# Slope - Degree, Gradient and Grade Calculator

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.

### 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

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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