Roofing Calculator
Pitch, rafter lengths, true roof area, shingle squares and underlayment — for gable, hip, shed and gambrel roofs, with the waste allowance built in.
Roof type
The building
Pitch — rise in inches per 12 inches of run
Roof area to cover
Rafters
Materials
| Material | Quantity | Basis |
|---|
Pitch reference for this building
| Pitch | Multiplier | Angle | Roof area | Rafter length |
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How to use this calculator
Step by step
- Pick the roof type first — it changes how the slopes are counted, and whether hip rafters apply.
- Enter the building length along the ridge and the width across it, then the horizontal overhang at the eaves. The overhang is included in every area and rafter figure.
- Set the pitch as rise per 12 inches of run — a 6/12 roof rises 6 inches for every foot across. The quick buttons cover every common pitch.
- The pitch multiplier is the number everything else depends on. Multiply your plan area by it to get true roof area; multiply your run by it to get rafter length.
- Set the rafter spacing and ridge thickness for exact rafter lengths, given in both decimal feet and feet-and-inches with sixteenths.
- The materials table converts the roof area into squares, bundles, rolls, sheets and nails, with your waste allowance already applied.
Good to know
- A roofing square is 100 square feet. Everything in the trade is quoted in squares, so the conversion is worth memorising.
- A hip roof covers exactly the same area as a gable of the same pitch and footprint — but it wastes more material, because every hip cut produces an offcut. Raise the waste allowance to 15% or more.
- Rafter length is the run times the pitch multiplier, where the run is half the width for a gable and the full width for a shed. Do not use the width by mistake.
- Half the ridge board thickness comes off each rafter at the top. On a 1½ inch ridge that is ¾ inch per rafter — small, but it matters when the birdsmouth has to land on the plate.
- Above about 8/12 you should not be walking the roof unsupported. Factor staging or roof jacks into the job before you price it.
- Order at least one extra bundle of shingles beyond what you calculate and store it. Matching a discontinued colour years later for a repair is far more expensive.
The maths behind it
- Pitch multiplier k = √( 1 + (rise ÷ 12)² ) The factor that turns plan measurements into slope measurements.
- Roof area A = plan area × k Plan area includes the overhang all round.
- Rafter length L = run × k Run is half the width for a gable, the full width for a shed.
- Hip rafter L = run × √( 2 + (rise ÷ 12)² ) The diagonal run makes the multiplier bigger.
- Pitch angle θ = arctan(rise ÷ 12) A 6/12 roof is 26.57°.
- Squares squares = ft² ÷ 100 The trade unit for roofing material.
- Ridge height h = run × rise ÷ 12 Above the wall plate, before the ridge board.
Why is my roof area so much bigger than my floor area?
Two reasons. The overhang extends the footprint past the walls all round, and the slope stretches every plan dimension by the pitch multiplier. On a 6/12 roof that multiplier is about 1.118, so a sloped roof is 12% larger than the ground it covers before the overhang is even counted. On a 12/12 roof it is 41% larger.
How do I measure the pitch of an existing roof?
Hold a level horizontally against the roof surface, mark 12 inches along it, and measure straight down from that mark to the roof. That vertical distance in inches is your rise, and the pitch is that number over 12. From inside the attic against a rafter is easier and much safer than from on top.
Does a hip roof really use the same amount of material as a gable?
The same area, yes — the surfaces just tilt in four directions instead of two. But the practical material use is higher, because every course running into a hip has to be cut on an angle and the offcut is usually unusable. Budget 15% waste on a hip against 10% on a straightforward gable.
What waste allowance should I use?
Ten percent for a plain gable with no penetrations. Twelve to fifteen for hips. Fifteen to twenty once you add valleys, dormers, skylights or chimneys, because each one produces cuts on both sides. The default of 12% suits a typical house.
Are the rafter lengths measured along the top edge or the centre line?
Along the top edge — from the outside corner of the birdsmouth to the plumb cut at the ridge, with half the ridge board already deducted. That is the measurement you actually mark on the stock. The overhang tail is additional and depends on how you cut it.