Metric Roof Pitch Calculator
Reviewed by the My Roof Pitch editorial team · Updated · Free, no sign-up, works offline after first load
Metric roof pitch is usually given in degrees. Divide the rise by the run in the same unit, then take the arctangent: a 1,000 mm rise over a 2,400 mm run is 22.62°. The same slope is a 1 : 2.4 ratio, 41.7 percent, or 5/12 in US terms.
Key takeaways
- Metric roof pitch is usually quoted in degrees: angle = arctan(rise ÷ run).
- A 1 : X ratio is run ÷ rise; 1 : 2.4 is 22.62°, 1 : 1.73 is 30°, 1 : 1 is 45°.
- Most interlocking concrete tiles are rated from about 15° to 22.5°; natural slate usually needs 20° to 25° or more; plain tiles often need 35°.
- Metal sheet and membranes can run much lower — check the manufacturer's published minimum.
- The area multiplier √(rise² + run²) ÷ run converts plan area in m² to sloped roof area.
Your measurements
Enter the values you know — results update live.
Vertical height from the top of the wall plate to the underside of the ridge, or the drop of a mono-pitch roof.
Horizontal distance the rise happens over — half the span for a gable roof, the full depth for a lean-to.
Common pitches
Analysis
Live results from your measurements.
Walkable with care. Most crews still use roof jacks and a harness.
Show the working
- Slope ratio:
1,000 ÷ 2,400= 0.4167 - Angle:
arctan(0.4167)= 22.62° - Ratio 1 : X:
2,400 ÷ 1,000= 1 : 2.4 - Rafter:
√(1,000² + 2,400²)= 2,600 mm - US pitch:
0.4167 × 12= 5:12
What this calculator does
In metric countries roof pitch is normally stated as an angle in degrees, sometimes as a ratio such as 1 : 2.4 or as millimetres of rise per metre. All of these describe the same right triangle as the US X/12 system: the rise of the roof over its horizontal run. This calculator works in millimetres by default but accepts centimetres, metres, inches or feet, so you can take measurements from drawings or from site and get the angle, ratio, rafter length and area multiplier in one step.
How to use it
- Measure the rise: the vertical distance from the top of the wall plate to the underside of the ridge, or the height difference between the high and low ends of a lean-to.
- Measure the run: the horizontal distance the rise covers. For a symmetrical gable roof this is half the building span.
- Enter both values in the same unit. Change the unit beside each field if your measurements are in metres or centimetres.
- Read the pitch in degrees and as a 1 : X ratio, then check it against the minimum pitch for your tile, slate or sheet.
The formula
Pitch in degrees
angle = arctan(rise / run) × (180 / π)
The angle at the eaves of the roof triangle, from horizontal.
Ratio and rise per metre
ratio = 1 : (run / rise); rise per metre = rise / run × 1000 mm
A 1 : 2.4 roof rises 1 mm for every 2.4 mm of run, which is about 417 mm per metre.
Rafter length
rafter = sqrt(rise^2 + run^2)
Length along the slope from plate to ridge, before adding the overhang or deducting half the ridge board.
Worked example
A 4.8 m wide gable roof rises 1,000 mm from wall plate to ridge.
- Run = 4,800 ÷ 2 = 2,400 mm
- Slope = 1,000 ÷ 2,400 = 0.4167
- Angle = arctan(0.4167) = 22.62°
- Ratio = 2,400 ÷ 1,000 = 1 : 2.4
- Rafter = √(1,000² + 2,400²) = 2,600 mm
The roof pitch is 22.62°, a 1 : 2.4 ratio or 41.7 percent slope, and each rafter is 2,600 mm before the overhang — the same slope as a US 5/12 roof.
Reference chart
| Angle (degrees) | Rise per 1 m run (mm) | Ratio 1 : X | US pitch (X/12) | Slope (%) |
|---|---|---|---|---|
| 2° | 35 | 1 : 28.64 | 0.42/12 | 3.5% |
| 5° | 87 | 1 : 11.43 | 1.05/12 | 8.7% |
| 7.5° | 132 | 1 : 7.6 | 1.58/12 | 13.2% |
| 10° | 176 | 1 : 5.67 | 2.12/12 | 17.6% |
| 12.5° | 222 | 1 : 4.51 | 2.66/12 | 22.2% |
| 15° | 268 | 1 : 3.73 | 3.22/12 | 26.8% |
| 17.5° | 315 | 1 : 3.17 | 3.78/12 | 31.5% |
| 20° | 364 | 1 : 2.75 | 4.37/12 | 36.4% |
| 22.5° | 414 | 1 : 2.41 | 4.97/12 | 41.4% |
| 25° | 466 | 1 : 2.14 | 5.6/12 | 46.6% |
| 30° | 577 | 1 : 1.73 | 6.93/12 | 57.7% |
| 35° | 700 | 1 : 1.43 | 8.4/12 | 70% |
| 40° | 839 | 1 : 1.19 | 10.07/12 | 83.9% |
| 45° | 1000 | 1 : 1 | 12/12 | 100% |
Common mistakes
- Using the full span instead of half the span as the run on a gable roof, which halves the calculated angle.
- Mixing units — a rise in mm and a run in metres gives an angle that is wildly wrong.
- Measuring rise to the top of the roof covering instead of the structure; tile batten and tile thickness add 50 to 75 mm.
- Assuming a tile can be used at any pitch. Each tile profile has a tested minimum, and some require extra headlap or underlay near it.
Assumptions and limits
- The roof plane is straight between eaves and ridge.
- Rise and run are measured in the same plane, at right angles to each other.
- Material minimums are typical published values and vary by manufacturer, exposure and local building regulations.
Frequently asked questions
How do I calculate roof pitch in metric?
Divide the rise by the run in the same unit, then take the arctangent. 1,200 mm of rise over 3,000 mm of run is arctan(0.4) = 21.8°.
What is a 1 in 4 roof pitch in degrees?
A 1 : 4 slope is arctan(0.25) = 14.04°, the same as a US 3/12 roof.
What is a 22.5 degree roof pitch as a ratio?
22.5° is a ratio of about 1 : 2.41, or 414 mm of rise per metre of run.
What is the most common roof pitch in Australia?
Many Australian project homes use 20° to 25° for tiled hip roofs and 5° to 15° for metal-sheet skillion and lean-to roofs.
What is the minimum pitch for a tiled roof in the UK?
It depends on the tile. Many interlocking concrete tiles are rated from 15° to 22.5°, natural slate usually needs 20° to 25°, and plain clay tiles typically need 35° or steeper.
How do I convert a metric pitch to X/12?
Multiply the rise ÷ run by 12, or multiply tan(angle) by 12. 30° is 12 × 0.5774 = 6.93/12.
Related guides
- Roof Pitch in Degrees: 5° to 45° Roofs Converted to X/12Builders outside the US, solar installers and product sheets talk in degrees; US framing plans talk in X/12. Here is every common angle translated, with what each one means on site.
- Roof Pitch for Sheds, Porches, Pergolas, Garages and Other ProjectsThe right pitch for a small project is a balance between headroom, drainage, the roofing material you want and how it ties into the house next to it.
Last updated 2026-10-25. Results are estimates for planning and are not a substitute for a licensed engineer or local code review.