What the Roof Pitch Calculator does
This calculator converts a roof pitch between its common forms - rise per 12 (such as 6/12), degrees, percentage slope and a rise-to-run ratio - and uses it to work out rafter length, ridge height, the true area of the roof surface, roofing squares and the number of sheets or bundles to order.
It rests on one fact that makes roof estimating simple: for any roof whose planes all share the same pitch - gable, hip or mono-pitch - the sloping area equals the plan area multiplied by the pitch factor, 1 / cos(angle).
How to use it
- Choose how you know the pitch: as x in 12, in degrees, as a percentage, or from a rise and run you measured with a level and tape.
- Choose metres or feet and the roof type. For a gable roof the run of each rafter is half the building width; for a mono-pitch (shed) roof it is the full width.
- Enter the building width (eaves to eaves) and length, and the eaves and gable overhangs.
- Optionally enter the coverage of one sheet or bundle in the same unit and a waste allowance, to get the number to order.
Reading the results
The pitch table shows the same slope in every form. 6/12, 26.57 degrees, 50% and 1:2 all describe the same roof.
The common rafter length runs from the ridge to the end of the eaves overhang along the slope; the wall-to-ridge figure excludes the overhang. Neither includes the ridge board thickness or the birdsmouth cut.
Roof area is the sloping surface including overhangs. A roofing square is 100 sq ft of it, the unit shingles are sold by in North America.
Worked example: a 6/12 gable roof
A house is 8 m wide and 10 m long, with 0.5 m eaves and 0.3 m gable overhangs, roofed at 6/12. That pitch is atan(6 / 12) = 26.57 degrees, a 50% slope, and its pitch factor is √(1 + 0.5²) = 1.1180.
Each rafter runs half the width, 4 m, so the ridge is 4 x 0.5 = 2 m above the wall plate. With the eaves overhang the rafter covers 4.5 m of run: 4.5 x 1.1180 = 5.03 m along the slope.
The plan area with overhangs is (10 + 2 x 0.3) x (8 + 2 x 0.5) = 10.6 x 9 = 95.4 m², so the roof surface is 95.4 x 1.1180 = 106.7 m², or 11.48 squares. With sheets covering 1.5 m² and 10% waste, order 106.66 x 1.1 / 1.5 = 78.2, so 79 sheets.
Formulas and scoring rules
- Pitch conversions
tan(angle) = rise / run; x in 12 = 12 x tan; percent = 100 x tan; angle = atan(rise / run)- Pitch factor
factor = 1 / cos(angle) = √(1 + (rise / run)²)- Rafter
common rafter = (run + eaves overhang) x factor; ridge rise = run x tanrun is half the span for gable and hip roofs, the full span for a mono-pitch.- Roof area
area = plan area including overhangs x factorTrue for gable, hip and mono-pitch roofs when every plane has the same pitch.- Hip rafter
hip = √(2 x run² + rise²)For a hip roof with equal pitches, measured corner to ridge without overhang.- Ordering
squares = area in sq ft / 100; sheets = ceil(area x (1 + waste) / cover per sheet)
Limitations: what the result does not prove
- Roofs with planes at different pitches, dormers, valleys between different roofs or curved sections need each plane calculated separately.
- Rafter lengths are geometric. Cutting lengths depend on the ridge board, birdsmouth depth, fascia detail and timber sizes.
- Every roofing material has a minimum pitch and its own coverage and lap rules. Check the manufacturer's figures before choosing a pitch or ordering.
- Structural questions - rafter size and spacing, snow and wind loads, bracing - are for a structural engineer and your local building code.
Privacy: where your data goes
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Standards and sources
- International Code Council - International Residential Code 2021, Chapter 9 Roof assemblies
- NIST - Unit conversion
Frequently asked questions
How do I convert roof pitch to degrees?
Divide the rise by the run and take the arctangent. A 6/12 pitch is atan(0.5) = 26.57 degrees; 4/12 is 18.43 degrees; 12/12 is 45 degrees. Enter any form in the calculator to see all the others.
What does a 4/12 roof pitch mean?
The roof rises 4 units for every 12 units of horizontal run - 4 inches per foot in US practice. It is an 18.4 degree slope, or 33.3%. The same notation works in any unit because it is a ratio.
How do I calculate roof area from the footprint?
Multiply the plan area, including overhangs, by the pitch factor 1 / cos(angle). For a 6/12 roof the factor is 1.118, so a 100 m² footprint has about 111.8 m² of roof surface. This works for gable, hip and mono-pitch roofs with one pitch.
How long is a rafter for my roof?
Multiply the horizontal run - half the building width for a gable roof, plus the eaves overhang - by the pitch factor. An 8 m wide house at 6/12 with 0.5 m eaves has rafters of 4.5 x 1.118 = 5.03 m along the slope, before cutting allowances.
How do I measure roof pitch myself?
Hold a spirit level horizontally against the underside of a rafter or on the roof surface, measure 12 inches (or 1 m) along it, and measure straight up from that point to the roof. Enter the rise and run you measured; the calculator gives the pitch in every form.
What is a roofing square?
It is 100 square feet of roof surface (about 9.29 m²). Shingles in North America are priced and sold by the square, usually as three bundles per square; check the coverage printed on your product.
Last reviewed by the A2Z.Tools team against the sources listed above.
