitch is a 26.57 degree angle, a 50% grade, and a 1-in-2 gradient. Percent grade is not degrees, and neither is a ratio you can cut timber to.
| Pitch | Angle | Grade | Multiplier | Typical lean-to use |
|---|---|---|---|---|
| 2/12 | 9.46° | 16.67% | 1.0138 | Lowest usual shingle slope, with special underlayment |
| 3/12 | 14.04° | 25.00% | 1.0308 | Metal panels and porch roofs |
| 4/12 | 18.43° | 33.33% | 1.0541 | Standard shingles without special underlayment |
| 5/12 | 22.62° | 41.67% | 1.0833 | Sheds and additions in wetter climates |
| 6/12 | 26.57° | 50.00% | 1.1180 | Steep end of the usual lean-to range |
| 8/12 | 33.69° | 66.67% | 1.2019 | Snow country, or matching a steep main roof |
Lean-to roofs typically sit between 2/12 and 6/12: enough slope to shed water, shallow enough for a single-slope frame against an existing wall. The minimums that matter are set by the covering, not by taste. The residential code’s roof assembly rules and shingle manufacturers both treat 2/12 as the floor for asphalt shingles, and then only with double underlayment or an approved low-slope system; 4/12 is the floor for a standard shingle install. Standing seam and corrugated metal can run at 3/12 and below depending on seam type and sealant, and single-ply membranes are built for near-flat work. The code chapters collected in the References, the International Residential Code chapter on roof assemblies in particular, are the place to confirm the floor for your covering before you fix the wall heights. For a two-plane roof rather than a lean-to, the gable roof area calculator sizes the surface once you know the pitch.
The rafter multiplier
The multiplier, √(1 + (rise ÷ run)²), converts any horizontal distance into slope distance at the same pitch. Multiply a run by it and you get the rafter length for that run: at 6/12, a 20 ft run needs 20 × 1.1180 = 22.36 ft of rafter before overhang and waste. Multiply the roof’s flat footprint area by it and you get the sloped surface area, which is the number shingle bundles and metal panels are ordered against. A 10 ft by 20 ft lean-to footprint is 200 square feet on plan and 200 × 1.1180 = 223.6 square feet of actual roof at 6/12. Order to the sloped figure, then add 5 to 10% waste for cuts and damage. At low pitches the multiplier stays close to 1, which tempts people to skip it; at 3/12 it still adds 3%, roughly one extra sheet on a small roof, and running short costs a second delivery.
Measure from the right points
Most wrong pitches are measurement errors, not math errors. Rise is the vertical distance from the top of the wall plate to the underside of the ridge or ledger, not the height of the building wall and not the length up the slope. Run is the horizontal distance from the wall plate to the vertical line below the ridge, measured level, not along the ground if the ground itself slopes. On an existing lean-to, the cleanest field method is the 12-inch level method from the pitch table above: level held against the underside of a rafter, vertical measurement at the 12-inch mark, and that measurement is the X in X/12 directly.
The rafter length the tool returns is the straight ridge-to-wall-plate length. It excludes the eave overhang, the ridge or ledger thickness deduction your framing method uses, and any birdsmouth seat cut. Add the overhang to the run before you finalise a cut length, because the overhang slopes too: a 12 ft run with a 1 ft horizontal overhang at 6/12 needs a rafter covering 13 ft of run, which is 13 × 1.1180 = 14.53 ft, plus waste, rounded up to the next standard board length. Related slope work on site uses the same rise-over-run habit: the ceiling slope calculator for raked ceilings, the deck slope calculator for drainage fall on a deck, and the gutter slope calculator for the much smaller falls a gutter needs.
What competing calculators miss
General roof pitch tools are strong on the triangle and weak on the lean-to. YardsCalculator and RoofGenius both return pitch, angle, grade and a multiplier, and RoofGenius adds a hip and valley factor, which is dead weight on a single-plane roof that has neither. Sage’s lean-to page is framed for the right roof but buries the calculator under benefit lists and code generalities, and its minimum-slope table states shingle and tile floors without tying them to a result you just computed. Firgelli’s engineering version gives the same four outputs with no lean-to framing at all. The plainest gap across the set: almost none of them handle a zero rise honestly, and several will show a 0/12 or a broken ratio where this tool prints a flat roof note with a 1.0000 multiplier. This page keeps the full output set, pitch to two decimals as the tool prints it, the multiplier to four, worked checks in three unit systems, and the material minimums stated next to the pitch table where you can compare your result against them.
Frequently asked questions
Divide the rise by the run. Multiply by 12 for the X/12 pitch, by 100 for the percent grade, or take the arctangent for the angle in degrees. A rise of 6 over a run of 12 gives a 6.00/12 pitch, a 50.00% grade and a 26.57 degree angle.
About 26.57 degrees. The conversion is angle = arctan(pitch ÷ 12), so arctan(6 ÷ 12) = arctan(0.5) = 26.57 degrees, with a 50.00% grade and a rafter multiplier of 1.1180.
Typically 2/12 to 6/12: steep enough to shed water, shallow enough for a single-slope frame. The roofing material sets the real floor. Asphalt shingles generally need at least 2/12 with special underlayment and 4/12 without it, while standing seam metal can run lower. Check the manufacturer’s minimum and your local code before framing.
Use Pythagoras: rafter = √(rise² + run²). At a rise of 6 ft and a run of 12 ft, the rafter is √180 = 13.42 ft. The tool gives the ridge-to-wall-plate length only, so add the eave overhang and 5 to 10% waste when ordering.
The multiplier is √(1 + (rise ÷ run)²). Multiply any horizontal run by it to get the rafter length, or multiply the roof’s flat footprint area by it to estimate the sloped surface area for panels or shingles. At 6/12 it is 1.1180.
No. Rise and run must share a unit, because pitch is a ratio and the rafter length comes out in whatever unit you picked. Convert both to feet, both to inches, or both to meters before calculating.
A rise of zero gives a flat roof note instead of a pitch ratio, with a 0.00 degree angle, a 0.00% grade, a rafter length equal to the run, and a multiplier of 1.0000. A real lean-to still needs a slight fall for drainage, so treat zero as a measurement check, not a design target.
No. The tool gives the straight ridge-to-wall-plate length. Add your eave overhang to the run before you work out the full cut length, and round up to the nearest standard board length.
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References
- International Code Council. International Building Code 2021, Chapter 15: Roof Assemblies and Rooftop Structures. Accessed October 22, 2026.
- International Code Council. International Residential Code 2021, Chapter 9: Roof Assemblies. Accessed October 22, 2026.
- National Roofing Contractors Association. NRCA Releases 2025 Roofing Manual Volumes and Boxed Set (The NRCA Roofing Manual: Steep-slope Roof Systems-2025). Accessed October 22, 2026.
- Whole Building Design Guide. Roofing Systems. Accessed October 22, 2026.
- Asphalt Roofing Manufacturers Association. Asphalt Roofing Manufacturers Association resources on shingle installation and slope requirements. Accessed October 22, 2026.