Stair Slope Calculator - Measure Stair Angle, Ratio, and Percent Grade

Last updated: 11 Jun 2025 | Author: Brij | Review By: Irshad

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Calculate the slope of stairs in degrees, ratio, and percentage using this easy Stair Slope Calculator. Just enter total rise and total run to get instant results.

Total Rise (Vertical Height):

Total Run (Horizontal Length):

Stair Slope Results

Slope (Degrees):

Slope Ratio (Rise:Run):

ratio

Slope Percentage:

Recommended Slope Guidelines:
• Standard stairs: 30°-35° (Rise:Run ≈ 7:11)
• Comfortable stairs: 25°-30° slope
• Maximum for residential: 42° (Steep ladder-like stairs)

What is Stair Slope?

Stair slope refers to the angle or steepness of a staircase. It is a critical design element in ensuring safety and comfort. An ideal stair slope lies between 30° and 35°.

By knowing the total rise (vertical height) and run (horizontal length), we can calculate:

Stair slope angle (in degrees)
Slope as a ratio (Rise:Run)
Slope percentage (Grade %)

Formulas Used in Stair Slope Calculator

1. Stair Slope in Degrees

The angle of the stair slope is calculated using the arctangent function:

$\theta = \tan^{-1} \left( \frac{\text{Rise}}{\text{Run}} \right)$

2. Stair Slope as a Ratio (Rise:Run)

This is a simple ratio of vertical rise to horizontal run:

$\text{Slope Ratio} = \text{Rise} : \text{Run}$

3. Stair Slope as a Percentage

Slope in percent represents how many units the stair rises vertically for every 100 units horizontally:

$\text{Slope (\%)} = \left( \frac{\text{Rise}}{\text{Run}} \right) \times 100$

Example Calculation

Let’s take an example to see how the stair slope is calculated.

Given:

Total Rise: 30 inches
Total Run: 36 inches

Step-by-Step:

1. Slope in Degrees:

$\theta = \tan^{-1} \left( \frac{30}{36} \right) = \tan^{-1}(0.8333) \approx 39.8^\circ$

2. Slope as Ratio:

$\text{Slope Ratio} = 30 : 36 = 5 : 6$

3. Slope as Percentage:

$\text{Slope (\%)} = \left( \frac{30}{36} \right) \times 100 \approx 83.33\%$

Final Output:

Slope Angle: 39.8°
Slope Ratio: 5:6
Slope Percentage: 83.33%

What is a Good Stair Slope?

Comfortable residential stairs: 30°–35°
Steeper stairs (like ladders): 45° or more
Slopes over 50° are not suitable for regular use

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Stair Slope Calculator - Measure Stair Angle, Ratio, and Percent Grade

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