# Slope - Degree, Gradient and Grade Calculator

## Converting 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.

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

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

(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.

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 |

5.74 | 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*