Why a 6 pitch is not six degrees#
The “6” is a vertical rise for each 12 horizontal units. A 6
roof rises half as much as it runs horizontally, so its slope is 0.5. Its angle is approximately 26.565° and its percent grade is 50%. Each describes the same geometry with a different unit or ratio.| Pitch | Angle, approximately | Area factor |
|---|---|---|
| 3 | 14.036° | 1.030776 |
| 4 | 18.435° | 1.054093 |
| 6 | 26.565° | 1.118034 |
| 8 | 33.690° | 1.201850 |
| 12 | 45° | 1.414214 |
The Roof Pitch Calculator accepts any of these measurements and returns the others without rounding pitch to the nearest whole inch. A measured slope may be 4.03
rather than exactly 4.Run and span: the factor-of-two mistake#
For a symmetrical gable spanning 27 ft, each roof face has a 13.5 ft horizontal run. At 7
pitch, rise is 13.5 × 7/12 = 7.875 ft, or 7 ft 10.5 in. The point-to-point diagonal is √(13.5² + 7.875²), approximately 15.628 ft.Using 27 ft as the run would double both the rise and diagonal. Full-span mode is appropriate only for that symmetrical gable relationship. For a shed roof, unequal gable or one face of a complex roof, enter the actual run associated with that face.
Geometric slope length is not a cut list#
If a 6
roof has a 12 ft run and a 1 ft horizontal eave overhang, the geometric line including the overhang is 13 × 1.118034 = 14.534 ft. That line does not locate cuts or size the member. Ridge thickness, bearing geometry, birdsmouth details, connections and loads require the construction plan.The sketch in the calculator is a schematic aid. Steep slopes are compressed to keep the illustration readable; use the numeric results rather than scaling the drawing.
Convert horizontal projection into roof surface#
For a uniform pitch, each projected square foot is stretched by the slope factor. A 40 × 30 ft projection at 6
pitch gives 1,200 × 1.118034 = 1,341.641 ft² of sloped surface. If the estimator chooses a 10% material allowance, that becomes 1,475.805 ft².Include all overhangs in the horizontal projection dimensions before applying the factor. The separate eave input controls the reported slope length and does not change these area dimensions. Use the Square Footage Calculator for non-overlapping projection sections.
Roof shapes with different pitches#
Calculate each pitch separately, then add the sloped areas. Do not average two pitch numbers and apply the average factor to the whole building: the square-root relationship is nonlinear. Openings and uncovered sections also need the corresponding projected area removed before multiplication.
A roofing square is 100 ft² of surface. It is a measurement unit, not a universal number of shingle bundles. Product package coverage, valleys, hips, starter strips and layout waste require a separate purchase takeoff.
Source and limits#
Johnson Level’s construction calculator manual illustrates roof angle conversions and the 27 ft span example. The formulas and area examples above follow right-triangle geometry. This guide does not determine structural capacity, code compliance or whether a specific roof covering is permitted at a given pitch.