Stair Stringer Calculation Formula & Guide

This calculator computes the exact length and angle for a stair stringer, the structural board that supports the treads and risers. You enter the total rise (floor-to-floor height), total run (horizontal distance), and the number of steps, and it returns the stringer length, the cut angle, and the individual step rise and run. The result is the precise measurement you need to mark and cut a stringer, using the standard Pythagorean relationship between rise, run, and the diagonal stringer length.

Formula

The stair stringer is the hypotenuse of a right triangle formed by the total rise and total run. The formula is:

Stringer Length = √(Total Rise² + Total Run²)

Where:

• Total Rise (in inches or mm) – vertical distance from the finished floor below to the finished floor above.
• Total Run (in inches or mm) – horizontal distance from the face of the first riser to the face of the last riser (not including any nosing or overhang).
• Stringer Length – the diagonal measurement along the top edge of the stringer board, from the bottom cut to the top cut.

The step rise and run are simply the total values divided by the number of steps. The cut angle (the angle of the bottom and top cuts relative to horizontal) is the arctangent of total rise divided by total run.

Worked Example

Using the default values: total rise = 105 in, total run = 120 in, and number of steps = 7.

1. Calculate stringer length: √(105² + 120²) = √(11025 + 14400) = √25425 = 159.45 in.
2. Step rise: 105 ÷ 7 = 15 in per step.
3. Step run: 120 ÷ 7 = 17.14 in per step.
4. Cut angle: atan(105 ÷ 120) = atan(0.875) ≈ 41.19°.

The calculator returns a stringer length of 159.45 inches, a step rise of 15 inches, a step run of 17.14 inches, and a cut angle of 41.19 degrees. These match the formula results exactly.

How to Use the Stringer Calculator

Enter your measured total rise and total run. The number of steps is usually determined by dividing the total rise by a comfortable step height (typically 7–8 inches for residential). Round to a whole number of steps, then adjust the rise accordingly. The calculator gives you the exact diagonal length of the stringer board and the angle for cutting the top and bottom notches. Always measure from finished floor surfaces, not subfloor, to avoid errors.

Common Mistakes and Misconceptions

• Forgetting the nosing: The total run is measured from the face of the first riser to the face of the last riser, not including the tread overhang. If you include nosing, the stringer will be too long.
• Using the wrong number of steps: The number of steps is the number of risers, not the number of treads. For a staircase, the top step is often the floor itself, so the number of risers equals the number of treads plus one.
• Ignoring the thickness of the treads: The stringer cutout depth must account for tread thickness. The vertical cut (riser cut) is typically reduced by the tread thickness so the step rise remains constant.
• Unit mix-ups: Mixing inches and millimeters will throw off the calculation. Use one unit throughout.

Practical Tips for Cutting Stringers

After you have the length and angle, lay out the stringer on a 2×12 board. Use a framing square with stair gauges to mark each step rise and run along the top edge. The bottom cut is made at the calculated angle, and the top cut is made to fit the upper floor framing. Always test-fit the stringer before cutting all of them. For wide stairs, you need at least three stringers – one on each side and one in the middle – to prevent flexing.

Limitations of the Formula

The Pythagorean formula assumes a straight, uniform staircase with no landings or turns. For L-shaped or U-shaped stairs, you must calculate each flight separately. The formula also does not account for the thickness of the stringer material itself, which affects the actual cut length. For a notched stringer, the length along the top edge is what you calculate, but the bottom bearing point may need adjustment. Always check local building codes for minimum tread depth (usually 10 inches) and maximum riser height (usually 7.75 inches) – these are legal requirements that vary by jurisdiction.

Frequently Asked Questions

How many steps do I need for a 10-foot rise? A 10-foot rise is 120 inches. With a 7-inch riser, you need about 17 steps (120 ÷ 7 = 17.14, round to 17). The actual rise per step becomes 120 ÷ 17 = 7.06 inches, which is within code.

What is the ideal stair angle? For residential stairs, the angle is typically between 30 and 37 degrees. The calculator gives the exact angle based on your rise and run; if it falls outside that range, adjust the run or rise.

Can I use a 2×6 for stringers? No, stringers are usually cut from 2×12 lumber. Cutting notches into a 2×6 leaves too little material to support the load safely. The minimum recommended is 2×12 for notched stringers.

What is the difference between a cut stringer and a solid stringer? A cut stringer has notches cut out for the treads and risers. A solid stringer is a straight board that supports the treads from underneath, often used with a closed riser design. The calculation for length is the same, but the cut stringer requires the notch layout.

How do I account for the thickness of the treads? Subtract the tread thickness from the vertical rise of each step. For example, if the tread is 1 inch thick and the step rise is 7 inches, the riser cut should be 6 inches so the top of the tread ends up at the correct height.

What if my staircase has a landing? Split the staircase into two separate flights, each with its own total rise and run. Calculate each stringer separately using the same formula.

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in total_rise | Total rise | in | 105 | 0
in total_run | Total run | in | 120 | 0
in n_steps | Number of steps | - | 7 | 1
out stringer_len | Stringer length | in | sqrt(total_rise^2 + total_run^2) | 2
out step_rise | Step rise | in | total_rise / n_steps | 2
out step_run | Step run | in | total_run / n_steps | 2
out angle | Cut angle | degrees | atand(total_rise / total_run) | 2