# Calculating Slope

There are three different ways to indicate the slope of a surface relative to the horizontal plane: degrees, gradient, and percentage.

## Calculating a Slope Gradient

Slope gradients are written as Y:X, where Y is a single unit in rise and X is the run. Both numbers must use the same units. For instance, if you travel 3 inches vertically and 3 feet (36 inches) horizontally, the slope would be 3:36 or 1:12. This is read as a "one in twelve slope."

## Calculating the Slope Percentage

Slope percentage is calculated in much the same way as the gradient. Convert the rise and run to the same units and then divide the rise by the run. Multiply this number by 100 and you have the percentage slope. For instance, 3" rise divided by 36" run = .083 x 100 = an 8.3% slope.

## Calculating a Slope in Degrees

The most complicated way to calculate slope is in degrees and it requires a bit of high-school math. The tangent of a given angle (in degrees) is equal to the rise divided by the run. Therefore, the inverse-tangent of the rise divided by the run will give the angle.

## Table of Common Slopes

The table below shows some common slopes. 1:20 slopes do not require handrails. 1:12 slopes are the maximum slope allowed by ADA codes, but they require handrails.

Degrees | Gradient | Percent | | Degrees | Gradient | Percent |

0.6 | 1 : 95.49 | 1.0% | 30 | 1 : 1.73 | 57.7% | |

1 | 1 : 57.29 | 1.7% | 45 | 1 : 1 | 100% | |

2.86 | 1 : 20 | 5% | 56.31 | 1: 0.67 | 150% | |

4.76 | 1 : 12 | 8.3% | 60 | 1 : 0.6 | 173.2% | |

7.13 | 1 : 8 | 12.5% | 63.43 | 1 : 0.5 | 200% | |

10 | 1 : 5.67 | 17.6% | 78.69 | 1: 0.2 | 500% | |

14.04 | 1 : 4 | 25% | 89.43 | 1 : 0.1 | 1000% | |

15 | 1 : 3.73 | 26.8% | 90 | 1 : 0 | inf. | |

26.57 | 1 : 2 | 50% |

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