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01 // Chart Studio02 // Visual Solvers03 // Calculators04 // Formulas05 // Unicode & Symbols
03 // Bidirectional STEM Calculators // EVERYDAYR = √(run² + rise²)

Roof Pitch, Rise, Run & Common Rafter Length Calculator

Common rafter framing forms a right triangle over horizontal half-span run and vertical ridge rise, giving sloped rafter length R = √(run² + rise²) and roof pitch (rise / run) × 12.

R = √(run² + rise²)
Pick which value you want to calculate (or type into any field):Solving for: R — Common Rafter Sloped Length
Calculated

Diagonal line-length from outer wall plate to ridge

0.5500

Horizontal distance from outer wall to ridge centerline

0.5500

Vertical height from top plate to ridge peak

0.1500
Calculated Result · Common Rafter Sloped Length (R)
6.7082m
Converted units:

Step-by-Step Calculation

01Canonical Law: R = √(run² + rise²)
02Given Inputs (Base Units): run = 6 m, rise = 3 m
03Solve for R (Common Rafter Sloped Length): R = 6.7082 m

Common rafter framing forms a right triangle over horizontal half-span run and vertical ridge rise, giving sloped rafter length R = √(run² + rise²) and roof pitch (rise / run) × 12.

Real-World Reference Values

6:12 Standard Gable PitchRise = 0.5 × Run (26.57° Angle)

Rafter multiplier = √(1 + 0.5²) = 1.1180× run

4:12 Minimum Asphalt Shingle PitchRise = 0.333 × Run (18.43°)

Minimum slope for standard shingle shedding without membrane

12:12 Steep Architectural PitchRise = 1.0 × Run (45.00°)

Rafter multiplier = √2 = 1.4142× run

20-Row Comparison Table

Common Rafter Sloped Length (R) · Horizontal Roof Run (Half-Span) (run)

Roof Pitch, Rise, Run & Common Rafter Length Calculator — Horizontal Roof Run (Half-Span) → Common Rafter Sloped Length
#Horizontal Roof Run (Half-Span) (m)Common Rafter Sloped Length (m)Δ %
010.5 m3.0414 m-54.66%
026 mCurrent6.7082 m0.00%
038.3086 m8.8336 m+31.68%
0412.2128 m12.5759 m+87.47%
0516.1171 m16.3939 m+144.39%
0620.0214 m20.2449 m+201.79%
0723.9257 m24.113 m+259.46%
0827.8299 m27.9912 m+317.27%
0931.7342 m31.8757 m+375.17%
1035.6385 m35.7645 m+433.15%
1139.5428 m39.6564 m+491.16%
1243.447 m43.5505 m+549.21%
1347.3513 m47.4463 m+607.29%
1451.2556 m51.3433 m+665.38%
1555.1599 m55.2414 m+723.49%
1659.0641 m59.1403 m+781.61%
1762.9684 m63.0398 m+839.74%
1866.8727 m66.94 m+897.88%
1970.777 m70.8405 m+956.03%
2074.6813 m74.7415 m+1014.18%
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Frequently Asked Questions

How do I convert Rise and Run into 'X in 12' carpenter roof pitch?+

Divide Rise by Run and multiply by 12: Pitch = (rise / run) × 12. At rise = 3 and run = 6, pitch is (3/6) × 12 = 6:12.

How do I find the roof slope angle in degrees?+

Slope angle equals arctan(rise / run). A 6:12 roof has arctan(6/12) = 26.565°.

Does R include the fascia eaves overhang (soffit tail)?+

R is the plumb-to-plumb line length from outer wall plate to ridge center; add your horizontal overhang × (R / run) for total lumber stock length.