BuildCalcENGINEERING
ROOFING & FRAMING · 0ms CLIENT MATH

Roof Pitch & Rafter Length Calculator

Calculate pitch angles in degrees, roof grade percentages, rafter line lengths, plumb and seat birdsmouth cuts, and roofing squares with real-time vector diagrams.

Framing Inputs

in/12
Vertical rise in inches per 12 inches of run
Feet
Run = Span ÷ 2
Feet
Inches
10%
0% (Net)10% (Standard)20% (Complex)

Rafter & Material Takeoff Spec Sheet

Includes 10% contractor waste factor

Pitch Ratio
6 : 12
Conventional / Medium
Pitch Angle
26.57°
Grade: 50%
Common Rafter Length
161"(13.42 ft)
Line length to top plate
Rafter with Overhang
174.41"(14.53 ft)
Includes 12" eave
Total Ridge Rise
72"(6 ft)
From top plate to ridge
Plumb Cut Angle
63.4°
Angle at ridge board
Seat Cut Angle
26.6°
Birdsmouth level cut
Roofing Squares
12.15SQ
37 Bundles (3 / SQ)
0ms Client Math EngineStandard Dimensional Tolerances
Vector Scale

2D Rafter Cross-Section Blueprint

Pitch: 6 in 12 (50% Grade)
Plumb Cut (Ridge)63.4°
Seat Cut (Birdsmouth)26.6°
Pitch Multiplier×1.118
Roof Grade50%

Roof Pitch Multiplier & Angle Conversion Table

PitchAngleGradeMultiplierCategory
3:1214.04°25.0%1.0308Low Slope
4:1218.43°33.3%1.0541Conventional
6:1226.57°50.0%1.1180Conventional
8:1233.69°66.7%1.2019High Pitch
10:1239.81°83.3%1.3017Steep Slope
12:1245.00°100.0%1.414245° Pitch

Why rafter length uses a slope multiplier, not a tape on the attic floor

Why the multiplier is 1+(rise/12)2\sqrt{1+(\text{rise}/12)^{2}}

A common rafter is the hypotenuse of a right triangle whose run is half the building span and whose rise is that run times (pitch rise ÷ 12). Dividing the sloped length by the run gives the same number for every pitch: 1+(rise/12)2\sqrt{1+(\text{rise}/12)^{2}}. You multiply run by that factor instead of walking a tape up the attic floor and guessing the ridge.

Run is span ÷ 2 only on a centered gable. A shed uses the full span. Hips and jacks are longer than the common. Angle is θ=arctan(rise/12)\theta=\arctan(\text{rise}/12); plumb is 90° minus that angle; seat is the pitch angle. Full squares and valleys belong on the squares tool. The pitch table on the right already lists multipliers — this guide does not reprint it.

run=span2(centered gable)\text{run} = \dfrac{\text{span}}{2} \quad (\text{centered gable})
multiplier=1+(rise12)2\text{multiplier} = \sqrt{1 + \left(\dfrac{\text{rise}}{12}\right)^{2}}
rafter=run×multiplier\text{rafter} = \text{run} \times \text{multiplier}
overhang on the slope=eave×multiplier\text{overhang on the slope} = \text{eave} \times \text{multiplier}
θ=arctan ⁣(rise12)\theta = \arctan\!\left(\dfrac{\text{rise}}{12}\right)
plumb=90θseat=θ\text{plumb} = 90^{\circ} - \theta \qquad \text{seat} = \theta

Worked field example

28-foot span, 7:12 pitch, 16-inch eave, 42-foot building length. Not the 24-foot / 6:12 / 12-inch default on the form.

Run is 14 feet. Multiplier for 7:12 is 1+(7/12)2=1.1577\sqrt{1+(7/12)^{2}}=1.1577. Common rafter to the plate is 14 × 1.1577 = 16.21 feet (194.5 inches). The 16-inch eave adds 16 × 1.1577 = 18.5 inches on the slope, so stock to the fascia is about 17.75 feet. Ridge rise from the plate is 14 × 7 = 98 inches. Plumb is 90 − 30.26 = 59.74°; seat is 30.26°.

Order commons from that line length plus cutoff, not from the 42-foot ridge. Hip and valley squares are a different takeoff — use the squares calculator.

What IRC R905 actually limits

R905 is a covering chapter, not a rafter-span table. It sets the lowest pitch a given product may see. Framing spans, snow, and wind live in the lumber tables and the engineer's drawing. This tool does not size those.

Covering minimums — not rafter design

Provision
IRC R905.2
Limit
Asphalt shingles generally 2:12 min; many makers want 4:12 without extra underlayment
Failure mode
Shingles on a 2:12 without the ice-and-water the label requires
Provision
IRC R905.3–.4
Limit
Clay/concrete tile and metal have their own min slopes
Failure mode
Using the shingle 2:12 number on tile
Provision
IRC R802 (not computed)
Limit
Rafter span, species, snow, ridge connection
Failure mode
Treating a line length as a span rating

Where the field usually goes wrong

Measuring rise in the attic from the joist to a collar, then treating that as the 12-inch-run pitch, mixes two different triangles. The collar is not 12 inches of run from the plate. Use a level and a 12-inch square on the rafter itself, or compute from span and ridge height.

Cutting hips to the common length is the next miss. A regular hip runs 17 inches on the level for every 12 of common run. Valley steel is a squares problem, not a 10 percent fudge on a common. An offset ridge needs two runs, not span ÷ 2. Heel height has to match; a deeper seat on one common drops the fascia.

Frequently asked questions

What is the difference between pitch and slope?

On a modern job they mean inches of rise per 12 of run. Older texts used pitch as rise over full span. If a drawing says 1/4 pitch it may mean 6:12.

Why is run half the span?

Only on a centered gable. A shed, saltbox, or offset ridge uses a different run. Punch the actual run.

Do I include the overhang in the common length?

Line length to the plate does not. Stock to the fascia is line length plus (overhang × multiplier).

Can I use this length for hip and jack rafters?

No. Commons only. Hips, valleys, and jacks use different triangles.

Where do I convert pitch to roofing squares?

On the roofing-squares page. This tool’s square figure is a gable estimate only.

Does a 2:12 roof take asphalt shingles?

R905.2 allows some products at 2:12 with the listed underlayment. Many architectural shingles still want 4:12. Read the wrapper.

What are plumb and seat cuts?

Plumb is the ridge cut at 90° minus pitch. Seat is the birdsmouth level cut, equal to the pitch angle.