For a floor height of 3 m, it is proposed to lay a single flight stair case. The riser is 150 mm. The number of treads will be:
Try it first: pick an option, then read the explanation.
Understanding the Concept: Risers and Treads
This question involves a fundamental relationship in staircase design between the vertical and horizontal components of a stair.
Riser: The vertical part of a step. The height of one step is the "rise". The total number of risers determines the total height of the staircase.
Tread: The horizontal part of a step where you place your foot. The number of treads is directly related to the number of risers.
The key principle is that for a single flight of stairs, there is always one less tread than the number of risers. This is because the final "step up" is onto the landing or floor, which serves as the last tread surface but is not counted as a step's tread.
The Key Relationship
The formula connecting the number of treads and risers in a flight is:
Step-by-Step Calculation
Let's calculate the required number of treads using the given information.
- List the Given Data:
- Total Floor Height = 3 m
- Height of one Riser (Rise) = 150 mm
- Convert Units:
- Ensure all units are consistent. Let's use millimeters (mm).
- Total Floor Height = 3 m * 1000 mm/m = 3000 mm
- Calculate the Number of Risers:
- The total number of risers is the total height divided by the height of a single riser.
- Number of Risers = (Total Floor Height) / (Height of one Riser)
- Number of Risers = 3000 mm / 150 mm = 20 Risers
- Calculate the Number of Treads:
- Using the key formula: Number of Treads = Number of Risers - 1
- Number of Treads = 20 - 1
- Number of Treads = 19