ConstructionCalculations

Roof Pitch Calculator

Enter the pitch — or a rise and run you measured — plus the horizontal run or span, and this tool returns the common rafter length, the hip/valley rafter length, the ridge rise, the roof angle, and (with a footprint) the sloped area in roofing squares.

Pitch and run

Example: 6/12 pitch on a 12 ft run → common rafter 13.42 ft, hip/valley 18 ft.

Units

… or leave the pitch blank and enter a measured rise over run (any matching units):

Enter a pitch and a run to size the rafters.

Quantity and geometry estimates only — rafter lengths run to the ridge centerline with no structural sizing, code compliance, or engineering. Verify dimensions and local code with a professional before cutting.

Two factors, one pitch

A common rafter is the hypotenuse over 12 in of run and the pitch of rise, so its length per foot of run is √(1 + (pitch ÷ 12)²). The worked roof at 6/12: factor 1.118, so a 12 ft run cuts a common rafter of 13.4164 ft rising 6 ft at 26.6°. A hip or valley rafter crosses the corner diagonally — 12√2 ≈ 16.97 in of plan run per 12 in of common run at the same rise — giving √(2 + (pitch ÷ 12)²): exactly 1.5 at 6/12, so the hip rafter runs 18 ft. Both factors are verified against published framing references (see the methodology page).

Pitch also stretches area: a 1,500 sq ft footprint at 6/12 carries 1,677.05 sq ft of actual surface — 16.77 roofing squares. Take the squares to the Roofing Shingle Calculator to turn them into bundles with waste applied.

Pitch-angle chart (printable)

Pitch Roof angle Common factor Hip/valley factor Rafter per 10 ft of run
1/12 4.8° 1.003 1.417 10.03 ft
2/12 9.5° 1.014 1.424 10.14 ft
3/12 14° 1.031 1.436 10.31 ft
4/12 18.4° 1.054 1.453 10.54 ft
5/12 22.6° 1.083 1.474 10.83 ft
6/12 26.6° 1.118 1.5 11.18 ft
7/12 30.3° 1.158 1.53 11.58 ft
8/12 33.7° 1.202 1.563 12.02 ft
9/12 36.9° 1.25 1.601 12.5 ft
10/12 39.8° 1.302 1.641 13.02 ft
11/12 42.5° 1.357 1.685 13.57 ft
12/12 45° 1.414 1.732 14.14 ft

Every row is generated at build time by the same rafterCalc engine the form calls. The Print the pitch chart button strips the site chrome so the chart and any results on screen print on one sheet for the job box.

Frequently asked questions

How do I measure my roof pitch?

Hold a level horizontally against the rafter (from the attic) or the roof surface, mark 12 inches along the level, and measure vertically from that mark down to the surface. That vertical distance is the rise in inches per 12 inches of run — enter it directly, or enter any rise/run pair you measured and the tool normalizes it.

What is the difference between the common rafter and the hip rafter figure?

A common rafter climbs straight up the slope, so its length per foot of run is √(1 + (pitch/12)²). A hip or valley rafter crosses the building corner at 45° in plan — about 17 inches of diagonal run for every 12 inches of common run — while climbing the same rise, which makes its factor √(2 + (pitch/12)²). At 6/12 those factors are 1.118 and exactly 1.5.

Is the rafter length the board I should order?

It is the slope distance from the wall plate to the ridge centerline. Framers deduct half the ridge-board thickness, add the overhang and tail cut, and cut the birdsmouth — so order stock longer than the figure. Structural sizing (species, grade, depth, spacing) is a separate engineering question this tool does not touch.

How does pitch change the shingle order?

The same footprint carries more roof surface as the pitch steepens: the sloped area is the footprint times the slope factor. Enter your footprint here for area and squares, then take the squares to the Roofing Shingle Calculator to convert them into bundles with waste.

What angle is a 6/12 roof?

atan(6/12) ≈ 26.6° from horizontal. The printable chart lists the angle and both rafter factors for every whole pitch from 1/12 to 12/12 — each row computed by the same functions the form calls.

Related tools: the Roofing Shingle Calculator turns squares into bundles, the Stair Calculator applies the same rise-run trigonometry to stringers, and the Feet & Inches Calculator chains the tape-measure math for layout.

Roof figures are computed locally and never transmitted. Formula sources and the shared pipeline are documented on the methodology page.