Calculate roof pitch, rafter length, roof area, and material cost with our free calculator. Convert between rise:12, degrees, percent, and ratio instantly.
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This roof pitch calculator turns a few measurements into the numbers you need for framing. Enter rise and run, or pitch and run, and it returns the pitch in rise:12, degrees, percent, and ratio. You’ll also get rafter length, overhang, roof area, rafter count, and a cost estimate. It’s built for contractors and DIYers who want accurate numbers before cutting lumber.
Roof pitch is the foundation of every rafter cut. Get it wrong and the whole roof is off. This calculator gives you the pitch in four formats at once, plus the rafter length and total material cost. It’s designed for framers, roofers, and anyone planning a roof replacement or new build. Whether you’re working from a set of plans or measuring an existing roof, the tool handles the math. Enter the numbers you have, pick a calculation mode, and read the results. No signup, no downloads, and it works on any device. The tool runs in your browser, so your measurements stay private. Use it to double-check a supplier’s quote or to plan a weekend project.
Choose your unit system. Imperial uses feet and inches; metric uses meters and millimeters.
Pick a calculation mode. Rise & Run finds pitch. Pitch & Run finds rise. Pitch & Rise finds run. Building Span mode works from wall-to-wall dimensions.
Enter the measurements you have. Rise, run, or span. For span mode, add the ridge board thickness.
Set the overhang, building length, and rafter spacing. These drive rafter count and total lumber.
Choose your currency and enter the lumber cost per foot or meter.
Adjust the waste factor. 10% is typical. Bump it to 15% for complex roofs.
Read the summary. You’ll see pitch in four formats, rafter length, roof area, and total cost.
The core relationship is simple: pitch is rise divided by run. Everything else builds off that ratio.
Formula: Pitch Ratio = Rise ÷ Run
Formula: Angle = atan(Pitch Ratio)
Formula: Slope Length = √(Rise² + Run²)
Formula: Total Rafter Length = Slope Length + (Overhang ÷ cos(Angle))
Formula: Roof Area = Plan Area × √(1 + Pitch Ratio²)
Formula: Rafters = 2 × (Ceiling(Building Length ÷ Spacing) + 1)
The tool converts pitch to four formats: rise:12, degrees, percent grade, and ratio (1:X). Rise:12 multiplies the ratio by 12. Degrees takes the arctangent. Percent multiplies the ratio by 100. Ratio inverts the pitch ratio.
Edge cases matter. If run is zero, the pitch is undefined. If pitch is zero, the roof is flat. The calculator rejects zero or negative inputs for run and pitch. For span mode, the run is half the span minus half the ridge thickness. If the ridge is thicker than the span, the calculation stops.
A gable roof with a 32-foot span, 1.5-inch ridge board, 7:12 pitch, 18-inch overhang, 50-foot building length, and 16-inch rafter spacing.
Step 1 — Run. (32 ft × 12 − 1.5 in) ÷ 2 = (384 − 1.5) ÷ 2 = 191.25 in = 15.94 ft.
Step 2 — Pitch ratio. 7 ÷ 12 = 0.5833.
Step 3 — Angle. atan(0.5833) = 30.26°.
Step 4 — Rise. 15.94 × 0.5833 = 9.30 ft.
Step 5 — Slope length. √(9.30² + 15.94²) = √(86.49 + 254.08) = √340.57 = 18.45 ft.
Step 6 — Overhang along slope. 1.5 ft ÷ cos(30.26°) = 1.5 ÷ 0.8632 = 1.74 ft.
Step 7 — Total rafter length. 18.45 + 1.74 = 20.19 ft.
Step 8 — Plan area. 50 × 15.94 × 2 = 1,594 ft².
Step 9 — Roof area. 1,594 × √(1 + 0.5833²) = 1,594 × 1.1577 = 1,845 ft². Squares = 18.45.
Step 10 — Rafter count. Spacing 16 in = 1.333 ft. Ceiling(50 ÷ 1.333) + 1 = 39 per side. Total = 78.
Step 11 — Total lumber. 20.19 × 78 = 1,575 ft. With 10% waste = 1,732 ft.
Step 12 — Cost at $0.85/ft, $2,500 labor. Lumber = $1,472. Total = $3,972. Cost per rafter = $50.93.
Interpretation: The roof has a 7:12 pitch (30.26°). Each rafter is 20.19 feet. You need 78 rafters and 1,732 feet of lumber with waste. Material and labor land around $3,972.
Measure the rise and run, then divide rise by run. Multiply by 12 for rise:12, or use arctangent for degrees. A 6-inch rise over 12 inches of run is a 6:12 pitch, or 26.57°.
Between 4:12 and 9:12 for most homes. 6:12 is the most common. It drains well, takes standard shingles, and is safe to walk on. Below 4:12 needs special underlayment; above 9:12 is steep.
At 16 inches on center, you need 39 rafters per side, so 78 total. The calculator rounds up to the nearest whole rafter, so actual spacing is slightly less than 16 inches.
A number that converts plan area to sloped area. It equals √(1 + pitch²). For a 6:12 pitch, it’s 1.118. Multiply building footprint by this to get roof surface area.
Divide rise by run to get the ratio. Take the arctangent. A 7:12 pitch is 7/12 = 0.5833, atan(0.5833) = 30.26°. The calculator shows this automatically.
Rise is vertical, run is horizontal. Rise goes from wall plate to ridge. Run goes from wall face to ridge centerline. For a gable roof, run is half the span minus half the ridge thickness.
Yes, but pitch will be near zero. Set rise to a very small number. For flat roofs, use direct area entry on a roofing calculator instead, since rafter length and pitch aren’t the main concern.
It uses standard trigonometry. Accuracy depends on your measurements. If you measure rise and run correctly, the pitch, rafter length, and area will be correct. Always double-check before cutting lumber.
The calculator will stop and ask for valid inputs. Run cannot be zero because pitch is rise divided by run. If you’re working from a flat roof, use a different tool.
Yes. 10% is typical. Bump to 15% for complex roofs with hips and valleys. Waste covers cuts and mistakes. The calculator adds waste to the total lumber length before calculating cost.
Yes. A shed roof has one run instead of two. Enter the actual run as run, or use span mode and treat the result as half the rafter length. The pitch math is the same.
Measure 12 inches horizontally along the roof slope, then measure the vertical rise at that point. The ratio of rise to 12 is your pitch. A level and tape measure are all you need.
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