Stair Stringer Calculator
Work out riser count, exact riser height, total run, stringer length and stair angle from a total rise, with the comfort rules that separate good stairs from tiring ones.
Finished floor to finished floor. Measure it after the flooring goes down, not before.
A preference, not a constraint — the count gets rounded so risers come out equal.
Excluding nosing. 10 to 11 in is the comfortable range.
Used for tread material only.
Adds depth underfoot without adding to the run.
Rise + run comes to 18.2 in and 2R + T to 25.9 in — both inside the range stair builders have used for a century. These stairs will feel normal to walk.
What this calculator does
You give it one measurement that cannot be argued with — the total rise, floor to floor — plus the riser height and tread depth you would like. It returns the riser count that divides that rise evenly, the exact riser height that results, the tread count, the total run, the diagonal length of stringer stock you need to buy, the stair angle, and whether the geometry sits in the range that comfortable stairs occupy.
Stairs are the one part of a house where an eighth of an inch of sloppiness is felt by every person who uses it, every day, for the life of the building. They are also, arithmetically, one of the simplest things to get exactly right.
Total rise is the only fixed number
Everything else on a staircase is negotiable. The total rise is not: the floor above is where it is.
So the design process runs backwards from most estimating. You do not pick a riser height and multiply. You pick a riser height you want, divide the total rise by it, round to a whole number of risers, and then divide the total rise by that count to find what each riser actually becomes.
A 108-inch rise with a 7.5-inch target: 108 ÷ 7.5 = 14.4, round to 14 risers, 108 ÷ 14 = 7.714 inches each. Not 7.5. Not 7-3/4. 7.714, or a hair under 7-23/32, and every one of the fourteen is exactly that.
Why so fussy? Because the human gait calibrates to the first two steps and then stops looking. A single riser that differs by even a quarter-inch from its neighbours is a trip hazard, and codes generally allow no more than 3/8 inch of variation across an entire flight. Equal risers are not a nicety.
Treads: always one fewer
The top riser brings you level with the floor above, and that floor serves as the last tread. Fourteen risers, thirteen treads. Every time.
This is the mirror image of the fencepost error that adds a stud in wall framing — here you subtract one instead of adding one, for exactly the same structural reason, and it catches people just as reliably.
The comfort rules, and why they work
Two old rules survive because they encode something real about how people walk.
Rise + run ≈ 17 to 18 inches. A 7.5-inch riser with a 10.5-inch tread gives 18. Comfortable.
2 × rise + run ≈ 24 to 25 inches. The same stair gives 25.5. Also fine.
The second is the better rule because it captures the asymmetry: lifting your foot vertically costs roughly twice what moving it horizontally does, so the riser gets weighted double. It is why a very shallow stair — a 5-inch riser with an 18-inch tread — is not restful but exhausting. Your stride does not fit it, so you either mince or take two at a time, and neither is comfortable.
The calculator flags geometry outside roughly 23 to 26 inches on that rule. Outside it, the stairs will work; they will just feel wrong to everyone who uses them, and you will not be able to say why.
Run, stringer stock, and headroom
Total run is treads × tread depth. Note that the nosing — the overhang at the front of each tread — adds depth underfoot without adding to the run, which is exactly why nosings exist. An inch of nosing buys an inch of foot room per step for free.
Stringer stock is the hypotenuse: √(rise² + run²). For our example, √(108² + 136.5²) ≈ 174 inches, or 14.5 feet. Buy the 16-foot board. The notches at the top and bottom eat material, and a stringer cut from stock that was exactly long enough has no margin for the layout error you will make on the first one.
The input this calculator does not take, and the one that ruins more basement staircases than any other, is headroom. Codes typically require around 6 feet 8 inches measured vertically from the nosing line to whatever is above. Check it against the framing before you cut, because the fix — moving the opening above — is expensive after the fact.
Materials, briefly
Tread material comes out in board feet, at nominal one-inch thickness across the stair width. Actual treads are usually thicker, so treat the figure as a comparison number for pricing rather than a cut list. Stringers are typically 2×12, because a 2×10 has very little material left after the notches are cut out of it.
What this leaves out
- Code compliance. Maximum riser height, minimum tread depth, minimum width, handrail height and graspability, guard height and baluster spacing all vary by jurisdiction and by occupancy. Residential and commercial rules differ substantially. Check yours.
- Headroom. Discussed above; not an input here.
- Winders, landings and turns. This handles a straight run only. Landings break the flight into two separate calculations.
- Stringer structural capacity. How many stringers a given width needs, and what they are attached to, is a framing question.
- Accessibility requirements. Where they apply, they are more restrictive than base code on nearly every dimension.
For an outdoor flight, the same geometry applies, but tread material and fastening change entirely — the deck boards calculator covers the decking side of that job.
How this is calculated
risers = round( total rise ÷ target riser ) actual riser = total rise ÷ risers ← always divides evenly treads = risers − 1 total run = treads × tread depth stringer = √( rise² + run² ) comfort : 2 × riser + tread ≈ 24–25 in
Frequently asked questions
- How do I calculate stair risers?
- Divide the total rise by roughly seven and a half inches, round to the nearest whole number, then divide the total rise by that count. The second division is the one that matters — risers must be equal, so the rise per step is whatever the total divided by the count gives you, not the number you started with. A 108-inch rise over 14 risers is 7.714 inches each.
- Why is there one fewer tread than riser?
- Because the top riser lands on the floor above, and that floor is the last tread. A flight with 14 risers has 13 treads. If you cut 14 treads you will have one left over and a stringer that is one tread too long.
- What is the 2R + T rule?
- Twice the riser height plus the tread depth should land between about 24 and 25 inches. It approximates the length of a human stride on an incline, and stairs that satisfy it feel effortless while stairs that miss it feel either cramped or like climbing a ladder. A 7.5-inch riser with a 10.5-inch tread gives 25.5 — comfortable. A 6-inch riser with a 16-inch tread also gives 28, and walking it is oddly exhausting.
- How long a board do I need for a stair stringer?
- The hypotenuse of the total rise and the total run, plus material at both ends for the cuts and the bearing. A 108-inch rise with a 136.5-inch run gives a 174-inch diagonal, so a 16-foot board is the practical order — a 14-foot board leaves nothing for the notches at either end.
- Does the bottom step need to be cut shorter?
- Yes. Subtract the tread thickness from the bottom riser cut of the stringer. Skip it and the first step is a full tread thickness taller than the rest, which most codes prohibit and every foot in the house notices at about eleven at night.