Roofing Calculator

Inches of rise per 12 in of horizontal run. 4:12 is a shallow roof, 12:12 is 45 degrees.
Almost always 12.
Added to every side of the footprint before the slope factor is applied.
Overrides the length derived from the footprint. Use this on any roof that is not a simple gable or hip.
NRCA practice: about 10% on a simple gable, 15% or more on a cut-up hip roof with many valleys.
Wrappers state one or the other. Both give the same answer when the two figures agree.
Three for most laminated and three-tab shingles; four or five for heavy shingles.
Read it off the wrapper. The 33.33 default is simply 100 sq ft (one square, per the NRCA definition) divided between three bundles; heavy and specialty shingles cover less.
400 sq ft (4 squares) for a roll of ASTM D226 Type I #15 felt; 200 sq ft for #30.
Linear feet of hip and ridge covered by one bundle of cap shingles.
IRC R905.2.5 requires at least four fasteners per strip shingle; 80 strip shingles per square gives 320. Use 480 for the six-nail high-wind pattern.
Squares to buy
1.160
Roofing Calculator
Pitch
4:12
Rise per 12 in of run
4.0000 in
Slope (pitch) factor
1.054093
Roof angle
18.4349 deg
Slope
33.333 %
Hip / valley factor
1.452966
Hip / valley rafter angle
13.2627 deg
Seat (level) cut angle
71.5651 deg
Horizontal footprint area
100.00 ft2
Actual roof surface area
105.41 ft2
Roof area including waste
115.95 ft2
Roofing squares
1.054
Shingle bundles
4
Underlayment rolls
1
Ridge, hip and valley length
10.00 ft
Hip and ridge cap bundles
1
Eave length (starter strip)
20.00 ft
Drip edge length (full perimeter)
40.00 ft
Common rafter length
5.270 ft
Fasteners needed
372
Worked out from NRCA Roofing Manual: Steep-slope Roof Systems (roof area from plan area x slope factor; one square = 100 sq ft) and 3 other sources.
Perimeter figures (eave, drip edge, rafter length) assume a square footprint because only an area was supplied.
Rafter, truss and sheathing sizing, and the ice-barrier, underlayment and fastening requirements for your wind zone, are set by the building code adopted locally and by the shingle manufacturer's installation instructions. Confirm quantities against a physical measure-up before ordering.

How this is worked out

9 steps
  1. Pitch 4:12 -> slope factor = sqrt(4^2 + 12^2) / 12 = 1.054093
  2. Slope angle = atan(4/12) = 18.4349 deg (33.333% grade)
  3. Hip / valley factor = sqrt(4^2 + 2 x 12^2) / 12 = 1.452966
  4. Hip / valley rafter angle = atan(4 / (12 x sqrt(2))) = 13.2627 deg; seat cut = 90 - 18.4349 = 71.5651 deg
  5. Plan area 100 sq ft x 1.054093 = 105.41 sq ft of roof = 1.054 squares
  6. Waste 10%: 115.95 sq ft = 1.16 squares
  7. Bundles = ceil(1.16 squares x 3) = 4
  8. Underlayment = ceil(115.95 / 400) = 1 roll(s)
  9. Ridge + hip + valley = 10 ft -> ceil(10/20) = 1 cap bundle(s)

Results are general information, not financial, tax, legal, medical or engineering advice.