# 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 distance (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 (%) *

### Slope Calculator

Calculate angle degrees, grade and length of slope.

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

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

Slopes vs. gradients vs. % grades are indicated below:

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 |

0.51 | 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 Distance and Slope Length

## Related Topics

## Related Documents

## Tag Search

- en: slope degrees gradient grade