Carpentry Stair Calculator: Rise, Run & Stringers

A carpentry stair calculator works out the number of steps, the rise and run of each step, and the stringer length for a straight staircase. You enter the total vertical rise (floor-to-floor height) and the total horizontal run (or available floor space), and it returns the individual step dimensions and the angle of the stair. This is the first step in laying out a safe, code-compliant stair before you cut any wood.

Formula

The core formulas for a straight stair are:

• Number of risers = ceil(Total Rise / Target Riser Height). The target riser height is usually 7 inches (178 mm) for comfort, but local codes may allow up to 7.75 inches (197 mm).
• Actual riser height = Total Rise ÷ Number of Risers.
• Tread depth (run) = Available Run ÷ (Number of Risers − 1). The last riser meets the upper floor, so there is one fewer tread than risers.
• Stringer length = √(Total Rise² + Total Run²), where Total Run = Tread Depth × (Number of Risers − 1).

Variables: Total Rise (in inches or mm) is the vertical distance from the finished floor below to the finished floor above. Available Run (in inches or mm) is the horizontal distance you have for the stair, measured from the edge of the upper floor to the point where the stair starts. Riser height is the vertical face of each step; tread depth is the horizontal depth of each step (not including any nosing overhang). Stringer length is the length of the diagonal board that supports the steps.

Worked Example

Using the defaults from the calculator above (Total Rise = 105 in, Available Run = 120 in):

1. Target riser height = 7.5 in (the calculator’s default). Number of risers = ceil(105 / 7.5) = ceil(14) = 14.
2. Actual riser height = 105 ÷ 14 = 7.5 in exactly.
3. Tread depth = 120 ÷ (14 − 1) = 120 ÷ 13 = 9.23 in.
4. Total run = 9.23 × 13 = 120 in. Stringer length = √(105² + 120²) = √(11025 + 14400) = √25425 = 159.45 in.

The calculator shows 14 steps, a 7.50-inch riser, a 9.23-inch tread, and a 159.5-inch stringer. This matches the manual calculation.

Why the Rise and Run Ratio Matters

The relationship between riser height and tread depth determines how comfortable and safe a stair is to climb. A step that is too tall or too shallow forces an awkward gait and increases fall risk. The classic rule is that twice the riser plus the tread (2R + T) should equal about 25 inches (635 mm). For the example above: 2 × 7.5 + 9.23 = 24.23 inches, which is within the common comfort range. Most building codes also require that riser heights vary by no more than 3/8 inch (9.5 mm) between adjacent steps, and tread depths vary by no more than 3/8 inch as well. The calculator gives you a uniform set of dimensions, but if you are working to a specific code, check the local limits before cutting.

How to Choose Your Inputs

The two inputs you control are the total rise and the available run. The total rise is fixed by your building’s floor-to-floor height, so measure it carefully from the finished floor surface (including tile, hardwood, or carpet) to the finished floor above. The available run is the horizontal space you can dedicate to the stair. If you have a tight space, you may need to increase the riser height (up to the code maximum) to reduce the number of steps, which shortens the run. Conversely, if you have plenty of space, you can use a lower riser and a deeper tread for a more comfortable stair. The calculator’s target riser height of 7.5 inches is a reasonable middle ground; adjust it if your local code or personal preference differs.

Common Mistakes and How to Avoid Them

• Forgetting the nosing: Tread depth is measured from the face of one riser to the face of the next riser, not including the nosing overhang. If you add a 1-inch nosing, the actual board you cut must be deeper by that amount.
• Mixing units: Always use the same unit (inches or millimeters) for both rise and run. Converting one to feet and the other to inches will give a nonsensical result.
• Counting steps wrong: The number of risers is the number of vertical climbs, which is one more than the number of treads. Many beginners cut one fewer or one more riser than needed.
• Ignoring the upper floor thickness: The total rise is from finished floor to finished floor, not from the subfloor. If you measure before flooring is installed, add the thickness of the flooring to both the lower and upper levels.
• Assuming the stringer is the same as the run: The stringer is the diagonal, so it is always longer than the horizontal run. Use the Pythagorean theorem, not just the run.

