Stair Stringer Layout Calculator: Rise, Run & Cuts

This calculator works out the exact dimensions for laying out stair stringers: you enter the total rise (floor-to-floor height), total run (horizontal span), and stair width, and it returns the number of treads, riser height, tread depth (going), stringer length, and the cut angles for the notches. It uses the standard stair geometry formula with the Pythagorean theorem, so you get precise numbers for marking and cutting stringers from a 2×12 or other lumber.

Formula

The calculator uses the basic relationship between the total rise (vertical distance from the finished floor below to the finished floor above), the total run (horizontal distance the stairs cover), and the resulting stringer length. The stringer is the diagonal board that supports the treads and risers; its length is the hypotenuse of a right triangle:

Stringer length = √(Total rise² + Total run²)

Where:

• Total rise (R) – vertical height from the top of the lower floor to the top of the upper floor, in inches (or cm).
• Total run (T) – horizontal distance from the face of the first riser to the face of the last riser, in the same units.
• Riser height – calculated by dividing the total rise by the number of risers. The number of risers is typically chosen so each riser is between 4 and 7.75 inches (building codes often cap at 7.75 in the US).
• Tread depth (going) – the horizontal depth of each step, usually 10–11 inches for comfortable walking.

The cut angle (the angle of the stringer relative to the floor) is found from the arctangent: angle = atan(R / T) in degrees.

Worked Example

Using the default values from the calculator: total rise = 105 inches, total run = 120 inches, tread depth = 10 inches.

1. First, find the number of risers. The calculator chooses the smallest number of risers such that each riser is ≤ 7.5 inches (a common comfortable maximum). 105 / 7.5 = 14, so it uses 14 risers.
2. Riser height = 105 / 14 = 7.5 inches exactly.
3. Number of treads = total run / tread depth = 120 / 10 = 12 treads. (In a real stair, the number of treads is usually one less than the number of risers, but here we treat the run as the total horizontal distance, which includes the last tread.)
4. Stringer length = √(105² + 120²) = √(11025 + 14400) = √25425 ≈ 159.45 inches.
5. Cut angle = atan(105/120) = atan(0.875) ≈ 41.2° from horizontal.

So for a 105-inch rise and 120-inch run, you’d mark a stringer about 159.5 inches long, with a 41.2° angle at the top and bottom, and cut out notches for each tread.

How to Use the Calculator

Enter your measured total rise and total run in inches (or convert to cm if you prefer). The calculator gives you the riser height, number of treads, stringer length, and angle. Use those numbers to lay out the stringer on a straight board:

• Measure the stringer length along the top edge of the board.
• Mark the angle at both ends using a framing square or protractor.
• For each step, mark a right-angled notch: the vertical cut (riser height) and the horizontal cut (tread depth). The notch depth is typically the tread thickness, but you’ll subtract that from the riser height when cutting (common practice: cut the riser height minus the tread thickness).
• Always check your local building code for minimum tread depth and maximum riser height.

Common Mistakes and Misconceptions

One frequent error is mixing units—using inches for rise and feet for run. Keep everything in the same unit. Another is forgetting that the total run is measured from the face of the first riser to the face of the last riser, not the overall stairwell length. Also, many people think the stringer length is just the sum of treads and risers, but it’s the diagonal, so it’s always longer than the horizontal run. Finally, don’t forget to account for the thickness of the tread material: if you use 1-inch thick treads, the actual riser height you cut should be the calculated riser height minus the tread thickness, otherwise the top step ends up too high.

Choosing the Right Tread Depth and Riser Height

Comfort and safety depend on the relationship between riser height and tread depth. A common rule is that twice the riser height plus the tread depth should be between 24 and 25 inches (the “blondel” formula). For example, a 7.5-inch riser with a 10-inch tread gives 2×7.5 + 10 = 25 inches, which is on the high end but acceptable. For outdoor stairs, you might use a 7-inch riser and an 11-inch tread for a more relaxed slope. The calculator lets you adjust the tread depth to see how the number of treads changes.

Safety and Code Considerations

Building codes (such as the International Residential Code in the US) typically limit riser height to a maximum of 7.75 inches and require a minimum tread depth of 10 inches. They also require a handrail on stairs with more than a few risers, and the stair width must be at least 36 inches in most residential applications. Always verify your local codes before cutting. For exterior stairs, consider slip-resistant treads and proper drainage. If the total rise is more than about 12 feet, a landing is usually required in the middle to break up the flight.

Alternatives to Stringer Layout

If you’re not comfortable cutting stringers by hand, you can buy pre-cut stringers from lumber yards or home centers—they come in standard rise/run combinations (like 7.5-inch rise, 10-inch run) and you just trim the bottom to fit your total rise. Another option is using metal stringers or adjustable steel stringers that you can set to your exact dimensions. For curved or spiral stairs, the layout is far more complex and usually requires specialized software or a professional. But for straight stairs, a simple calculator like this gives you the core numbers to start.

Frequently Asked Questions

How many stringers do I need? For a typical residential stair, you need at least three stringers: one on each side and one in the middle. For wider stairs (over 36 inches), add one more for every 16–18 inches of width. Check your local code.

What is the maximum riser height allowed? In most US jurisdictions, the maximum riser height is 7.75 inches, and the minimum tread depth is 10 inches. However, some areas have different rules, so always check with your local building department.

Do I subtract tread thickness from the riser height? Yes. If you’re using 1-inch thick treads, the actual vertical cut on the stringer should be the riser height minus the tread thickness (e.g., 7.5 – 1 = 6.5 inches). This keeps the finished riser height consistent.

Can I use this calculator for outdoor stairs? Yes, but for outdoor stairs you might want a slightly lower riser (around 7 inches) and a deeper tread (11 inches) to be more comfortable and safer in wet conditions. Also, use pressure-treated lumber for ground contact.

What if my total run is not a multiple of the tread depth? The calculator rounds up to the next whole number of treads, which means the actual tread depth will be slightly less than your input. For example, if you have a 120-inch run and want 10-inch treads, you get 12 treads exactly, but if the run were 125 inches, you’d get 13 treads with an actual tread depth of 125/13 ≈ 9.62 inches, which may be too shallow. In that case, adjust the run or use a different tread depth.

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in rise | Total rise | in | 105 | 0
in run | Total run | in | 120 | 0
in tread | Tread depth (going) | in | 10 | 0
out riser_h | Riser height | in | rise / ceil(rise / 7.5) | 2
out n_treads | Number of treads | - | ceil(run / tread) | 0
out stringer_len | Stringer length (hypotenuse) | in | sqrt((rise)^2 + (run)^2) | 2
out angle_deg | Cut angle (from horizontal) | deg | atan(rise / run) * 180 / pi | 1