Roof pitch converter: X in 12, degrees and rafter length
Published · Updated · By Sai Nath
Free roof pitch calculator: convert X in 12, degrees and per cent, or find the pitch and rafter length from a rise and run.
Source: Lysaght Custom Orb minimum slope.
Roof pitch calculator
This calculator needs JavaScript, which is turned off or didn't load. You can still do it by hand: the formulas and worked examples below give the same answers.
Pitch in any form, or from a rise and run, and the rafter line length. The same maths as the Pitch calculator in the MeisterCalc app.
This free roof pitch calculator converts a pitch between X in 12, degrees and per cent, works it out from a rise and run, and gives the rafter line length with the overhang, in millimetres or feet and inches, with the same maths as Pitch in the MeisterCalc app.
Roof pitch is rise ÷ run. Multiply it by 12 for X in 12, or take its arctangent for degrees: 6 in 12 is a slope of 0.5, 26.57° and a 50% grade. The rafter line length is the run plus the level overhang, times √(1 + slope²): 4000 + 450 mm at 6 in 12 is 4975.3 mm. The least pitch a roof covering needs comes from its maker and the building code: Lysaght, for one, lists a 5° minimum roof slope for Custom Orb corrugated steel.
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How does the roof pitch calculator work?
Every way of writing a roof pitch is the same number, the slope: how far the roof rises for each unit it runs across, measured level. The calculator turns what you type into the slope and writes it out. These are the formulas MeisterCalc's Pitch calculator uses.
- Slope = rise ÷ run, both in the same unit.
- X in 12 = slope × 12. A 6 in 12 roof rises 6 inches for every 12 inches of run. It also shows to the nearest 1/16, the way the app writes it: 3.215 in 12 reads 3-3/16.
- Angle = arctan(slope), in degrees. From an angle, slope = tan(angle), for angles above 0° and below 90°.
- Grade = slope × 100 per cent. 100% is 45°.
- Rise = run × slope, and the rafter line from the wall line to the ridge = √(rise² + run²). That is the app's Hypotenuse.
The rafter part follows from the same right triangle. Divide √(rise² + run²) by the run and you get √(1 + slope²), the slope factor: the length along the roof for each unit of level run. A level overhang sits on the same slope, so it is that factor longer along the rafter. So the rafter line length with the overhang = (run + overhang) × √(1 + slope²), which is what the app's Pitch calculator gives as Hypotenuse if you enter the run with the overhang added.
Worked example: a 6 in 12 roof
- Slope = 6 ÷ 12 = 0.5. Angle = arctan(0.5) = 26.57°. Grade = 50%.
- Slope factor = √(1 + 0.5²) = 1.1180.
- Run of 4000 mm (an 8000 mm span): rise = 4000 × 0.5 = 2000 mm.
- Rafter line to the wall line: √(2000² + 4000²) = 4472.1 mm.
- A 450 mm overhang along the rafter: 450 × 1.1180 = 503.1 mm.
- Rafter line length with the overhang: 4450 × 1.1180 = 4975.3 mm.
Worked example: 22.5° on an 8000 mm span
- Slope = tan(22.5°) = 0.4142, which is 4.97 in 12 (5 to the nearest 1/16) and a 41.42% grade.
- Run = 8000 ÷ 2 = 4000 mm. Rise = 4000 × 0.4142 = 1656.9 mm.
- Slope factor = √(1 + 0.4142²) = 1.0824. Rafter line to the wall line: 4000 × 1.0824 = 4329.6 mm.
- With a 450 mm overhang: 4450 × 1.0824 = 4816.6 mm, of which 487.1 mm is the overhang.
Adding the 450 straight onto 4329.6 would give 4779.6 mm, 37 mm short. The same example, with the cut allowances, is in rafter length from pitch and span.
Worked example in feet and inches
Choose Feet and inches and enter a 6 in 12 pitch, a 12 ft run (a 24 ft span) and a 12 in overhang. The calculator works in millimetres inside and shows lengths to the nearest 1/16":
- Rise: 12 ft × 0.5 = 6' 0".
- Rafter line to the wall line: 144 in × 1.1180 = 161.0 in, which is 13' 5".
- Overhang along the rafter: 12 in × 1.1180 = 1' 1 7/16".
- Rafter line length with the overhang: 156 in × 1.1180 = 14' 6 7/16".
