Roof Pitch Calculator — Free Online Tool

Calculation results

Pitch

— :12

Roof angle

— °

Rise

— ft

Rafter length

— ft

Rafter length is the structural rafter span (run to ridge). Add overhang length separately when cutting full rafter stock.

Informational only. These results are geometric estimates for planning. Structural rafter sizing requires a span table check or engineer review for load, species and grade.

Understanding the formula

All roof pitch calculations are right-triangle geometry: the run is the horizontal leg, the rise is the vertical leg, and the rafter is the hypotenuse.

rafter = √(run² + rise²) · angle = atan(rise / run) · pitch = (rise / run) × 12

The x:12 convention means “X inches of rise for every 12 inches of run”. A 6:12 pitch rises 6 inches for every horizontal foot, giving a 26.6° angle and a slope of 50 %. Converting to degrees is atan(6/12) × 180/π.

Worked example

A house 24 ft wide with a 6:12 pitch (run = 12 ft for a symmetric gable):

Rise = 12 × (6 / 12) = 6 ft
Rafter = √(12² + 6²) = √(144 + 36) = √180 = 13.416 ft
Angle = atan(6/12) = 26.57°
Slope = (6/12) × 100 = 50 %

Common roof pitches at a glance

Reference table for the most common residential pitches:

Pitch	Angle	Slope %	Rafter factor*	Common use
2:12	9.5°	16.7 %	1.014	Low-slope, sheds
4:12	18.4°	33.3 %	1.054	Ranch homes
6:12	26.6°	50.0 %	1.118	Most common residential
8:12	33.7°	66.7 %	1.202	Steeper residential
9:12	36.9°	75.0 %	1.250	Cape cod style
12:12	45.0°	100 %	1.414	Very steep / decorative

* Rafter factor = rafter / run = 1 / cos(angle). Multiply footprint width by this factor to get roof surface width per side.

Common mistakes & tips

Run is half the span. For a symmetrical gable roof on a 24-ft-wide building, the run is 12 ft — not 24 ft. Enter the half-width.
Rafter ≠ rafter stock length. The calculator gives the structural rafter (ridge to wall plate). Add the overhang (tail) separately when ordering lumber.
Check local codes for minimum pitch. Asphalt shingles typically require 2:12 minimum; some materials (standing seam metal, TPO) go lower.
Hip roofs vs. gable roofs. The calculator applies to one plane of a gable roof. Hip roofs have diagonal hip rafters that are longer — use a dedicated hip rafter calculator or add ~15 % to the hip rafter length.

Frequently asked questions

What is a 4:12 roof pitch?

A 4:12 pitch rises 4 inches for every 12 inches of horizontal run, giving an angle of 18.4° and a slope of 33 %. It is a standard low-slope pitch common on ranch-style homes.

What roof pitch is 30 degrees?

A 30° angle equals a pitch of about 6.93:12 (since tan(30°) × 12 = 6.93) and a slope of 57.7 %.

How do I measure roof pitch?

Place a level on the roof, hold it horizontal, and measure 12 inches from one end. At that 12-inch mark, measure vertically up to the underside of the level — that measurement in inches is your pitch (e.g., 4 inches = 4:12).

What is a steep roof pitch?

Pitches above 9:12 (36.9°) are generally considered steep. They shed water and snow efficiently but are more difficult and dangerous to work on. Steep pitches are common on Victorian, Gothic and Cape Cod homes.

What is the run of a roof?

The run is the horizontal distance from the wall plate to directly below the ridge. For a symmetric gable roof, it equals half the building width. For an asymmetric or shed roof, measure the horizontal distance to the high point.

How long is a rafter for a 6:12 pitch on a 24 ft wide house?

The run is 12 ft. Rafter = √(12² + 6²) = √180 = 13.42 ft. Add the overhang length (typically 12–24 in) to get the full rafter stock length.

Roof geometry