Stringer Layout and Cutting

Once you have the riser height and tread depth, you can lay out the stringer on a 2×12 board. Use a framing square with stair gauges: set the square so the long leg (the body) is at the tread depth and the short leg (the tongue) is at the riser height. Place the square on the board, mark the first cut, then slide the square along the board, repeating the marks for each step. The top of the stringer must be cut to fit against the upper floor (usually a notch), and the bottom must be cut to sit on the lower floor. Always subtract the thickness of the tread material from the bottom riser cut if you are installing treads on top of the stringer. A common error is to cut all risers the same height, forgetting that the bottom riser should be shorter by the tread thickness so the actual step height remains uniform.

Limitations of a Simple Calculator

This calculator handles straight, single-flight stairs only. It does not account for landings, winders (angled steps), or open risers. It also assumes the stair is uniform and that the available run is a straight horizontal line. For L-shaped or U-shaped stairs with landings, you need to break the stair into multiple flights and calculate each separately. Additionally, the calculator does not check headroom clearance (the vertical distance between the stair and the ceiling above), which is typically required to be at least 6 feet 8 inches (2032 mm). You must verify headroom separately, especially for basement stairs or stairs under a sloped ceiling. Finally, local building codes may have specific requirements for riser height, tread depth, and handrail placement that override the general comfort guidelines used here. Always consult the code that applies to your area before building.

Frequently Asked Questions

What is the standard stair rise and run?

Most residential building codes in the US allow a maximum riser height of 7.75 inches (197 mm) and a minimum tread depth of 10 inches (254 mm) with a nosing. A commonly used comfortable target is a 7-inch riser with an 11-inch tread, which gives a 2R + T of 25 inches. However, the exact numbers vary by jurisdiction, so check your local code.

How many steps do I need for a 10-foot ceiling?

A 10-foot ceiling means the total rise is about 120 inches (10 ft × 12 in/ft) plus the floor thickness. Using a 7-inch target riser, you would need about 17 or 18 risers (120 ÷ 7 = 17.14, round up to 18). The actual riser height would be 120 ÷ 18 = 6.67 inches. The number of treads would be one less, so 17 treads.

How do I measure total rise for a stair?

Measure the vertical distance from the finished floor of the lower level to the finished floor of the upper level. Use a straight edge and a level to transfer the upper floor level down to a wall or use a laser level. Be sure to include the thickness of any flooring that will be installed, such as hardwood or tile, in that measurement.

What is a stair stringer and how many do I need?

A stringer is the diagonal structural board that supports the treads and risers. For a typical residential stair, you need at least three stringers for a 36-inch-wide stair (one on each side and one in the middle). For wider stairs or heavier loads, add more stringers, spacing them no more than 18 inches apart.

Can I use this calculator for outdoor stairs?

Yes, the same rise/run math applies, but outdoor stairs often use a slightly lower riser and deeper tread for safety in wet conditions. Also, outdoor stringers must be made of pressure-treated lumber or a rot-resistant material. The calculator does not account for the extra thickness of outdoor treads, so adjust the bottom riser cut accordingly.

What is the maximum riser height allowed by code?

Most US building codes (based on the International Residential Code) allow a maximum riser height of 7.75 inches (197 mm) for residential stairs. Some local codes may be stricter. The minimum tread depth is usually 10 inches (254 mm) with a nosing, or 11 inches (279 mm) without. Always verify with your local building department.

Related

• Buco Concrete Calculator: How to Use It
• Buco Brick Calculator: How to Estimate Bricks
• BPM Pitch Calculator: Find Key & Tempo

in rise | Total rise (floor to floor) | in | 105 | 0
in run_avail | Available horizontal run | in | 120 | 0
out step_count | Number of steps (risers) | - | ceil(rise / 7.5) | 0
out riser_h | Riser height | in | rise / step_count | 2
out tread_d | Tread depth (run) | in | run_avail / (step_count - 1) | 2
out stringer_len | Stringer length (hypotenuse) | in | sqrt((riser_h * step_count)^2 + (tread_d * (step_count - 1))^2) | 1