Roof pitch calculator degrees, ratio and rafters
Enter the rise and the span or run of a roof to get its pitch in degrees, the ratio, the rafter length and, if you add the roof length, the area on the slope. Free, for roofers, carpenters and anyone checking whether a tile will work on their roof. Your measurements are kept in this browser only and never sent to us.
- Pitch in degrees and as x in 12
- Rafter length and roof area on the slope
- Minimum pitches from Marley and Redland
Pick dual or mono pitch and whether you know the span or the run, then enter the rise and that measurement in millimetres. The overhang is optional and starts at 0.
The working
| Run | 3,600 mm |
|---|---|
| Pitch: tan⁻¹(2,400 ÷ 3,600) | 33.69° |
| Slope: √(2,400² + 3,600²) | 4.327 m |
Check the tile or slate maker's minimum pitch for your product and exposure zone before you choose a covering.
How the calculator finds the pitch
Roof pitch is the angle between the rafter and the horizontal. It comes from two measurements: the rise, which is the vertical height from the wall plate to the ridge, and the run, which is the horizontal distance the rafter covers. On a dual pitch roof the run is half the span. On a mono pitch or lean-to it is the full width, so choose Run (one slope) and enter that width as the run.
The rise and run make a right-angled triangle with the rafter as its long side. So the pitch is the inverse tangent of rise ÷ run, and the rafter length is the square root of rise² + run², plus any overhang you enter. The calculator shows that working step by step.
It opens on this example: a dual pitch roof with a span of 7,200mm, a rise of 2,400mm and a roof 9m long.
- Run: 7,200 ÷ 2 = 3,600mm.
- Pitch: inverse tangent of 2,400 ÷ 3,600 (0.667) = 33.7°.
- Ratio: 12 × 2,400 ÷ 3,600 = 8 in 12, which is a rise of 1 for every 1.5 of run.
- Rafter length, wall plate to ridge: √(2,400² + 3,600²) = 4,327mm.
- Roof area on the slope: 4.327 × 9.0 × 2 slopes = 77.9m². The floor plan under it is only 7.2 × 9.0 = 64.8m², so the slope adds about a fifth.
Measuring the rise and the run
Take both measurements from the same reference points, or the angle comes out wrong. For a new roof, work from the drawings: the span between the outside faces of the wall plates and the height of the ridge above the plate. For an existing roof, the easiest place to measure is inside the loft.
In the loft, use a spirit level and a tape. Hold one end of a 1m level against the underside of a rafter, get it level, then measure straight up from the free end to the rafter. That gap is the rise over 1,000mm of run. Choose Run (one slope), then enter 1,000 as the run and your gap as the rise. A gap of 470mm gives 25.2°.
A digital angle finder laid on the rafter does the same job faster. Check it on two or three rafters, because old cut roofs sag and one rafter can read a degree or two out.
Do not measure along the slope and call it the run. The run is always horizontal. A rafter of 4,327mm at 33.7° only covers 3,600mm of building.
Minimum pitch by roof covering
Every tile and slate has a minimum pitch set by its maker. Below it, rain blown up the slope can get past the laps. The figure depends on the exact product, its finish and the headlap (how far each course overlaps the one below), and makers ask you to talk to them on long rafters or exposed sites. These are the published figures for some common products:
Marley Modern (concrete interlocking)
17.5° smooth at 100mm headlap, 22.5° at 75mm. Granular finish needs 25° at 100mm or 30° at 75mm. From the Marley Modern product page.
Redland 49 (concrete interlocking)
Through colour: 17.5° at 100mm headlap, 25° at 75mm. Granular: 22.5° at 100mm, 30° at 75mm. From BMI's Redland 49 product page.
Low pitch concrete tiles
Marley lists Mendip 12.5 down to 12.5° and Mendip and Wessex at 15° in its minimum pitch guide.
Plain tiles (concrete and clay)
35°. Marley's concrete Plain tile is 35° in the same guide, and BMI gives Redland Rosemary Clay Classic as 35° at 100mm headlap.
Natural slate
20° is the floor, and only with long slates and a big headlap in moderate exposure. Cupa Pizarras quotes BS 5534 as 20° for a 500mm slate with a 115mm lap. On a steeper roof the slate needs less headlap.
