# Slope - Degree, Gradient and Grade Converter

## Converting slopes 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 degrees *

### 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 (%) *

### Inclination or Slope Calculator

Calculate angle degrees, grade and length of slope.

* y - vertical rise (m, ft, in ....)*

* x - horizontal run (m, ft, in ....)*

### 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.

### 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 |

5.74 | 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*

### Vertical Rise, Horizontal Run and Slope Length

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