How to use the stair calculator
Everything starts with the total rise: the vertical distance from the finished surface at the bottom to the finished surface at the top. Get this number right and the rest follows.
- Indoors: measure floor to floor, then allow for any flooring not yet installed. Adding ¾ in of hardwood upstairs makes the top step ¾ in taller than the rest unless you plan for it.
- Deck stairs: measure from the deck surface down to where the bottom step will land, not to the ground at the deck's edge. On a slope, the landing spot can be several inches lower. Estimate the run, find that spot, extend a level or a straight board out from the deck, and measure down from there.
Then set the maximum riser height you'll allow. The calculator finds the fewest risers that stay under it and divides the rise evenly among them. Tread depth is measured horizontally from the face of one riser to the next (nosing to nosing). The nosing is the extra overhang on top of that.
Stair formulas
Riser height = total rise ÷ risers
Treads = risers − 1
Total run = treads × tread depth
Stringer length = √(total rise² + total run²)
Angle = arctan(riser height ÷ tread depth)
There is one fewer tread than risers because the top "step" is the upper floor or deck itself. The stringer length is the diagonal from the bottom floor to the top landing. The board you cut it from must be longer, to allow for the top and bottom cuts, so buy the next standard length up. The stair angle is the pitch of the line along the nosings, which is set by each riser and tread. Dividing the total rise by the total run would overstate it slightly, because the run leaves out the top floor, which acts as the last tread.
A long-standing comfort rule is that twice the riser plus the tread (2R + T) should come to about 24–25 in (61–64 cm). Stairs built to the code maximum riser and minimum tread come out slightly steeper than that.
Worked example: interior stairs, 108 in rise
108 ÷ 7.75 = 13.9, which rounds up to 14 risers of 108 ÷ 14 = 7.71 in each, just under 7¾ in. That gives 13 treads. At 10 in each the total run is 130 in (10 ft 10 in). The stringer is √(108² + 130²) = 169.0 in (14.1 ft), so you'd cut it from a 16 ft 2×12, and the stair angle is arctan(7.71 ÷ 10) = 37.6°. The comfort check gives 2 × 7.71 + 10 = 25.4 in, a little steep. If you have the room, a 7¼ in maximum riser gives 15 risers of 7.2 in. With 10½ in treads, that's 14 treads, a 147 in run and a 2R + T of 24.9 in.
Deck example: 30 in rise
30 ÷ 7.75 = 3.9, so 4 risers of 7.5 in, 3 treads and a 30 in run. The stringer is 42.4 in, the angle is arctan(7.5 ÷ 10) = 36.9°, and 2R + T = 25 in. With a 1 in nosing, each tread board is 11 in deep, close to two 2×6 boards (5½ in each) with a small gap between them.
Common code limits for home stairs
These are the main values in recent editions of the International Residential Code (IRC), which most US jurisdictions adopt, often with local amendments. Commercial buildings follow the IBC, which is stricter (a 7 in maximum riser and an 11 in minimum tread). Always confirm with your building department.
| Item | IRC value |
|---|---|
| Maximum riser height | 7¾ in |
| Minimum tread depth (nosing to nosing) | 10 in |
| Nosing projection (solid risers, treads under 11 in) | ¾–1¼ in |
| Largest minus smallest riser or tread in a flight | ⅜ in max |
| Minimum headroom | 6 ft 8 in |
| Minimum width | 36 in |
| Maximum rise between floors or landings | 151 in (12 ft 7 in) |
| Handrail | Required with 4 or more risers; 34–38 in above the nosings |
The ⅜ in tolerance is why the total rise has to be measured accurately. If the first or last step comes out different from the others, it is the step people trip on.
How stringers are cut
Most stringers are cut from 2×12 lumber. Set stair gauges (small clamps) on a framing square at the riser height on one leg and the tread depth on the other. Then "walk" the square along the board, marking one notch per step. Two adjustments matter:
- Drop the stringer. Trim the bottom of the stringer by the thickness of one tread. Otherwise the first step ends up taller than the rest once the treads are on.
- Mind the top. Depending on how the stringer attaches (hung below a deck rim, or flush with it), the top riser may need adjusting so it matches the others.
Cut one stringer, test it in place, then use it as a pattern for the rest. Space stringers to suit the tread material. Thin or composite treads often need 12 in centers, and the stringer count here uses the spacing you enter.
Deck stairs vs. interior stairs
Deck stairs usually have open risers, so the gap between treads must not let a 4 in sphere pass through when the total rise is more than 30 in. They also need a firm landing at the bottom, such as a concrete pad or compacted gravel; the concrete calculator handles the pad. Stringer attachment and guards on the open sides are covered in deck guides such as AWC's DCA 6. Interior stairs have the added constraint of headroom: check the 6 ft 8 in clearance along the full length of the stair, measured up from the line of the nosings. For the deck itself, see the deck calculator.
Frequently asked questions
How many steps do I need for a 9 ft rise?
A 108 in rise needs 14 risers at a 7¾ in maximum. Each one is 7.71 in, with 13 treads. You step up 14 times, but the 14th step lands on the upper floor.
What is the maximum stair riser height?
The IRC allows up to 7¾ in for homes, with a minimum tread of 10 in. Commercial buildings under the IBC are limited to 7 in risers and 11 in treads. Local codes can differ.
What is the 2R + T stair rule?
Twice the riser height plus the tread depth should be about 24–25 in for a comfortable stride. For example, 7 in risers and 10½–11 in treads (2 × 7 + 10.5 = 24.5).
How long should a stair stringer be?
Use the Pythagorean theorem: √(total rise² + total run²). For a 108 in rise and 130 in run that is about 169 in, or 14.1 ft. Buy a longer board, here a 16 ft 2×12, to allow for the end cuts.
How many stringers do I need?
Enough to keep stringer spacing within what your treads can span. For a 36 in wide stair at 16 in maximum spacing, that is 4 stringers. Many composite treads need 12 in spacing, so check the manufacturer.
Why is there one fewer tread than risers?
The top riser steps up onto the upper floor or deck, which acts as the last tread. A stair with 14 risers has 13 treads.