The stair dimensions need to be calculated precisely for the accurate measurements of staircases. It is essential to know the material required for the stair and stair stringer calculator to ensure that their stair designs meet accessibility requirements.
The terms used in stair measurements are:
Rise Per Step: Rise/Step is the height of each of the individual steps of the stairs
Easily measure the standard mount and flush mount for your stairs with the stair calculator, simplifying your project planning.
| Measurement | Description |
|---|---|
| Total Rise | The vertical distance from the finished floor at the bottom to the finished floor at the top of the stairs. |
| Desired Rise per Step | Ideal height for each step, is typically between 7 to 8 inches (17.78 to 20.32 cm) for residential stairs. |
| Number of Steps | Total number of steps needed, is calculated by dividing the Total Rise by the Desired Rise per Step. |
| Total Run | Horizontal distance from the front of the first step to the end of the last step. |
| Desired Tread Depth | Ideal depth for each step, typically between 10 to 11 inches (25.4 to 27.94 cm) for residential stairs. |
| Actual Run | Horizontal depth of each step, calculated by dividing the Total Run by the Number of Steps. |
| Landing Size | Dimensions of landings, if applicable, based on local building codes and design requirements. |
| Headroom | Vertical clearance above the stairs to accommodate standing individuals, typically 6 feet 8 inches (203 cm) minimum. |
| Handrail Height | Height of handrails, typically between 34 to 38 inches (86.36 to 96.52 cm) above the nosing of the tread. |
| Tread Overhang | Overhang of the tread beyond the riser, typically between 3/4 to 1 1/4 inches (1.91 to 3.18 cm). |
The formulas for calculating the stair parameters are:
The stair calculation formula for rise per step is:
Rise-Per-Step = Total Rise/Number of Steps
Total-Run = Run × Number of stairs
Number of stairs = Total Rise / Rise
Tread-Depth = Total Run/Number of Steps
The tread widths range between (10 - 11 inches or 25.4 - 27.9 cm)
The stair stringer length from Pythagoras' theorem is
stringer length² = total run² + stinger height²
Stair-Angle = Arcsin(Stringer Height/Stringer Length)
Let's suppose the total Rise of the stair is 100 inches, the desired Rise of each step is 7 Inches and the tread depth is 10 inches. Then what is the total number of steps, Run, and Tread width of the stairs?
Given
Total Rise = 100 inches
Desired Rise per Step = 7 inches
Tread Depth = 10 inches
Solution
Number of Steps
\[ \text{Number of Steps} = \frac{100}{7} \approx 14.29 \]
Number of steps = 14.29
Since we can't have a fractional step, we round up to 15 steps.
Total Run
\[ \text{Total Run} = 15 \times 10 = 150 \]
Total Run = 150
Tread Width
Tread width = 10 to 11 inches
OR
Tread width = (25.4 to 27.9 cm)
Stringer length² = total run² + stinger height²
Stringer length² =(100)² + (150)²
Stringer length² = 180.28 Inches
Stair-Angle = Arcsin(Stringer Height/Stringer Length)
Stair-Angle = Arcsin(100/150)
Stair-Angle = Arcsin(0.6667)
Stair-Angle = 33.69 degrees
Our stair calculator helps you determine the stair stringer and stair angle, for maximum comfort and usability of your stairs.
| Parameter | Description | Calculation | Result |
|---|---|---|---|
| Total Rise | Total vertical distance from lower to upper level | N/A | 100 inches |
| Rise per Step | Height of each individual step | Total Rise / Number of Steps | 100 / 7 = 14.29 inches |
| Total Run | Total horizontal distance covered by staircase | Number of Steps × Tread Depth | 15 steps × 10 inches = 150 inches |
| Number of Steps | Total number of steps required | Total Rise / Rise per Step | 100 / 7 ≈ 14.29 steps (round up to 15 steps) |
| Tread Depth | Depth or horizontal distance of each step | Total Run / Number of Steps | 150 inches / 15 steps = 10 inches |
| Tread Width | Width or horizontal space available for each step | Typically 10 to 11 inches (25.4 to 27.9 cm) | 10 inches |
| Headroom Clearance | Vertical clearance between top of tread and ceiling | Typically 6 feet 8 inches (203 cm) or local code requirement | 6 feet 8 inches (203 cm) |
| Handrail Height | Height of handrail measured from nosing of treads | Typically 34 to 38 inches (86.4 to 96.5 cm) | Varies based on code requirements |
| Stair Pitch | Angle of inclination of staircase | Calculated based on the rise and run | Varies based on rise and run |
You can evaluate the number of steps and stir angle with the stair builder.
The 17th-century French architect François Blondel developed a formula for calculating the stair number.
The stair rise and run of François Blondel is
2 Risers + 1 Tread = 25 inches ( 63-65 cm )
In Australia find the number of treads or steps you want and then simply take the height of the deck then divide the figure by 175 (rise height). You can make the stair measurement error-free by stair calculator, to streamline your project planning process.
If the handrail is provided on one side the minimum width is 31.5 inches. On the other side if the provided on both sides then the minimum clear width is 27 inches
The average length of a residential staircase is between 9 and 12 feet. Our stair calculator assists in measuring the stair size for residential and commercial properties.
