Stair Stringer Calculator with Drawing

This stair stringer calculator works out the dimensions of the stringer—the angled board that supports the treads and risers—from the total rise, total run, and desired tread depth. You enter the floor-to-floor height, the horizontal distance the stairs cover, and the number of treads or risers, and it returns the stringer length, the cut angle, and the rise and run per step. The result is a set of measurements you can mark directly on a board, which is why the drawing is included: it shows where each cut goes.

Formula

The calculator uses the Pythagorean theorem to find the stringer length, which is the hypotenuse of a right triangle whose legs are the total rise (vertical distance) and total run (horizontal distance). The formulas are:

• Number of risers = ceil(total rise / 7.5) — this assumes a typical 7.5-inch riser height, which you can adjust.
• Riser height = total rise ÷ number of risers
• Stringer length = √(total run² + total rise²)
• Cut angle = atan(total rise ÷ total run), in degrees

Variables: total rise (inches), total run (inches), tread depth (inches), riser height (inches), stringer length (inches), cut angle (degrees). The drawing is generated from these values: the stringer is a straight line at the cut angle, with horizontal lines marking each tread and vertical lines marking each riser.

Worked Example

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

1. Number of risers = ceil(105 ÷ 7.5) = ceil(14) = 14
2. Riser height = 105 ÷ 14 = 7.5 in
3. Stringer length = √(120² + 105²) = √(14400 + 11025) = √25425 = 159.45 in
4. Cut angle = atan(105 ÷ 120) = atan(0.875) = 41.2°

The stringer length is 159.45 inches (about 13 feet 3.5 inches), and the cut angle is 41.2 degrees. The drawing shows a 14-step stringer with 7.5-inch risers and 10-inch treads.

When to Use This Calculator

Use this calculator when you are building a new set of stairs—deck stairs, porch steps, or interior stairs—and need to cut stringers from a straight board. It is also useful for checking an existing staircase to see if it meets typical building guidelines. The calculator assumes a single straight flight of stairs with no landings or turns. For L-shaped or U-shaped stairs, you would calculate each section separately.

Local building codes often specify maximum riser height (commonly 7.75 inches) and minimum tread depth (commonly 10 inches). This calculator uses 7.5 inches as a default riser height, but you can change the total rise or the number of risers to match your code. Always check your local code before cutting.

How to Read the Results

The number of risers is the count of vertical steps, not the number of treads (which is one less). The riser height is the vertical distance between each step. The stringer length is the measurement along the angled board from the top to the bottom—this is the board length you need to buy. The cut angle is the angle of the stringer relative to the floor; you set your saw to this angle to make the top and bottom cuts.

The drawing shows the stringer as a straight line with right-angle notches for each tread and riser. Each notch is the tread depth wide and the riser height tall. The bottom of the stringer is cut at the angle so it sits flat on the floor, and the top is cut to attach to the upper floor or deck.

Common Mistakes and How to Avoid Them

• Mixing units: Enter all measurements in inches. If you measure in feet, convert to inches first (1 ft = 12 in). A common error is entering feet and inches together without conversion.
• Forgetting the tread thickness: The calculator gives the riser height as the vertical distance between treads. If your treads are 1.5 inches thick, the actual cut riser height on the stringer should be the calculated riser height minus the tread thickness. Many builders cut the stringer with a riser height that is smaller by the tread thickness to keep the final step height consistent.
• Rounding too early: Round the riser height to the nearest 1/16 inch only after all calculations. Rounding the number of risers to a whole number is necessary, but do not round intermediate values.
• Ignoring the overhang: Treads often overhang the riser by 1 to 1.5 inches. This does not affect the stringer cut, but it does affect the total run if you measure from the front of the treads.

Limitations of the Formula

The formula assumes the stringer is a single straight board with no notching for the treads and risers—it only calculates the hypotenuse length and angle. In practice, you will cut notches into the stringer to hold the treads and risers, which removes material and shortens the effective length slightly. The calculator gives the minimum board length needed; you should add a few inches of extra length to allow for cutting errors and for the top and bottom attachment points.

The formula also does not account for the thickness of the treads or the angle of the top and bottom cuts. For a finished set of stairs, you may need to adjust the top cut to sit flush against the upper floor and the bottom cut to sit on the ground. The drawing is schematic, not a full construction plan.

Safety and Code Considerations

Stair building is subject to building codes for good reason: incorrect riser heights and tread depths cause trips and falls. Common guidelines include a maximum riser height of 7.75 inches, a minimum tread depth of 10 inches, and a maximum variation of 3/8 inch between the tallest and shortest riser in a flight. The rise plus run (in inches) should be between 17 and 18 for comfortable steps. This calculator uses a 7.5-inch riser default, which fits most codes, but you must verify with your local authority.

When cutting stringers, always use a level and a framing square to mark the notches, and double-check your measurements before cutting. Wear safety glasses and use a sharp saw. If you are not confident in your measurements, have a professional review your layout.

Frequently Asked Questions

How many stringers do I need?

For most residential stairs, you need at least three stringers: one on each side and one in the middle. For wider stairs (over 36 inches), add a stringer every 16 to 24 inches across the width. The calculator gives you the dimensions for one stringer; you will cut multiple identical stringers.

What is the ideal riser height?

Most building codes allow riser heights between 4 and 7.75 inches, with 7 to 7.5 inches being common for comfortable stairs. The calculator defaults to 7.5 inches, but you can change the total rise or the number of risers to achieve a different riser height.

Can I use this for deck stairs?

Yes, the same formula applies to deck stairs. The only difference is that the total rise is the height from the ground to the deck surface, and you may have an open stringer (without risers) if your code allows. The calculator works for both open and closed stringers.

Does the drawing show the actual cuts?

The drawing is a schematic representation. It shows the stringer as a straight line with right-angle notches, which is how you would mark the board. It does not show the top and bottom angled cuts or the tread thickness adjustments. Use the drawing as a visual guide, not a full template.

What if my total run is not a whole number?

The calculator accepts decimal inches. For example, a total run of 120.5 inches is fine. The stringer length and angle will be calculated accordingly. Just ensure you measure accurately to the nearest 1/8 inch.

Why does the calculator give a different number of risers than I expected?

The calculator uses a default riser height of 7.5 inches to determine the number of risers. If you have a specific riser height in mind, you can adjust the total rise or the number of risers manually. The calculator is a starting point; you may need to tweak the values to meet your code or preference.

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in rise | Total rise | in | 105 | 0
in run | Total run | in | 120 | 0
in tread | Tread depth | in | 10 | 0
out steps | Number of risers | - | ceil(rise / 7.5) | 0
out riser_h | Riser height | in | rise / steps | 2
out stringer_len | Stringer length | in | sqrt(run^2 + rise^2) | 2
out angle | Cut angle | deg | atand(rise / run) | 1