Why use this calculator
Roof pitch is quoted three different ways on the same job. The plans give degrees, the roofer talks in rise per twelve, and the material supplier wants an area in squares or square metres. Converting between them by hand is where mistakes creep in, and the mistake that costs money is forgetting the slope factor entirely: a roof is always larger than the building it sits on, and on a steep pitch it is dramatically larger.
Ordering tiles or sheets against the floor plan leaves you short, and being short on the last row of a roof means a second delivery, a second scaffold hire and a weather risk. This calculator gives all three representations at once along with the rafter length you need to cut to.
How to use it
- Pick metric or imperial first, since that governs the span, length and overhang but not the pitch ratio, which is always expressed as rise per twelve units of run regardless of system.
- Then tell the calculator how you know the pitch: choose ratio if you have a figure like six in twelve from a roofer, or degrees if you are reading it off a drawing.
- Enter the building span measured across the gable from outside wall to outside wall rather than along the ridge, then the length along the ridge line, and finally how far the eaves project past the wall, entering zero for a flush gable end.
What each result means
- Total roof area
- The real surface to be covered, including eaves and the effect of the slope. Order materials against this figure, then add wastage.
- Rafter length per side
- Along the slope from the wall plate to the ridge, including the overhang. Cut length before the birdsmouth and ridge plumb cut are taken off.
- Pitch angle
- The roof's angle from horizontal. Most coverings specify a minimum pitch below which they will not shed water reliably.
- Pitch as a ratio
- Rise per 12 units of run, the form roofers and framing squares use. A 6:12 is the most common residential pitch.
- Slope factor
- Multiply any flat plan area by this to get the sloping area. Forgetting it is the single most common roofing quantity error.
- Ridge height above the wall plate
- How far the ridge sits above the top of the wall, which drives gable cladding, scaffold height and often planning height limits.
- Plan area covered
- The flat footprint including eaves. It is what the roof shades, not what it takes to cover it.
- Roofing squares
- One square equals 100 square feet of roof surface. North American suppliers and quotes almost always use this unit.
The formula
Pitch angle in degrees = arctangent of rise divided by run
The slope factor, also called the pitch multiplier, is 1 divided by the cosine of that angle, which is equivalent to the square root of 1 plus rise over run squared.
Rafter length per side = (half the span plus the overhang) multiplied by the slope factor
Ridge height above the wall plate = half the span multiplied by the tangent of the angle
Plan area = (span plus twice the overhang) multiplied by (length plus twice the overhang)
Total roof area = plan area multiplied by the slope factor
How this number is used in practice
Minimum pitch is a covering specification, not a style preference, and getting it wrong causes leaks that no amount of sealant fixes. Concrete and terracotta tiles generally need at least 15 to 20 degrees unless the manufacturer approves a low-pitch system with sarking. Asphalt shingles are typically rated to 4:12 as standard and down to 2:12 only with a double underlayment.
Corrugated and trapezoidal metal sheets go lower, often to 5 degrees, and standing seam lower still. Always check the specific product's minimum before committing to a pitch, because the covering you want may not be available for the roof you have drawn.
The slope factor is where budgets go wrong. A 4:12 roof is only 5 per cent larger than its footprint, which most people absorb without noticing. A 12:12 roof is 41 per cent larger, so the same house footprint needs roughly 40 per cent more tiles, battens, sarking, fixings and labour.
When someone increases a pitch late in design for appearance or for attic space, the material cost rises along a curve they usually have not been shown, and the labour cost rises faster still because a steep roof needs anchors, edge protection and slower work.
For cutting, remember this calculator gives the theoretical rafter length along the slope from the wall plate to the ridge centreline. A carpenter still deducts half the ridge board thickness at the top and sets out the birdsmouth at the wall plate, and on a hip or valley the common rafter length here is only the starting point, since hips and valleys run at a different and longer effective pitch. Use this figure to order timber lengths and to check a set-out, not as a final cut list.
Worked examples
A 10 m by 14 m building with a 6:12 pitch and 600 mm eaves
Roof area of 190.3 m2, rafter length 6.26 m per side and a ridge 2.50 m above the wall plate
The same building at a 10:12 pitch instead
The slope factor rises to 1.3017 and the roof area climbs to 221.6 m2, some 31 m2 more material
A 32 ft by 48 ft house at 22.5 degrees with 2 ft eaves
About 2,026 ft2 of roof, which is 20.3 roofing squares for ordering shingles
When people use it
- Ordering tiles, sheets or shingles against the true sloping area rather than the floor plan
- Converting a pitch given in degrees on a drawing into the rise per 12 a roofer will use
- Checking whether a chosen roof covering meets its minimum pitch requirement
- Estimating rafter timber lengths and quantities before a delivery
- Working out ridge height for scaffold hire or a planning height limit
Tips
- Always order against the sloping area, never the floor plan. A 12:12 roof is 41 per cent bigger than the building beneath it.
