Calculating steps on a slope involves determining the total vertical rise and horizontal run, then dividing these measurements to create evenly sized, safe, and code-compliant steps.
This process is critical for building outdoor stairs for decks, landscapes, and hilly terrain.
The key measurements
To begin, you need to find two critical measurements for the overall slope:
- Total Rise: The total vertical height from the bottom of the slope to the top.
- Total Run: The total horizontal length the stairs will cover.
Step-by-step calculation
Step 1: Measure the total rise
Accurately measure the overall vertical distance using a long, straight board and a level.
- Place one end of a straight board on the top landing or at the top of the planned staircase.
- Extend the board horizontally and use a level to ensure it is perfectly flat.
- Measure the vertical distance from the bottom of the board to the ground at the end of the run.
- If the slope is very long or uneven, you may need to use multiple stakes and boards, adding the vertical measurements from each section to find the total rise.
Step 2: Estimate the number of steps
You must first determine how many steps are needed by dividing your total rise by an ideal riser height.
- Choose an ideal riser height: For most exterior stairs, a comfortable riser height is between 6 and 7.5 inches. Check local building codes for the maximum allowed riser height. A common code-compliant maximum is 7.75 inches.
- Divide total rise by the ideal riser height: This calculation gives you an estimated number of steps. Round up to the nearest whole number to ensure your steps are not too tall.
- Formula: Estimated number of risers = Total Rise / Ideal Riser Height
Step 3: Calculate the exact individual riser height
With a fixed number of risers, you can calculate their exact height, ensuring all steps are uniform.
- Divide total rise by the estimated number of steps: Use the rounded number from the previous step to get the exact, uniform riser height.
- Formula: Exact Riser Height = Total Rise / Estimated Number of Risers
Step 4: Calculate the individual run (tread depth)
The run is the horizontal depth of each step, and it should be consistent for safety.
- Measure the total run: Measure the total horizontal length from the base of the stairs to the top.
- Divide the total run by the number of steps:
- Formula: Exact Run (Tread Depth) = Total Run / Number of Steps
- It is important to note that the number of treads is usually one less than the number of risers, as the top landing serves as the final step. For example, a project with 6 risers will have 5 treads.
Step 5: Check your calculations against building code
Confirm your calculated rise and run fall within standard, safe ranges.
-
Ideal range: A common rule of thumb is that the sum of two risers and one tread should equal between 24 and 27 inches (2R+T=24"โ27"2 cap R plus cap T equals 24 " minus 27 "
2๐ +๐=24"โ27"
).
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Stair angle: A comfortable and safe angle is typically between 30 and 37 degrees. You can calculate the angle using the arctangent function:
-
Formula: Angle = arctana r c t a n
๐๐๐๐ก๐๐
(Exact Riser Height / Exact Run)
-
Advanced considerations for building on a slope
- Creating the base: When building on a natural slope, you will need to prepare a stable foundation.
- Excavation: Dig a flat, level area at the base for the first step or a landing pad.
- Material: For concrete stairs, excavate and set forms. For wood stringers, set the base on a solid footing like concrete blocks or a compacted gravel pad.
- Planning stringer length: The length of your stringers (the sides of the staircase) can be calculated using the Pythagorean theorem, where the total run and total rise are the two sides of a right triangle.
- Formula: Stringer Lengthยฒ = Total Runยฒ + Total Riseยฒ
- Dealing with uneven terrain: For long, varying slopes, it may be safer to build a series of smaller staircases with landings between them. This helps to maintain consistent rise and run, reducing tripping hazards.
- Incorporating a tread slope: For outdoor steps, a slight forward slope (1โ2%) on the treads will prevent water from puddling, which can be a slip hazard or cause wood rot.