Method for Calculating a Staircase
Learn how to calculate a comfortable and safe staircase with this concrete example.
In our example, we will have the following initial dimensions:
Height = 3000 mm
Stairwell length = 3500 mm
Stairwell thickness = 250 mm
Blondel's law
Calculating a staircase involves finding the best compromise between the going and the step height.
To calculate these two values, simply use blondel's law:
Blondel's law = Going + 2 × Step height = 630 mm
In reality, Blondel's law can be equal between 590 and 650 mm.
Step number
Divide the height of the staircase by the ideal step height (175 mm):
Number of steps = Round(Height / Step Height) - 1
Number of steps = Round(3000 / 175) - 1
Number of steps = Round(17.14) - 1
Number of steps= 17 - 1
Number of steps= 16
Step height
Divide the height of the staircase by the number of steps:
Step height = Height / (Number of steps + 1)
Step height = 3000 / (16 + 1)
Step height = 3000 / 17
Step height = 176.47 mm
The step height must be between 150 and 200 mm.
Its ideal value is 175 mm.
Going
Using blondel's law, we can calculate the going:
Going = 630 - 2 × Step height
Going = 630 - 2 × 176.47
Going = 277.06 mm
The going must be between 230 and 330 mm.
Its ideal value is 280 mm.
Overlap
The overlap improves the comfort of the staircase when going up and rounds out the depth of the step.
A value of 40 or 50 mm is ideal.
First, you need to calculate the step depth:
Step depth = Round(Going + Overlap)
Step depth = Round(277.06 + 45)
Step depth = Round(322.06)
Step depth = 320 mm
We can now calculate the overlap:
Overlap = Step depth - Overlap
Overlap = 320 - 277.06
Overlap = 42.94 mm
Landing step
A landing step is an optional step that extends from the upper floor. It offers several advantages:
- It allows for an overlap on the last step.
- It makes it easier to connect the string and the handrail to the upper floor.
- It hides the mounting plate at the top of the staircase.
In our example, we'll choose a landing step that is slightly longer than the overlap:
Landing step = Round Up(Overlap)
Landing step = Round Up(42.94)
Landing step = 50 mm
Angle
We use trigonometry with arctangent to calculate the angle:
Angle = Arctan(Step height / Going)
Angle = Arctan(176.47 / 277.06)
Angle = 32.49°
As long as blondel's law is followed, the staircase will be comfortable to climb.However, the angle is important for the comfort of the staircase, particularly when going down.The angle of a staircase must be between 20° and 50°, and its ideal value is between 30° and 35°:
| Angle | Type of Staircase | Desired angle |
|---|---|---|
| 0° → 20° | Ramp | 7° → 15° |
| 20° → 50° | Staircase | 30° → 35° |
| 50° → 75° | Miller's ladder | 50° → 60° |
| 75° → 90° | Ladder | 75° → 85° |
Total Run
Multiply the number of steps by the going, adding the landing step if there is one:
Total run = Number of steps × Giron + Landing step
Total run = 16 x 277.06 + 50
Total run = 4,482.06 mm
Headroom
We use trigonometry to calculate the headroom:
Headroom = tan(Angle) × (Stairwell Length - Landing Step) - Stairwell Thickness
Headroom = tan(32.49) × (3500 - 50) - 250
Headroom = tan(32.49) × 3450 - 250
Headroom = 1947.45 mm
The headroom must be greater than 1900 mm.
Its ideal value is greater than or equal to 2100 mm.
Adjustments
You can adjust the dimensions by changing the number of steps and/or the value used for blondel's law.
By reducing the number of steps and/or the blondel's law, the total run will decrease and the headroom will increase.
By increasing the number of steps and/or the blondel's law, the total run will increase and the headroom will decrease.
All you have to do then is recalculate all the other values:
| Step number | 15 | 16 | 16 | 16 | 17 |
| Blondel's law | 630 mm | 620 mm | 630 mm | 640 mm | 630 mm |
| Step height | 187.5 mm | 176.47 mm | 176,47 mm | 176.47 mm | 166.67 mm |
| Going | 255 mm | 267.06 mm | 277.06 mm | 287.06 | 296.67 mm |
| Step depth | 300 mm | 310 mm | 320 mm | 330 mm | 340 mm |
| Overlap | 45 mm | 42.94 mm | 42.94 mm | 42.94 mm | 43.33 mm |
| Landing step | 50 mm | 50 mm | 50 mm | 50 mm | 50 mm |
| Angle | 36.33° | 33.46° | 32.49° | 31.58° | 29.33° |
| Total Run | 3875 mm | 4322.96 mm | 4482.06 mm | 4642.96 mm | 5043.39 mm |
| Headroom | 2286.75 mm | 2029.74 mm | 1947.45 mm | 1870.9 mm | 1688.16 mm |
Vincent Le Nagard
Founder of Easystair