Common roof pitches
| X in 12 | Degrees | Grade, % | Slope factor |
|---|---|---|---|
| 1 in 12 | 4.76 | 8.33 | 1.0035 |
| 2 in 12 | 9.46 | 16.67 | 1.0138 |
| 3 in 12 | 14.04 | 25 | 1.0308 |
| 4 in 12 | 18.43 | 33.33 | 1.0541 |
| 5 in 12 | 22.62 | 41.67 | 1.0833 |
| 6 in 12 | 26.57 | 50 | 1.1180 |
| 7 in 12 | 30.26 | 58.33 | 1.1577 |
| 8 in 12 | 33.69 | 66.67 | 1.2019 |
| 9 in 12 | 36.87 | 75 | 1.2500 |
| 10 in 12 | 39.81 | 83.33 | 1.3017 |
| 12 in 12 | 45 | 100 | 1.4142 |
All values come from the formulas above, rounded. Multiply the level run by the slope factor for the rafter line length: a 4000 mm run at 9 in 12 is 4000 × 1.25 = 5000 mm. Roofs in Australia and the UK are usually given in degrees: 15° is 3.22 in 12, 22.5° is 4.97, 30° is 6.93 and 35° is 8.40. For a longer chart, see roof pitch to degrees.
What the rafter length is, and isn't
The rafter line length is the straight distance along the rafter's line, from the centre line of the ridge to the tail, for the run and overhang you enter. It is the figure to set out from, not a cut list. Before cutting, allow for:
- The ridge. The run is to the ridge's centre line, so shorten the rafter by half the ridge board thickness, measured level, times the slope factor.
- The birdsmouth and plumb cuts. Where the rafter sits on the wall plate and how the tail is cut change the timber length, not the line length.
- A level fascia line. If the overhang is set by a fascia height rather than a level distance, work out the level overhang first.
Rafter sizes and spacing come from span tables, the engineer or the truss maker, not from this sum. In Australia, see the NCC Housing Provisions and AS 1684; elsewhere, your local code.
Pitch, slope and span: avoid the mix-ups
- Run is half the span on a gable roof. X in 12 uses the run from the wall to the ridge's centre line, not the full width of the building. Using the full span halves the pitch.
- Some sources call rise ÷ span the pitch. A rise of one quarter of the span is a pitch of 1/4 in that style, but the slope is rise ÷ run = 0.5, which is 6 in 12 and 26.57°.
- The overhang is level. Measure how far the eaves stick out from the wall, level, and let the slope factor turn it into a length along the rafter.
- Grade is not degrees. A 33% grade is 18.26°, not 33°. Enter it in the per cent box.
For slopes that are not roofs, such as falls, ramps and land, the slope calculator gives 1 in X, per cent, degrees and millimetres per metre.
Questions people ask
How do I convert roof pitch to degrees?
Divide the pitch by 12 and take the arctan: for 6 in 12, arctan(6 ÷ 12) = 26.57°. The calculator does it when you type the pitch in the first box.
What is a 4/12 pitch in degrees?
arctan(4 ÷ 12) = 18.43°, a 33.33% grade.
How do I calculate rafter length?
Add the level overhang to the run, then multiply by the slope factor √(1 + slope²), or divide by the cosine of the angle. 4450 mm at 6 in 12 is 4450 × 1.1180 = 4975.3 mm.
How do I find the pitch of an existing roof?
Hold a level against the underside of a rafter, measure 12 in (or 300 mm) along the level, and measure straight up to the rafter. That is the rise for that run. Enter both in The rise and run. More in how to calculate roof pitch.
What is a 5/12 pitch in degrees?
22.62°: the slope is 5 ÷ 12 = 0.4167, a 41.67% grade, and its arctangent is 22.62°. The common roof pitches table above has 1 in 12 to 12 in 12.
Is 45 degrees a 12 in 12 pitch?
Yes. At 45° the rise equals the run, so the slope is 1, the grade is 100% and the pitch is 12 in 12.
What this calculator doesn't do
- Common rafters only: no hip, valley or jack rafters, birdsmouths, plumb cuts or ridge deductions, and no roof area.
- It doesn't say what pitch a roof needs. The least pitch for a roof covering is set by the product maker, the building code and your council.
- Values must be greater than 0, and angles under 90°. Results are rounded for display: two decimal places for the pitch, millimetres to one place, inches to the nearest 1/16".
Add this calculator to your site
You can put the calculator on your own page for free. Copy the code below. It loads the tool from MeisterCalc and includes a link to the MeisterCalc roof pitch calculator.
Pitch in MeisterCalc
The same maths is in MeisterCalc's Pitch calculator (Home ▸ Pitch). You pick which two values you know, such as Rise + Run, Run + Pitch or Run + Angle, and it shows Pitch, Angle, % Grade, Slope Ratio and Hypotenuse, with a live diagram. For a rafter line length, enter the run with the overhang added; it doesn't do hips, valleys or cuts. It works offline on site, on Android 7.0 or later. Pitch is one of the 13 calculators that unlock with a weekly subscription that starts with a 3-day free trial, or a one-time lifetime unlock; Google Play shows the prices in your currency. Concrete, Stairs and Check Square are free. More in the roof pitch calculator app for Android.