Stair Calculator

How to use this stair calculator

1. Measure the total rise. Finished floor to finished floor, or deck surface to the finished landing pad at the bottom. This is the one measurement that has to be right — everything else is derived from it. If the concrete pad or the flooring isn't down yet, add its thickness now rather than discovering it later.
2. Set your target riser. Seven inches is the number most people find comfortable. The calculator divides your rise into equal risers as close to that target as it can get, and if your target would push a step past the legal 7 3/4 inch maximum it quietly adds a riser and tells you it did.
3. Set the tread depth and material. Tread depth is measured nosing to nosing, not board width. The material picker matters more than it looks: tread thickness is what sets the bottom cut, and getting it wrong is the single most common way a first stair ends up with an uneven first step.
4. Pick the mount and width. Standard mount hangs the stringer off the face of the rim, so the landing is your top step. Flush mount cuts that top step into the stringer. Width drives how many stringers you need.
5. Read the code panel, then take the cut card. Every line cites the section it's checking. When it's green, hit "Cut card PDF" — you get the square settings, the bottom-cut drop, the running mark-out and the board length to buy, on one page you can fold into a pocket.

Why this stair calculator is different

There are a dozen stair calculators online and most of them do the same arithmetic correctly. They stop in the same place, too — they hand you a riser height and a stringer length and leave the two questions that actually stall a project unanswered.

• It tells you whether the stair is legal, rule by rule. Most calculators park a wall of code text next to the result and let you compare the numbers yourself. This one checks riser height, tread depth, nosing, headroom, flight rise, width and handrail against the specific IRC section each rule lives in, and shows you a pass or a fail on each.
• It checks the two things that fail an inspection but never appear in a calculator. How much uncut board is left behind your notches (the throat — five inches minimum), and how many stringers your width needs at eighteen inches on center. Cut a stair on 2x10 stock and the numbers all look fine right up until the stringer flexes.
• It gives you a mark-out, not just dimensions. A running table of cumulative rise and run to every step, so you pull from one point instead of stepping the square up the board and stacking a sixteenth of error into each riser.
• It knows the bottom step is different. The first cut is one tread thickness shorter than the rest — "dropping the stringer." Miss it and every finished step is right except the first one, which is the one people trip on.
• Free to embed, no ads, no cart. Two of the pages ranking above this one exist to sell you steel framing or composite decking. This one just does the math, and you can put it on your own site.

How it works (the math)

All of it is arithmetic and one right triangle. Nothing here is proprietary:

Number of risers  N = round(total rise / target riser)
                      (add risers while total rise / N > 7.75)
Riser height      R = total rise / N
Steps on stringer D = N - 1  (standard mount)  |  N  (flush mount)
Total run         G = D x tread depth
Bottom cut        E = R - tread thickness
Stringer below
  the landing     H = R + tread thickness (standard) | tread thickness (flush)
Stringer length   L = sqrt((total rise - H)^2 + G^2)
Stair angle       A = arctan(R / tread depth)
Throat left       T = stock width - (R x tread depth) / sqrt(R^2 + tread depth^2)
Stringers         n = max(3, ceil(width / 18) + 1)

Why the rise gets divided evenly. The code allows no more than 3/8 inch of variation between the tallest and shortest riser in a flight, and your foot notices far less than that. Dividing the total rise by a whole number of risers is the only layout that is uniform by construction, so that's what this does — you nominate a target, and it picks the riser count that lands closest to it.

Why the bottom cut is short. Cut every notch identically and the first step ends up one tread thicker than the others once the treads go on, because the stringer is sitting on the ground while every other tread sits on a notch. Taking one tread thickness off the bottom cut — "dropping the stringer" — makes all the finished steps equal.

Why the throat matters. Cutting a sawtooth into a board removes material from the middle of it. What's left behind the notch is the beam. The corner of each notch sits (rise x run) / sqrt(rise² + run²) below the line through the notch tips, so a 2x12 at a 7 inch rise and 10 1/2 inch run leaves about 5 3/8 inch of throat. The same cut in a 2x10 leaves about 3 3/8 inch, which is why deck guides specify 2x12 minimum and nothing smaller.

The geometry here was checked against the two calculators currently ranking first and second for this search, and every fixture in sites/diy/src/data/tools/stair-calculator/fixtures.json runs in CI before each deploy. If the math drifts, the build fails.