Worked example: a lean-to that is too flat
Low lean-to roofs are where pitch catches people out. Say a rear extension projects 3,000mm from the house, and there is only room for 750mm between the wall plate on the extension and the bottom of the bedroom window above. Select mono pitch and Run (one slope), then enter a run of 3,000 and a rise of 750:
- Pitch: inverse tangent of 750 ÷ 3,000 (0.25) = 14.0°.
- Ratio: 3 in 12, or 1 in 4.
- Rafter length: √(750² + 3,000²) = 3,092mm to the wall plate.
- What that rules out: plain tiles at 35°, Marley Modern and Redland 49 at 17.5°, and Mendip at 15°. Of the Marley products above, only Mendip 12.5 is listed that low.
- The options: raise the abutment, shorten the projection, or choose a covering made for low pitches. Lifting the rise to 950mm gives 17.6°, which brings the smooth interlocking tiles at 100mm headlap back in.
Degrees, ratios and slope factors
UK tile makers give minimum pitches in degrees. American apps and some timber guides use a ratio of rise to 12 units of run. The calculator shows both, so you can check one against the other.
The slope factor is the rafter length divided by the run. Multiply a plan area by it to get the area on the slope, which is what you buy membrane, battens and tiles for. These are worked from the same trigonometry as the calculator:
- 15°: 3.2 in 12, slope factor 1.035.
- 22.5°: 5.0 in 12, slope factor 1.082.
- 30°: 6.9 in 12, slope factor 1.155.
- 35°: 8.4 in 12, slope factor 1.221.
- 40°: 10.1 in 12, slope factor 1.305.
- 45°: 12 in 12, slope factor 1.414. Rise equals run.
What the calculator does not do
It gives the geometry of a simple roof. It does not design one. Rafter and joist sizes depend on span, spacing, timber grade and loads, and trussed rafters are designed by the truss maker. Use the figures here to plan and price, then check them against the structural design.
With the overhang at 0, the rafter length runs from the wall plate line to the ridge line. The overhang field takes the eaves overhang measured along the slope and adds it to the rafter length and the roof area. If you know the horizontal overhang, divide it by the cosine of the pitch first: 300mm at 33.7° is 300 ÷ 0.832 = 361mm along the slope. Take off half the ridge board where the rafters meet it, and mark the birdsmouth from the actual plate.
It treats each slope as a plain rectangle. Hips, valleys, dormers and roofs with two different pitches need working out slope by slope.
The minimum pitches above are the makers' starting points, not a sign-off. Marley's page asks you to contact its technical team where the roof slope is over 6m long or the site is in a severe exposure category, and Welsh Slate says its slate recommendations apply to rafters up to 9m in moderate exposure and 6m in severe. Check the data sheet for the exact tile you are quoting.
Pricing the re-roof? The area on the slope is the number to build the quote from. Set your labour with the day rate calculator and put the area, the tile and its headlap in a written quote.
Common questions
How do I calculate roof pitch?
Divide the rise by the run and take the inverse tangent. On a dual pitch roof the run is half the span. A rise of 2,400mm over a run of 3,600mm is 33.7°.
How do I measure the pitch of my roof?
From inside the loft, hold a 1m spirit level level against the underside of a rafter and measure up from its free end to the rafter. Choose Run, then enter that gap as the rise and 1,000 as the run. An angle finder on the rafter also works.
How do I work out rafter length from pitch and span?
Halve the span to get the run, then divide the run by the cosine of the pitch. A 6m span at 35° gives 3,000 ÷ 0.819 = 3,662mm to the wall plate, before any overhang.
What is the minimum pitch for concrete roof tiles?
It depends on the tile. Marley Modern and Redland 49 in smooth finish go to 17.5° at 100mm headlap. Marley Mendip 12.5 goes to 12.5°. Granular finishes and shorter headlaps need more.
What is the minimum pitch for plain tiles?
35° for both Marley's concrete plain tile and Redland's Rosemary Clay Classic. Plain tiles are double lap tiles, and they need the steeper slope to shed water.
What is the minimum pitch for a slate roof?
20° at the very lowest, for long slates with a large headlap in moderate exposure. The headlap you need grows as the pitch falls and the site gets wetter and windier, so check the slate maker's headlap tables for your slate size and location.
How do I convert a roof pitch ratio to degrees?
Divide the first number by the second and take the inverse tangent. 6 in 12 is 0.5, which is 26.6°. 12 in 12 is 45°.
How do I work out the area of a pitched roof?
Multiply the rafter length by the length of the roof, then by the number of slopes. Or multiply the plan area by the slope factor. Hips and valleys need each slope worked out separately.
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