What Angle Is a Japanese "Sun" Roof Pitch? Angles and Slope Factors for 3-, 4- and 5-Sun Pitches

Sun pitch means "how many sun of rise per 10 sun of run"

Sun pitch (sun koubai) is a way of expressing slope long used in Japanese construction: how many sun (a traditional unit of length) the roof rises for every 10 sun (1 shaku) of horizontal run. A 4-sun pitch rises 4 for every 10 of run and is written "4/10" or "4寸" on drawings. Because it only expresses the ratio of rise to run, it works the same in centimetres or metres: a roof that rises 40 cm over 1 m of run is also a 4-sun pitch. In imperial terms, a 4-sun pitch is the same as a 4.8:12 pitch.

To convert to an angle, put rise ÷ run (4 ÷ 10 = 0.4 for a 4-sun pitch) into the inverse tangent (arctan). arctan(0.4) ≈ 21.80°, so a 4-sun pitch is about 21.8°. As a percentage it's "rise ÷ run × 100", so the sun number times 10 is the percentage: a 4-sun pitch is 40% and a 5-sun pitch is 50%.

Quick-reference table: angle, %, slope factor and hip factor by sun pitch

Here are the 1-sun to 12-sun pitches commonly used on houses. The slope factor is the length of the slope per 1 unit of horizontal length, and the hip factor is the coefficient for working out the length of hip rafters (the diagonal members at the four corners) on a hipped roof. How to use both is explained in the next section.

To get the sun pitch from an angle, use tan in reverse: sun = tan(angle) × 10. 30° is about 5.77 sun, 35° about 7 sun and 20° about 3.64 sun. This is useful for converting a solar panel installation angle, or an angle measured from a photo of a roof, into sun pitch.

Low, standard and steep pitches, plus kane pitch and kaeshi pitch

Roof pitches have different names depending on their steepness. The boundaries vary slightly between companies and sources, but they're roughly divided as follows.

On steep pitches of 6 sun or more, workers can't brace themselves on the roof surface, so it's standard to build scaffolding on the roof itself (roof scaffolding). If a painting or re-roofing quote includes items such as a "pitch surcharge" or "roof scaffolding", check the pitch.

Typical minimum pitches by roofing material

Each roofing material has a minimum pitch, "install at this pitch or steeper", to shed rainwater reliably. Below the minimum, rainwater can be drawn up through the overlaps and cause leaks, and the manufacturer's warranty may not apply. Typical guidelines in Japan are as follows.

Using the slope factor for roof area, rafter and hip rafter length

Roof plans and floor plans show horizontal lengths as seen from directly above. The actual roof is longer by the amount it's tilted, so multiply the horizontal length by the slope factor to get the length along the slope. The slope factor is √(1 + pitch²): for a 4-sun pitch, √(1 + 0.4²) = 1.0770.

1. 1

   Work out roof area

   Multiply the roof area seen from above (the horizontal projected area, including eaves) by the slope factor. With a 60 m² projected area and a 4-sun pitch, 60 × 1.0770 = about 64.6 m². The same 60 m² at a 6-sun pitch is about 70.0 m², so you need about 10% more paint or roofing.

2. 2

   Work out rafter length

   Multiply the horizontal distance from eave to ridge by the slope factor. For a 3.0 m horizontal distance at a 4-sun pitch, 3.0 × 1.0770 = about 3.23 m. For the actual material, add the eave overhang and a cutting allowance.

3. 3

   Work out hip rafter length

   On a hipped roof, hip rafters run at 45° in plan, so their horizontal length is √2 times longer. The hip factor is therefore √(2 + pitch²): 1.4697 for a 4-sun pitch. If the horizontal distance from wall plate to ridge (the common rafter's run) is 3.0 m, the hip rafter is 3.0 × 1.4697 = about 4.41 m.

When asked for roof area in tsubo (the Japanese unit of area), divide the m² figure by 3.3058. Converting between tsubo and m² is explained in detail in How many m² is 1 tsubo?.

How to find your current roof pitch

• Check the drawings: section details (kanabakarizu), elevations and roof plans often show it as "4/10" or "4寸". Finding the full set of documents from when the house was built is the surest way.
• Measure in the loft: if you can get into the loft through an access hatch, hold the long edge of your phone against a rafter or sloping beam to measure the angle and convert it to sun pitch.
• Measure on the barge board or verge: another method is to measure along the bottom edge of a barge board you can reach from a first-floor window. Don't lean out.
• Read it from a photo: measure the angle of the roof line in a photo taken straight from the side (the gable end) with a protractor app. Lens distortion and shooting angle can throw it off by a few degrees, so treat it as a rough guide.

Converting and measuring sun pitch in one place

In the "Convert slope" tab of the Slope & Angle Meter (Phone Level), enter a sun pitch to see the angle, %, 1/n, mm per metre, slope factor and hip factor all at once, with a triangle diagram to visualise the slope. Enter the horizontal distance or slope length in the "Height, length & ramp" tab to get rafter length or the height to the ridge. Open it on a phone and you can hold the long edge against a rafter to measure the current pitch.

The thinking behind converting with % and 1/n is in Converting slope percentages and angles: how many degrees is 10%?, and tips for accurate measurement with a phone in How to measure floor tilt with a phone.

FAQ

How many degrees is a 4-sun pitch?

About 21.8°. It rises 4 for every 10 of horizontal run, so arctan(4 ÷ 10) ≈ 21.80°. As a percentage it's 40%, and the slope factor is 1.0770.

How many degrees are 3-sun, 5-sun and 6-sun pitches?

A 3-sun pitch is about 16.7°, a 5-sun pitch about 26.6° and a 6-sun pitch about 31.0°. Sun and degrees aren't proportional, so the more sun, the less each extra sun adds in degrees.

What sun pitch is a 30° roof?

About 5.77 sun. Use sun = tan(angle) × 10. 45° is exactly 10 sun (kane pitch), and 20° is about 3.64 sun.

What is a roof slope factor?

A coefficient showing how long the slope is per 1 unit of horizontal length, calculated as √(1 + pitch²). Multiply the horizontal projected area by the slope factor to get the actual roof area. It's 1.0770 for a 4-sun pitch and 1.1180 for a 5-sun pitch.

From what sun pitch can a tiled roof be laid?

Ordinary clay tiles are typically 4 sun or more. Some products, such as storm-resistant tiles, can be laid from around 3 sun. Check each roofing material's minimum pitch in the product's installation manual.