Roof Rise and Run: How to Calculate Pitch, Slope, and Rafter Lengths

Roof rise and run are fundamental for designing, building, and inspecting roofs. This article explains definitions, formulas, conversions, practical examples, code considerations, and troubleshooting to help homeowners, builders, and designers make accurate calculations. Clear examples and formulas make it easy to convert between rise/run, pitch, degrees, and rafter length.

Term	Meaning	Quick Formula
Rise	Vertical height of roof from eave to ridge	Measured in inches or feet
Run	Horizontal distance from wall to ridge (half span)	Often in inches per foot
Pitch	Rise Over Run (e.g., 6/12)	Rise ÷ Run
Slope	Rise ÷ Run (decimal) or tangent in degrees	tan(θ)=rise/run
Rafter Length	Hypotenuse of rise and run triangle	sqrt(rise^2+run^2)

What Roof Rise And Run Mean

Roof rise is the vertical distance from the top of the wall plate to the ridge. Roof run is the horizontal distance from the outside of the wall plate to the ridge, commonly expressed per 12 inches of run. Rise and run together define the roof’s geometry and load behavior.

How Pitch, Slope, And Rise/Run Relate

Pitch is commonly written as rise over run (for example, 6/12) and indicates that for every 12 inches of horizontal run the roof rises 6 inches. Slope is the ratio rise/run expressed as a decimal or percentage. Both terms describe steepness but are used differently in carpentry and architecture.

Essential Formulas And Conversions

Accurate calculations use basic geometry. Core formulas: Pitch = Rise ÷ Run; Slope(decimal) = Rise ÷ Run; Rafter Length = sqrt(Rise^2 + Run^2); Angle θ = arctan(Rise ÷ Run).

To convert pitch to degrees: θ = arctan(pitch). To convert degrees to pitch: pitch = tan(θ). To convert pitch to slope percent: slope% = (rise/run) × 100.

Step-By-Step Example Calculations

Example 1: Find pitch for a roof with 8-inch rise per 12-inch run. Pitch = 8/12 = 0.6667, commonly called a 8/12 roof. Angle = arctan(8/12) ≈ 33.69 degrees. Slope percentage ≈ 66.67%.

Example 2: Calculate rafter length for a span of 24 feet (total) with 8/12 pitch. Run is half span = 12 ft = 144 in. Rise per inch-run = (8/12) = 0.6667 so rise = 0.6667 × 144 ≈ 96 in = 8 ft. Rafter length = sqrt(144^2 + 96^2) in = sqrt(20736 + 9216) = sqrt(29952) ≈ 173.05 in ≈ 14.42 ft. Use consistent units and account for overhang and seat cuts in framing.

Common Roof Pitches And Uses

Low slope roofs: 1/12 to 3/12, often used on commercial buildings and modern homes. Medium slopes: 4/12 to 7/12, common for many residential roofs. Steep slopes: 8/12 and above, typical for historic, cottage, or snowy regions. Choice of pitch affects water shedding, material selection, and aesthetic direction.

Rafter Length With The Rise/Run Formula And Tables

The common carpentry formula uses the unit run of 12 inches. Rafter length per foot of run = sqrt(rise_per_12^2 + 12^2)/12 feet. For an 8/12 roof this gives rafter multiplier = sqrt(8^2 + 12^2)/12 = sqrt(64+144)/12 = sqrt(208)/12 ≈ 14.422/12 ≈ 1.2018. Multiply by actual run in feet to get rafter length. Carpenters use rafter tables or calculators to speed this conversion.

Calculating Roof Rise From Span And Desired Pitch

When span and pitch are known, rise = (span/2) × (pitch/12). For a 30-foot span at 6/12: half span = 15 ft = 180 in; rise = (6/12) × 180 = 90 in = 7.5 ft. This formula is essential during framing layout and when ordering ridge beams.

Accounting For Overhangs, Birdsmouth, And Plate Thickness

Rafter length must include overhangs and allowances for birdsmouth cuts. Typically, add the overhang projection to the run before calculating rafter length. Also deduct the wall plate thickness when setting rise from the top of the plate to the ridge. Neglecting these details leads to errors in rafter seat and roofline alignment.

Practical Tools And Methods

Useful tools include: rafter tables, construction calculators, smartphone apps, and a framing square. A framing square can directly read rise/run combinations using standard stair and rafter tables stamped on the square. Digital calculators reduce human error when converting between units and angles.

Building Code And Structural Considerations

Local building codes may specify minimum slopes for roofing materials (e.g., asphalt shingles typically require slopes above 2/12). Structural loads, snow zones, and wind ratings influence required pitch and rafter sizing. Always consult local codes and structural engineers for nonstandard or high-load roofs.

Converting Between Pitch, Degrees, And Percentage

Quick conversions: Pitch 4/12 = tan^-1(4/12) ≈ 18.43°. Pitch 9/12 ≈ 36.87°. Percentage slope = (rise/run) × 100 so a 5/12 pitch ≈ 41.67%. These conversions help in communicating with roofers, architects, and inspectors who may use different conventions.

Common Mistakes And Troubleshooting

Mistake: Confusing total span with run. Run is half the span. Mistake: Mixing units—always convert feet to inches or vice versa consistently. Mistake: Forgetting overhangs and plate thickness. Double-check measurements, sketch the cross-section, and run sample calculations before cutting rafters.

How To Measure Rise And Run On An Existing Roof

From inside an attic, measure vertical rise from the top of the wall plate to the ridge board and horizontal run from the wall plate to the ridge foot. When attic access is limited, measure from outside at gable or use triangulation with a level and tape. Confirmation with two independent measurements reduces errors.

Material Selection And Drainage Impact

Steeper roofs shed water and snow faster, affecting underlayment and flashing requirements. Low-slope roofs require specific membranes and installer experience to prevent leaks. Choose roofing materials compatible with the calculated pitch to ensure warranty coverage and longevity.

Example Project: Estimating Rafters For A Gable Roof

Project: 28-foot span, desired pitch 7/12, overhang 1 ft. Half span = 14 ft = 168 in. Run including overhang = 168 + 12 = 180 in. Rise = (7/12) × 168 = 98 in ≈ 8.167 ft. Rafter length = sqrt(180^2 + 98^2) in ≈ sqrt(32400 + 9604) = sqrt(42004) ≈ 204.88 in ≈ 17.07 ft. Round up for waste and seat cuts; confirm with a framing square.

When To Hire A Professional

For complex rooflines, structural modifications, or limited attic access, hiring a licensed roofer or structural engineer is recommended. Professionals ensure that rise/run calculations meet load, flashing, ventilation, and code requirements. Professional input reduces rework, improves safety, and ensures long-term performance.

Quick Reference Table: Pitch, Angle, Rafter Multiplier

Pitch (Rise/12)	Angle (Degrees)	Rafter Multiplier
3/12	14.04°	1.0308
4/12	18.43°	1.0541
6/12	26.57°	1.1180
8/12	33.69°	1.2018
10/12	39.81°	1.3043

Additional Resources And Calculators

Online rafter calculators, building code websites, and roofing manufacturer installation guides are valuable. Many university extension services and trade organizations publish rafter tables and slope recommendations. Use manufacturer guidelines for material-specific minimum slopes and underlayment requirements.

For quick checks, free smartphone apps and web calculators allow input of span, pitch, and overhang to produce rafter length, ridge height, and cut layouts.