- Check the minimum pitch for your covering before fixing the design. Tiles typically need 15 to 20 degrees, shingles 4:12.
- Measure the span across the gable, wall face to wall face. Measuring along the ridge is the most common input error.
- Add 5 to 10 per cent wastage on a simple roof and 15 per cent or more where there are hips, valleys and penetrations.
- A framing square reads pitch directly as rise per 12, which is why roofers use that form rather than degrees.
- For a hip roof, the common rafters use this length but hips and valleys run longer at a shallower effective pitch.
What it assumes, and where it stops being accurate
- Assumes a simple gable roof with two equal planes. Hips, valleys, dormers and unequal pitches all add area this does not model.
- Assumes the overhang applies equally on all four sides. Many roofs have different eaves and gable overhangs.
- The rafter length is to the ridge centreline and excludes the ridge board deduction, birdsmouth and any plumb cut allowance.
- No wastage allowance is included. Add 5 to 10 per cent for simple roofs and 15 per cent or more where there are many cuts and penetrations.
- Ignores penetrations such as skylights and chimneys, which reduce covering needed but add flashing and labour.
- Structural sizing of rafters is not covered. Span tables and an engineer govern member size, not this geometry.
Terms used on this page
- Pitch
- A roof's steepness, given either as rise per 12 of run or as an angle from horizontal.
- Slope factor
- The multiplier converting flat plan area into true sloping roof area; one over the cosine of the pitch.
- Rafter
- The sloping structural member running from the wall plate to the ridge.
- Wall plate
- The horizontal timber on top of the wall that the rafters bear on.
- Roofing square
- One hundred square feet of roof surface, the standard North American quoting unit.
Questions people ask
- What does a 6:12 pitch mean?
- The roof rises 6 units vertically for every 12 units travelled horizontally, which works out to 26.57 degrees. It is the most common residential pitch because it sheds water well, suits nearly every covering, and remains walkable for maintenance without special equipment.
- Why is my roof area bigger than my floor area?
- Because the roof is sloping and the floor is flat. The slope factor is one divided by the cosine of the pitch angle, so a 6:12 roof is about 12 per cent larger than its footprint and a 12:12 roof is 41 per cent larger. Eaves add more on top.
- What is a roofing square?
- One hundred square feet of roof surface, the unit North American roofers and suppliers quote in. A typical single-storey house roof runs between 15 and 30 squares, and bundles of shingles are usually sold three to the square.
- What is the minimum pitch for tiles?
- Usually 15 to 20 degrees depending on the profile, though some manufacturers approve lower pitches with a fully sarked and battened low-pitch system. Always check the specific product's technical data, because going below the rated minimum will cause wind-driven rain to enter.
- How do I measure pitch on an existing roof?
- Hold a spirit level horizontally against a rafter or the roof surface, mark 12 inches or 300 mm along it, then measure vertically from that mark down to the roof. That vertical measure over the horizontal one is your rise per run directly.
- Does this work for a hip roof?
- The pitch conversion and slope factor apply to any plane, and the area is a reasonable approximation for a simple hip of equal pitch. Hip and valley rafters themselves run at a different effective angle and are longer than the common rafters given here.
Use this with
Roof Pitch and Rafter Calculator answers one part of the question. These pick up where it stops: Stair Rise and Run Calculator, Brick and Block Calculator, Area Calculator and Concrete Volume Calculator.
Where these figures come from
This calculation is jurisdiction-neutral arithmetic. No country-specific rules are applied.
- Australian Building Codes Board: National Construction Code. Roof construction requirements and referenced standards
- International Code Council: International Residential Code. US minimum roof pitch and underlayment requirements by covering
- NHBC Standards. UK guidance on pitched roof design and minimum pitches
Roof Pitch and Rafter Calculator produces an estimate for general information. It is not financial, tax, medical, legal or engineering advice. read the full disclaimer. Spotted a wrong number? Report it and it gets fixed. The form picks up this calculator and the inputs you used.