How to use the stair calculator
- Enter the total height from the lower floor to the upper floor in inches.
- Set your ideal rise, which is the target height of each individual step.
- Enter the tread depth, the horizontal surface you step on.
- Read the calculated number of risers, actual rise, total run and stringer length below.
How the stair math works
A stair calculator determines how many steps fit into a given vertical space. The first calculation divides the total height by the ideal rise and rounds to the nearest whole number to get the count of risers. Then it divides the total height by that count to find the exact actual rise.
For example, with a total height of 108 inches and an ideal rise of 7.5 inches: 108 / 7.5 = 14.4, which rounds to 14 risers. The actual rise becomes 108 / 14 = 7.7143 inches. The number of treads is always one fewer than the number of risers because the top floor acts as the final landing. With 14 risers there are 13 treads. If each tread is 10 inches deep, the total run is 13 x 10 = 130 inches.
Stringer length formula
The stringer is the structural board cut into a zigzag pattern to support the treads and risers. Its length is the hypotenuse of a right triangle formed by the total rise and the total run. Using the Pythagorean theorem:
Stringer = sqrt(totalRun² + totalHeight²)
Continuing the previous example: sqrt(130² + 108²) = sqrt(16900 + 11664) = sqrt(28564) = 169.01 inches. Always add a few extra inches at the top and bottom for plumb and level cuts when ordering lumber. For those interested in the geometry behind this, the slope calculator explains the same rise-over-run relationship used to determine pitch.
Common stair dimensions reference
Building codes set limits on how tall and shallow a step can be. The International Residential Code (IRC) caps the maximum rise at 7.75 inches and sets the minimum tread depth at 10 inches. Here are typical configurations for common floor heights assuming a 10-inch tread depth.
| Total height | Risers | Actual rise | Treads | Total run |
|---|---|---|---|---|
| 96 in (8 ft) | 13 | 7.3846 in | 12 | 120 in |
| 105 in (8 ft 9 in) | 14 | 7.5 in | 13 | 130 in |
| 108 in (9 ft) | 14 | 7.7143 in | 13 | 130 in |
| 120 in (10 ft) | 16 | 7.5 in | 15 | 150 in |
The 2R + T rule for comfort
Architects use a simple formula to check whether a stair feels natural to walk on: 2 x Rise + Tread = 24 to 25 inches. This accounts for the average human stride. If your actual rise is 7.5 inches and your tread depth is 10 inches, the result is 2 x 7.5 + 10 = 25, which sits perfectly within the comfortable range.
If the sum falls below 24, the stairs feel too shallow and people may trip. Above 25, they feel steep and tiring to climb. Adjusting either the rise or the tread depth in this stair calculator lets you test combinations until the ratio lands in the safe zone.
Practical tips for cutting stringers
Once you have the stair dimensions, layout matters as much as the math. Use a framing square with stair gauges clamped at the exact rise and run measurements to mark each step on the stringer board. Always start from the same reference edge to avoid compounding small errors across 14 or more cuts.
Remember that the bottom riser will be one tread thickness shorter than the others once the treads are installed. If your treads are 1 inch thick, subtract 1 inch from the first riser cut so all finished steps end up the same height. Uneven risers are a leading cause of stair falls and violate most building codes.
Worked examples
Each result below was produced by the same code the tool runs, so you can check your own numbers against them.
| Example | Input | Result |
|---|---|---|
| Standard 9-foot ceiling | Total height (inches): 108; Ideal rise per step (inches): 7.5; Tread depth (inches): 10 | Number of risers: 14; Actual rise: 7.7143; Number of treads: 13; Total run: 130; Stringer length: 169.01; 2R + T: 25.43 |
| 8-foot ceiling with joist | Total height (inches): 105.5; Ideal rise per step (inches): 7.5; Tread depth (inches): 10 | Number of risers: 14; Actual rise: 7.5357; Number of treads: 13; Total run: 130; Stringer length: 167.42; 2R + T: 25.07 |
| Deck stairs (36 inches) | Total height (inches): 36; Ideal rise per step (inches): 7; Tread depth (inches): 11 | Number of risers: 5; Actual rise: 7.2; Number of treads: 4; Total run: 44; Stringer length: 56.85; 2R + T: 25.4 |
| Steep basement stairs | Total height (inches): 96; Ideal rise per step (inches): 8; Tread depth (inches): 9 | Number of risers: 12; Actual rise: 8; Number of treads: 11; Total run: 99; Stringer length: 137.9; 2R + T: 25 |
FAQ
What is the standard rise for a stair step?
Most residential building codes limit the maximum rise to 7.75 inches. A comfortable target is between 7 and 7.5 inches per step.
How do I measure total height for stairs?
Measure vertically from the finished lower floor to the finished upper floor. Include the thickness of any flooring material that will be installed later.
Why is the number of treads one less than the number of risers?
The top floor serves as the last walking surface, so you need one fewer tread than riser. Fourteen risers require thirteen treads.
What thickness of lumber should I use for a stringer?
A 2x12 board is standard for residential stringers because it leaves enough wood behind the notches to remain structurally sound after cutting.
Can I use this stair calculator for deck stairs?
Yes. Enter the height from the ground to the top of the deck surface as the total height. Deck stairs often use slightly deeper treads, such as 11 inches.
Does this tool store or send my measurements?
No. All calculations happen locally in your browser. Nothing is uploaded to any server.