Japanese Slope-Table

Slopes are in percentages (decimal format), and the rest are lengths in relation to a run of 1 shaku. Conversions can be made easily as all lengths are percentages of 1 shaku, and as such, are not necessarily units of measure but can be treated as ratios against unity. For example, 1.0770 under the highlighted hypotenuse column is the hypotenuse of a 40 percent slope (0.40; 四寸勾配) with 1 as its run (adjacent leg). Angles are in degrees-minutes. Divide the second half of the angle by 60 minutes to get the decimal.

(If viewing from a smart phone or small screen and the table cuts out of the screen to the right, rotate 90 degrees to a ‘landscape’ orientation.)

Roof slope – 平勾配 Angle – 角度 Hypotenuse – 玄 Altitude – 中勾 Long Hypo. – 長玄 Short Hypo. – 短玄 2nd Altitude – 欠勾 Hip Hypo. – 隅玄 Hip Altitude – 隅中勾 Hip Slope – 隅勾配
0.10 5°-52′ 1.0049 0.0995 0.9950 0.0100 0.0990 1.4177 1.0706 0.0707
0.20 11°-19′ 1.0198 0.1961 0.9806 0.0392 0.1924 1.4283 0.1400 0.1414
0.25 14°-02′ 1.0308 0.2425 0.9701 0.0606 0.2353 1.4361 0.1792 0.1768
0.30 16°-42′ 1.0440 0.2874 0.9579 0.0862 0.2753 1.4475 0.2059 0.2121
0.35 19°-16′ 1.0595 0.3303 0.9438 0.1156 0.3118 1.4569 0.2381 0.2475
0.40 21°-48′ 1.0770 0.3714 0.9285 0.1486 0.3448 1.4697 0.2695 0.2828
0.45 24°-13′ 1.0964 0.4104 0.9118 0.1846 0.3742 1.4841 0.3032 0.3182
0.50 26°-34′ 1.1180 0.4472 0.8945 0.2236 0.4000 1.5000 0.3333 0.3536
055 28°-48′ 1.1413 0.4819 0.8762 0.2650 0.4222 1.5174 0.3625 0.3889
0.60 30°-58′ 1.1662 0.5145 0.8575 0.3087 0.4412 1.5362 0.8906 0.4243