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Slope or gradient of a line describes the direction and the steepness of a line. Slope can be expressed in angles, gradients or grades.

### Slope expressed as Angle

Sangle = tan-1(y / x)                        (1)

where

Sangle = angle (rad, degrees (°))

x = horizontal run (m, ft ..)

y = vertical rise (m, ft ...)

#### Example - Slope as Angle

Slope as angle for an elevation of 1 m over a distance of 2 m can be calculated as

Sangle = tan-1((1 m)/(2 m))

=  26.6 °

Sgrade(%) = (100 %) y / x                        (2)

where

#### Example - Slope as Grade

Slope as grade for an elevation of 1 m over a distance of 2 m can be calculated as

=  50 (%)

### Slope and Roof Pitch

Roof pitch is the slope created by the rafter. You can find the roof pitch in the form of x:12 like 4/12 or 9/12.

Roof pitch on the form x:12 can be expressed in grades as

Sgrade(%) = (100 %) x / 12                     (3)

#### Example - Roof Picth 4/12 as Grade

Sgrade(%) = (100 %) 4 / 12

= 33.3 %

Roof pitch on the form x:12 can be expressed in angles as

Sangle = tan-1(x / 12)                    (3b)

#### Example - Roof Picth 4/12 as Angle

Sangle = tan-1(4 / 12)

= 18.4 °

### Inclination or Slope Calculator

Calculate angle degrees, grade and length of slope.

(enable pop-up)

### Inclination or Slope Chart

Use this chart to estimate the inclination or slope. Measure the horizontal run and the vertical rise and draw the lines in the chart to estimate inclination.

Angle
(degrees)
(%)
YX
0.1 1 573.0 0.17
0.2 1 286.5 0.35
0.3 1 191.0 0.52
0.4 1 143.2 0.70
0.5 1 114.6 0.87
0.57 1 100 1
0.6 1 95.49 1.05
0.7 1 81.85 1.22
0.8 1 71.62 1.40
0.9 1 63.66 1.57
1 1 57.29 1.75
2 1 28.64 3.49
3 1 19.08 5.24
4 1 14.30 6.99
5 1 11.43 8.75
5.71 1 10 10
6 1 9.514 10.5
7 1 8.144 12.3
8 1 7.115 14.1
9 1 6.314 15.8
10 1 5.671 17.6
11 1 5.145 19.4
12 1 4.705 21.3
13 1 4.331 23.1
14 1 4.011 24.9
15 1 3.732 26.8
16 1 3.487 28.7
17 1 3.271 30.6
18 1 3.078 32.5
19 1 2.904 34.4
20 1 2.747 36.4
21 1 2.605 38.4
22 1 2.475 40.4
23 1 2.356 42.4
24 1 2.246 44.5
25 1 2.145 46.6
26 1 2.050 48.8
27 1 1.963 51.0
28 1 1.881 53.2
29 1 1.804 55.4
30 1 1.732 57.7
31 1 1.664 60.1
32 1 1.600 62.5
33 1 1.540 64.9
34 1 1.483 67.5
35 1 1.428 70.0
36 1 1.376 72.7
37 1 1.327 75.4
38 1 1.280 78.1
39 1 1.235 81.0
40 1 1.192 83.9
41 1 1.150 86.9
42 1 1.111 90.0
43 1 1.072 93.3
44 1 1.036 96.6
45 1 1.000 100.0
46 1 0.9657 103.6
47 1 0.9325 107.2
48 1 0.9004 111.1
49 1 0.8693 115.0
50 1 0.8391 119.2
51 1 0.8098 123.5
52 1 0.7813 128.0
53 1 0.7536 132.7
54 1 0.7265 137.6
55 1 0.7002 142.8
56 1 0.6745 148.3
57 1 0.6494 154.0
58 1 0.6249 160.0
59 1 0.6009 166.4
60 1 0.5774 173.2
61 1 0.5543 180.4
62 1 0.5317 188.1
63 1 0.5095 196.3
64 1 0.4877 205.0
65 1 0.4663 214.5
66 1 0.4452 224.6
67 1 0.4245 235.6
68 1 0.4040 247.5
69 1 0.3839 260.5
70 1 0.3640 274.7
71 1 0.3443 290.4
72 1 0.3249 307.8
73 1 0.3057 327.1
74 1 0.2867 348.7
75 1 0.2679 373.2
76 1 0.2493 401.1
77 1 0.2309 433.1
78 1 0.2126 470.5
79 1 0.1944 514.5
80 1 0.1763 567.1
81 1 0.1584 631.4
82 1 0.1405 711.5
83 1 0.1228 814.4
84 1 0.1051 951.4
85 1 0.08749 1143
86 1 0.06993 1430
87 1 0.05241 1908
88 1 0.03492 2864
89 1 0.01746 5729
90 1 0.00000
• 1% grade = 0.57 degrees = 1 cm per 100 cm = 1 inch per 100 inches = 0.125 inch per foot

### Visual Tool Slope Diagram

Print this diagram and hold it up against an object to estimate the slope.

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