How Stair Stringer Math Actually Works
Every deck stair comes down to one number: total rise, the exact vertical distance from the ground (or landing pad) up to the top of your deck surface. Everything else — how many steps you need, how deep each tread is, how long to cut your 2×12 — falls out of that single measurement.
The calculator above starts by dividing your total rise by the tallest riser height your code allows (7¾" by default) and rounding up to a whole number of steps. Rounding up matters — round down instead and your riser height would land above the legal maximum. Once the step count is set, dividing total rise by that number again gives you the actual riser height, split perfectly evenly across every step. That evenness isn't a nice-to-have: an inspector will fail a staircase where one riser is even 3/8" taller than the rest, because an uneven step is one of the most common causes of a stair fall. Your brain memorizes the rhythm of the first two steps and stops paying close attention, so it doesn't adjust for the one step that breaks the pattern.
The Two Formulas Behind Every Cut
Once you know your riser height and tread depth, two formulas give you everything you need to start cutting:
- Stringer length — the Pythagorean theorem: length = √(total rise² + total run²). Picture the stringer as the hypotenuse of one big right triangle, where rise is one leg and run (tread depth × number of treads) is the other. That's the length of 2×12 you need before any cuts are made.
- Cut angle — basic trigonometry: angle = arctan(rise ÷ run). This is the "plumb cut" angle you'd set on a speed square for the vertical riser cuts. Subtract it from 90° and you get the "level cut" angle for the horizontal tread cuts.
Most carpenters skip the protractor entirely and use a framing square with a pair of stair gauges clamped at the riser height and tread depth instead. It's faster, it's more accurate, and it's genuinely how stringers get laid out on real job sites — not just how it's explained in theory.
What Code Actually Requires (and Why It Depends on Where You Live)
The baseline most US builders work from is the International Residential Code: a maximum riser height of 7¾" and a minimum tread depth of 10", with no more than 3/8" difference between the tallest and shortest riser — or deepest and shallowest tread — in a single flight. That's the default this calculator uses.
But "IRC" doesn't mean identical rules everywhere. States adopt the model code and then amend it. Virginia and Pennsylvania, for example, allow risers up to 8¼" with a 9" minimum tread — noticeably more permissive than the baseline. Before cutting anything, it's worth a two-minute call to your local building department to confirm exactly what they enforce; the "Max riser height" field above is adjustable for this exact reason.
A few other numbers worth knowing: stairways need at least 36" of clear width, a handrail is required once you have four or more risers, and any deck surface more than 30" off the ground needs a guard rail at least 36" tall. If your total rise runs past about 12 feet, most jurisdictions expect a landing partway up rather than one continuous flight.
Buying Lumber for Your Stringers
Stringers are almost always cut from pressure-treated 2×12 — its 11¼" actual width leaves enough solid wood at each notch for a standard rise and run, with room to spare. When you buy your board, add roughly a foot beyond the calculated stringer length; that extra material becomes the "seat cut" at the bottom, where the stringer sits on a pad or footing, and the plumb cut at the top where it meets the deck framing.
How many stringers you need comes down to width, not looks. Keep stringers no more than 16" apart on-center for standard wood treads, and plan on a minimum of four for any stairway wider than 36". Composite decking is stiffer underfoot but often needs tighter support — many manufacturers call for 10"–12" spacing, so check your product's install guide. And don't skip the base: every stringer needs to land on a concrete pad, poured footing, or compacted gravel, never bare dirt, or the wood will start rotting and the stairs will settle unevenly within a season or two.
Deck Board Spacing, in Short
The IRC doesn't actually specify a gap number for deck boards — it defers to the manufacturer's instructions. In practice, most builders default to a 1/8" gap between dry, kiln-treated boards. Freshly pressure-treated lumber is usually still wet when you buy it and shrinks as it dries, so it's common to install it nearly tight and let a natural 1/8"–3/16" gap open up on its own over the following weeks. Composite decking (Trex, TimberTech, and similar) expands and contracts more with temperature, and most brands specify around a 3/16" side gap — always check your specific product line before you start, since a gap that looks right in spring can close up or gape open by the following summer.
Quick Questions
Do I need a permit for deck stairs? Usually, yes — especially once the deck itself is more than about 30" off the ground. Permit rules are set locally, so check with your city or county before digging footings.
Can two stringers ever be enough? Only for narrow stairs under 36" wide using thick 2× treads placed right at the edges. Three stringers — both edges plus a center support — is the safe default almost everyone should use.
What angle should deck stairs be built at? Most comfortable residential stairs land between 30° and 35° from horizontal. The classic "7-11" combination — a 7" riser with an 11" tread — works out to about 32.5°, which is why so many builders default to it.
Why does the calculator round up to a whole number of steps instead of to the nearest one? Rounding to the nearest step can push an individual riser above your code's legal maximum. Rounding up, then splitting the total rise evenly across that many steps, always keeps every riser at or under your limit.