Slope  Degree, Gradient and Grade Calculator
Convert slopes pitch between degrees, gradients and grades.
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
S_{angle} = tan^{1}(y / x) (1)
where
S_{angle} = 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
S_{angle} = tan^{1}((1 m)/(2 m))
= 26.6 °
Slope expressed as Grade
S_{grade(%)} = (100 %) y / x (2)
where
S_{grade(%)} = grade (%)
Example  Slope as Grade
Slope as grade for an elevation of 1 m over a distance of 2 m can be calculated as
S_{grade(%)} = (1 m)/(2 m)
= 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
S_{grade(%)} = (100 %) x / 12 (3)
Example  Roof Picth 4/12 as Grade
S_{grade(%)} = (100 %) 4 / 12
= 33.3 %
Roof pitch on the form x:12 can be expressed in angles as
S_{angle} = tan^{1}(x / 12) (3b)
Example  Roof Picth 4/12 as Angle
S_{angle} = tan^{1}(4 / 12)
= 18.4 °
Inclination or Slope Calculator
Calculate angle degrees, grade and length of slope.
x  horizontal run (m, ft, in ....)
y  vertical rise (m, ft, in ....)
(enable popup)
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.
Download and print Inclination/Slope Chart
Slopes vs. gradients vs. % grades
Slope  

Angle (degrees)  Gradient  Grade (%)  
Y  X  
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.
Download Visual Tool Slope Diagram as pdf file
Vertical Rise, Horizontal Run and Slope Length
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