Stair Stringer Layout Calculator: Rise, Run & Cuts

This calculator works out the horizontal and vertical layout of a stair stringer from the total rise, total run, and chosen tread depth, giving you the number of steps, each riser height, each tread run, and the stringer length. You enter the total vertical rise from finished floor to finished floor, the total horizontal run available, and your desired tread depth (or unit run), and it returns the exact dimensions you need to mark and cut a 2×12 stringer.

Formula

The stair stringer layout is based on the Pythagorean theorem and the building code limits for riser height and tread depth. The core formulas are:

• Number of steps = ⌈total rise ÷ maximum riser height⌉ (round up to the nearest whole number).
• Actual riser height = total rise ÷ number of steps.
• Actual tread run = total run ÷ number of steps (if you have a fixed total run) or your chosen unit run.
• Stringer length = √(total rise² + total run²).

Where:

• Total rise (in inches) – vertical distance from the finished floor at the bottom to the finished floor at the top.
• Total run (in inches) – horizontal distance from the face of the bottom riser to the face of the top riser (not including any nosing or overhang).
• Riser height – vertical distance from one tread surface to the next.
• Tread run – horizontal depth of each tread, not counting the nosing.

Worked Example

Using the default values from the calculator above:

• Total rise = 105 inches
• Total run = 120 inches
• Desired tread depth = 10 inches

1. First, find the number of steps: 105 ÷ 7.5 = 14, exactly. So steps = 14.
2. Riser height = 105 ÷ 14 = 7.5 inches.
3. Tread run = 120 ÷ 14 = 8.57 inches (rounded to two decimals).
4. Stringer length = √(105² + 120²) = √(11025 + 14400) = √25425 = 159.45 inches (rounded to one decimal).

The calculator shows 14 steps, a 7.50-inch riser, an 8.57-inch tread run, and a 159.5-inch stringer length. Notice that the desired tread depth of 10 inches is not used because the total run is fixed; if you want a 10-inch tread, you need a total run of 140 inches (14 × 10).

How to Read the Results

The number of steps is the count of risers, not the count of treads. For a straight staircase, the top tread is the upper floor itself, so you actually cut (steps – 1) treads. The riser height is the vertical distance between the top surfaces of two consecutive treads. The tread run is the horizontal depth of each tread, measured from the nosing (front edge) to the back of the tread, not including the nosing overhang. The stringer length is the hypotenuse of the right triangle formed by the total rise and total run; it is the length of the 2×12 board before you cut the notches.

Common Mistakes and Misconceptions

• Forgetting to subtract tread thickness: If you use 1.5-inch thick treads, the actual riser height you cut on the stringer must be reduced by the tread thickness. The calculator gives the finished riser height; you must adjust the vertical cut on the stringer accordingly.
• Mixing units: Always work in inches or convert everything to the same unit. A common error is entering feet and inches without converting to inches.
• Rounding too early: Rounding the number of steps up changes the riser height. Always compute the riser height after rounding the step count, not before.
• Ignoring the nosing: The tread run in the calculator is the depth of the tread itself, not the total horizontal distance including the nosing. If you add a 1-inch nosing, the actual tread depth is tread run + nosing.
• Assuming the total run is flexible: In many renovations, the total run is fixed by the opening. If the run is fixed, the tread depth is whatever the math gives, not what you want.

How to Choose the Right Tread Depth and Riser Height

Building codes in most regions limit riser height to a maximum of 7.75 inches and require a minimum tread depth of 10 inches (measured from nosing to nosing). However, these are minimums, not ideal dimensions. A comfortable stair has a riser height between 7 and 7.5 inches and a tread depth between 10 and 11 inches. The classic rule of thumb is: riser height + tread depth = 17 to 18 inches. For example, a 7.5-inch riser pairs well with a 10.5-inch tread (7.5 + 10.5 = 18). If you have the space, aim for that combination. If the total rise is fixed, you cannot change the riser height without changing the number of steps, so you adjust the tread depth to fit the run.

Alternatives and When to Use Them

For straight stairs, a single stringer board with notches is standard. But there are alternatives:

• Housed stringers: The treads and risers are set into routed grooves in the stringer, which is often stronger and more attractive but harder to build.
• Steel or aluminum stringers: These are prefabricated and can be used for exterior stairs, but they require exact dimensions and are not adjustable.
• Concrete stairs: For outdoor steps, concrete is common, but the formwork requires the same rise/run calculations.
• Spiral stairs: These use a different geometry; the stringer is a helical curve, and the treads are wedge-shaped.

If your stairs have a landing or a turn, you must calculate each flight separately, and the total rise and run for each flight are measured independently.

Safety and Code Considerations

Stair building is regulated by local building codes, which typically specify:

• Maximum riser height: usually 7.75 inches
• Minimum tread depth: usually 10 inches
• Maximum variation between risers: 3/8 inch
• Minimum width: 36 inches for residential
• Handrails required for stairs with more than a few steps

Always check your local code before cutting. The calculator gives you the geometric layout, but it does not account for the thickness of treads, the presence of a nosing, or the need for a landing at the top or bottom. A stair that is too steep or has uneven risers is a leading cause of falls, so precision matters.

Frequently Asked Questions

Q: How do I account for the thickness of the treads when cutting the stringer?
A: If you are using 1.5-inch thick treads, you must subtract that thickness from the riser height when marking the vertical cut on the stringer. For example, if the finished riser is 7.5 inches, you cut the vertical leg of the notch to 6.0 inches (7.5 – 1.5). The horizontal cut remains the tread run.

Q: What is the maximum riser height allowed by code?
A: Most residential codes cap riser height at 7.75 inches, but some allow 8 inches for existing stairs. Always confirm with your local building department, as codes vary by jurisdiction.

Q: Can I use a 2×10 instead of a 2×12 for stringers?
A: A 2×12 is standard because the notches remove material, leaving less wood to support the load. A 2×10 can be used for short, low-traffic stairs if the notches are shallow, but it is safer to use 2x12s, especially for wider stairs.

Q: How do I calculate the stringer length if I have a landing?
A: Measure the total rise and total run for each flight separately, from the top of the landing to the next floor. The landing itself is treated as a step, so include it in the step count.

Q: What if my total run is too short for the desired tread depth?
A: You have two options: increase the total run (if the opening allows) or reduce the tread depth to the minimum code requirement. If neither works, you may need to add a landing or change the stair configuration.

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in rise | Total rise (floor to floor) | in | 105 | 0
in run | Total run available | in | 120 | 0
in tread | Desired tread depth | in | 10 | 0
out steps | Number of steps | - | ceil(rise / 7.5) | 0
out riser | Riser height | in | rise / steps | 2
out tread_run | Tread run (unit run) | in | run / steps | 2
out stringer | Stringer length (hypotenuse) | in | sqrt((rise)^2 + (run)^2) | 1