Stair stringer calculator

The stringer is the notched 2x12 that carries everything else, and it's the part people cut twice. The tool gives you four numbers for it:

• Square settings — the rise and the run, which are the two marks you set your framing-square gauges to. Every notch is laid out from the same two numbers.
• Bottom cut — the shortened first rise, as described above.
• Stringer length — tip to tip of the finished cut, which is the minimum board you can lay it out on. The cut card rounds it up to the next stock length so you know what to actually buy.
• Throat — the uncut material left behind the notches, checked against the 5 inch minimum.

Cut one stringer, carry it to the opening and test it in place before you cut the other two. A stringer that's a quarter inch off is a ten minute fix on the first board and an afternoon on the third. A good circular saw takes each notch to the corner and no further; finish the inside corners with a handsaw or a jigsaw rather than overcutting, because every overcut takes strength out of the throat you just measured.

Deck stair calculator

Deck stairs are the same math with three extra rules, all of which the tool applies when you pick "Deck" at the top:

• 2x12 stringers, minimum. The prescriptive deck guide doesn't allow smaller, and the throat calculation shows you why.
• Three cut stringers, minimum, no more than 18 inches apart. A 36 inch stair gets three; a 48 inch stair gets four. The tool sizes this from your width.
• An intermediate landing over 12 feet of rise, which is also where the IRC's per-flight limit lands.

Measure the total rise to the finished landing pad, not to the dirt — if the pavers or the concrete aren't there yet, add their thickness or your bottom step will be short by exactly that much. Treads are usually two 2x6 or two 5/4x6 boards with a gap, which is why a "10 1/2 inch" deck tread is two boards and a space rather than one wide board.

The stair rules this checks

Your jurisdiction can and often does amend these. Stair rules are amended locally more than almost anything else in the residential code, so treat a green panel as "this meets the model code" and make the phone call to your building department before you buy lumber.

Three worked examples

A 56 3/4 inch deck, standard mount

Divide 56.75 by a 7 inch target and you get 8.1, so eight risers at 7 1/16 inch each. Standard mount means the deck surface is the eighth step, so seven treads get cut into the stringer and the total run is 73 1/2 inch — call it six feet one and a half. The stringer runs about 7 feet 4 inch tip to tip, so an 8 foot 2x12 does it with a little to spare. Bottom cut is 5 9/16 inch, and the throat comes out at 5 3/8, safely past the minimum. Everything passes.

The same deck, flush mount

Nothing about the risers changes — still eight at 7 1/16. But now the top step is cut into the stringer rather than being the deck itself, so you're cutting eight notches, the run grows to 84 inch, and the stringer needs a 10 foot board instead of an 8. That extra 10 1/2 inch of run is exactly the kind of thing that turns out to matter when the stairs were going to land right at the edge of a patio.

A full-storey interior stair, 108 inch rise

Fifteen risers at 7 3/16 inch, fourteen treads at 10 inch, a 140 inch run and a stringer just over 14 feet — you're buying 16 foot stock. At a 10 inch tread you're at the legal minimum with no margin, so if the space allows, going to 10 1/2 or 11 buys comfort and, at 11 inch, drops the nosing requirement entirely. Open the headroom check on a stair like this: 108 inch of rise through a floor opening is where the 6 foot 8 inch minimum actually gets tight.

What affects how accurate this is

• Your total rise measurement. Every other number is derived from it. Measure to finished surfaces at both ends, and measure at the point the stringer will actually land, not at the middle of a sloped yard.
• Ground that isn't level. Outdoor stairs land on a pad you pour or set. Until that's at a known height, the total rise is a guess.
• Rounding to sixteenths. Displayed dimensions are marked to the nearest 1/16 inch, which is what a tape reads. Use the running mark-out table rather than repeating a single riser mark up the board, and the rounding never accumulates.
• Nosing and tread overhang. Tread depth here is nosing to nosing, the way code measures it. Board width plus overhang is a different number.
• Local amendments. Plenty of jurisdictions run tighter than the model code on risers and headroom, and some are stricter on stringer spacing than the deck guide.
• Lumber that isn't straight. Crown your stringer stock and lay out from the crowned edge. A bowed 2x12 will not produce a flat run of stairs no matter how good the numbers are.

Frequently asked questions

How do you calculate stair stringers?

