Stair calculator
Enter your total rise — steps, riser height, run and stringer length update live.
Stair elevation
Standard mount: drop the bottom seat cut by one tread thickness so the first step finishes the same height as the rest.
Advanced calculator
Mount type, riser sizing, tread depth or total run, nosing, lumber and both drawings.
Stringer cut layout
One notch per riser, laid out along the board. Cut the first riser 5 13/16" so the finished first step matches the rest.
Plan view
The stair seen from above, drawn to scale: 15 treads at 10 1/2" filling 157 1/2" of floor.
| Step | Rise | Run | Riser cut | Height to top |
|---|---|---|---|---|
| 1 | 6 13/16" | 10 1/2" | 5 13/16" | 6 13/16" |
| 2 | 6 13/16" | 10 1/2" | 6 13/16" | 13 5/8" |
| 3 | 6 13/16" | 10 1/2" | 6 13/16" | 20 7/16" |
| 4 | 6 13/16" | 10 1/2" | 6 13/16" | 27 1/4" |
| 5 | 6 13/16" | 10 1/2" | 6 13/16" | 34 1/16" |
| 6 | 6 13/16" | 10 1/2" | 6 13/16" | 40 7/8" |
| 7 | 6 13/16" | 10 1/2" | 6 13/16" | 47 11/16" |
| 8 | 6 13/16" | 10 1/2" | 6 13/16" | 54 1/2" |
| 9 | 6 13/16" | 10 1/2" | 6 13/16" | 61 5/16" |
| 10 | 6 13/16" | 10 1/2" | 6 13/16" | 68 1/8" |
| 11 | 6 13/16" | 10 1/2" | 6 13/16" | 74 15/16" |
| 12 | 6 13/16" | 10 1/2" | 6 13/16" | 81 3/4" |
| 13 | 6 13/16" | 10 1/2" | 6 13/16" | 88 9/16" |
| 14 | 6 13/16" | 10 1/2" | 6 13/16" | 95 3/8" |
| 15 | 6 13/16" | 10 1/2" | 6 13/16" | 102 3/16" |
| 16 | 6 13/16" | landing | 6 13/16" | 109" (floor) |
Step 1’s riser cut is 5 13/16" — one tread thickness shorter, so the finished first step matches the rest.
Code checks (IRC residential)
- Riser height ≤ 7 3/4"Pass — 6 13/16" per riser
- Tread depth ≥ 10"Pass — 10 1/2" excluding nosing overlap
- 2 × riser + tread between 24" and 25"Pass — 24.13"
- Comfort angle 30–37°Pass — 33.0° from horizontal
- Stringer throat ≥ 3 1/2"Pass — 5 9/16" left on a 2x12 (11 1/4")
How the stair calculation works
Total rise is fixed by the building: it is the vertical distance from the finished lower floor to the finished upper floor, including any flooring you still plan to install. Divide it by your target riser height and round to a whole number — you cannot build a fraction of a step. Dividing the total rise by that whole number gives the exact riser height, and every riser in the flight must match it.
With a standard mount the top step lands flush with the upper floor, so that floor serves as the final tread and tread count is one less than riser count. With a flush mount the stringer hangs off the header level with the floor, so tread count equals riser count and the flight consumes one more tread of run. Multiplying tread count by tread depth gives total run; stringer length is the diagonal across rise and run, so add extra material for the plumb cut at the top and the seat cut at the bottom.
Throat depth is what is left of the stringer board behind the notch, measured square to the back edge. Each notch removes riser × tread ÷ the notch hypotenuse, which is why a steep stair on a 2x10 can be cut down to a dangerously thin stringer. Most inspectors want at least 3 1/2 inches remaining; if you cannot hit that, move to a 2x12 or reduce the riser height.
Reading the results
A comfortable residential stair usually lands near a 7 inch riser with an 11 inch tread and an angle between 30 and 37 degrees. Steeper than 38 degrees feels like a ladder; shallower than 28 degrees eats floor space. Nosing overhangs the riser below and adds walking depth without adding run, which is why it is listed separately from tread depth.
The bottom riser cut matters more than it looks. On a standard mount, the stringer sits on the lower floor and the first tread adds its own thickness, so you must shorten the bottom of the stringer by exactly one tread thickness or the first step will be taller than every other one.
Formulas
risers = round(total rise ÷ target riser height)— rounded to the nearest whole number; you cannot build a fraction of a step.
riser height = total rise ÷ risers— the exact height every riser must be cut to.
treads = risers − 1 (standard mount) or risers (flush mount)— with a standard mount the upper floor acts as the last tread.
total run = treads × tread depth— the horizontal floor space the flight occupies. Nosing is not included.
stair angle = arctan(riser height ÷ tread depth)— measured from horizontal.
stringer length = √(total rise² + total run²)— the tread-line length. Buy at least one foot longer for the plumb and seat cuts.
bottom riser cut = riser height − tread thickness (standard mount)— so the first step matches the others once treads are installed.
Worked example
A basement stair with a total rise of 109 inches and a target riser of 7 inches. 109 ÷ 7 = 15.57, which rounds to 16 risers. The exact riser height is 109 ÷ 16 = 6.8125 inches, or 6 13/16". With a standard mount there are 15 treads; at 10 1/2" each the total run is 157 1/2". The angle is arctan(6.8125 ÷ 10.5) ≈ 33.0°, comfortably inside the 30–37° range. Stringer length is √(109² + 157.5²) ≈ 191 9/16", so an 18-foot 2x12 (board length ≈ 200") is the board to buy. Both 6 13/16" risers and 10 1/2" treads pass the IRC limits, and 2 × 6.81 + 10.5 = 24.1 satisfies the comfort rule.
Frequently asked questions
How do I measure total rise correctly?
Measure vertically from the finished lower floor to the finished upper floor, not to the subfloor or joists. If you still plan to install flooring on either level, add its thickness now. A mistake here shifts every riser in the flight.
What is the standard riser height and tread depth?
Most residential stairs land around a 7" riser and a 10–11" tread. The IRC caps risers at 7 3/4" and requires treads of at least 10". A 7" riser with an 11" tread is the classic comfortable stair.
How many steps do I need for an 8-foot or 9-foot ceiling?
Total rise is ceiling height plus the upper floor thickness, so an 8-foot ceiling is usually about 105–109" of rise and needs 15–16 risers. A 9-foot ceiling is roughly 117–121" and needs 17 risers. Enter your measured rise above for the exact count.
What is the difference between standard and flush mount?
With a standard mount the stringer sits below the upper floor and the floor itself is the last tread, so there is one fewer tread than risers. With a flush mount the top tread is level with the upper floor, so treads equal risers and the stringer is one tread longer.
How long should my stringer board be?
The calculator gives the tread-line length, the diagonal from bottom to top. Add about 12" for the plumb cut at the top and the seat cut at the bottom, then round up to the next standard board length. A 2x12 is the usual choice because it leaves enough solid wood under the notches.
Does this calculator meet building code?
The code checks follow the International Residential Code (IRC R311.7) for one- and two-family homes: 7 3/4" maximum riser, 10" minimum tread, 3/8" maximum variation, 6' 8" headroom. Many jurisdictions amend these numbers and commercial stairs follow stricter rules, so confirm with your local building department before cutting.