Divide your total rise by a target riser height to get a whole number of risers, then divide the total rise by that number for the exact riser height. Multiply the tread depth by the number of treads for the total run. The stringer length is the hypotenuse of those two legs — the square root of the rise squared plus the run squared, measured from where the stringer attaches down to the ground. Then cut the bottom rise short by one tread thickness so all the finished steps come out equal.

What are the ideal rise and run for stairs?

A riser near 7 inch with a tread near 11 inch is about as comfortable as a stair gets, and it clears the code with margin at both ends. The old carpenter's rule is that two risers plus one tread should land between 24 and 25 inch; the calculator flags you when your combination drifts outside that. Code-wise you have room between a 7 3/4 inch maximum riser and a 10 inch minimum tread, but the extremes of that range are noticeably steeper to climb.

How long of a 2x12 do I need for a stair stringer?

Enter your numbers above and the cut card gives you the exact tip-to-tip length plus the stock length to buy. As a rough guide: a three or four step stair fits on an 8 foot board, a typical 4 foot-high deck needs 8 to 10 feet, and a full storey at 108 inch of rise needs 16 feet. Always buy the next size up rather than the closest — a stringer laid out with no waste at either end leaves you nothing to correct with.

Do you use 2x10 or 2x12 for stair stringers?

2x12, and the throat number in the result panel is the reason. Notching a typical 7 inch rise and 10 1/2 inch run out of a 2x12 leaves roughly 5 3/8 inch of uncut board behind the notches; the same cut in a 2x10 leaves about 3 3/8 inch, below the 5 inch minimum. The prescriptive deck guide requires 2x12 minimum for cut stringers, and inspectors do check it.

How many stringers do I need for 3-foot-wide deck stairs?

Three — one at each side and one down the middle. That's both the prescriptive minimum for cut stringers and what 18 inch on-center spacing works out to at 36 inch wide. Go to 48 inch wide and you need four. Enter your width above and the tool sizes it, including the actual on-center spacing to lay out.

Related tools

• Lumber Calculator — studs, joists, headers and board feet for the framing around the stair
• 2x4 Actual Size Chart — the real dressed dimensions of every board, including the 11 1/4" a 2x12 actually measures
• Sonotube Calculator — concrete for the footings under a set of deck stairs
• Flooring Calculator — material for the landing at the top or bottom
• Browse all free tools by Jake →

Tools for cutting stringers

Stairs are a layout job first and a cutting job second, but the cutting is unforgiving — here's what Jake keeps within reach:

• Best Circular Saws — the primary stringer tool. Look for a clear blade sightline and a base that doesn't wander, because you're stopping every cut exactly at a marked corner.
• Best Jigsaws — finishes the notch corners the circular saw can't reach without overcutting into the throat.
• Best Miter Saws — square crosscuts on treads and risers, which is what keeps a wide stair parallel.
• Best Impact Drivers — structural screws into pressure-treated stringers without stripping heads.
• Beginner's Guide to Power Tools — first stair? Start here for what to buy and in what order.
• How to Read a Tape Measure — every dimension on this page is in sixteenths.

Sources & methodology

• Riser height, tread depth and uniformity — 7 3/4" maximum riser, 10" minimum tread, 3/8" maximum variation within a flight. (IRC 2021 R311.7.5.1 and R311.7.5.2)
• Nosing — 3/4" to 1 1/4" projection, not required where the tread is 11" or deeper. (IRC 2021 R311.7.5.3)
• Headroom, width and flight rise — 6' 8" minimum headroom, 36" minimum clear width, 12' 7" maximum rise between landings. (IRC 2021 R311.7.2, R311.7.1, R311.7.3)
• Stringer stock, count, spacing and handrail height — 2x12 minimum, three cut stringers minimum, 18" on center maximum, handrail 34"–38" on any stair with four or more risers. (AWC DCA6-2015, Prescriptive Residential Wood Deck Construction Guide, pp. 20–22)
• Geometry cross-validation — riser count, first-step drop, stringer placement, total run, stringer length and angle were checked case by case against the two calculators currently ranking first and second for this search, and match to the decimals they display.

This calculator is reviewed annually against the current IRC cycle. About Jake · Last reviewed August 14, 2026.

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  Stair calculator by
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  &middot; Reviewed by Jake Morrison, Licensed GC
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