Stair Calculator

What Is a Stair Calculator?

It answers one question — how many equal risers fit into your rise without any of them breaking the code maximum — and then reports everything that follows from the answer. The rise is fixed by the building, so that count is the whole layout.

A stair's dimensions come out of arithmetic before they come out of taste. A floor-to-floor rise of 106 inches cannot be walked down in fourteen and a half steps, and it cannot be walked down in risers that differ from one another, so the layout begins by asking how many equal parts that 106 inches divides into without any one of them getting too tall.

Answer that and the rest is fixed. The tread count is one less than the riser count, the run is the tread count times the tread depth, the stringer is the diagonal across rise and run, and the floor the stair consumes downstairs follows from the run. Get the riser count wrong by one and every other figure on the drawing moves with it.

Rise, Run, Riser, Tread, Nosing, Stringer

Six words, and for three of them the code specifies exactly where you put the tape.

The tread-depth definition is the one that catches people out. Because the code measures nosing to nosing, an overhanging nosing adds nothing to tread depth and nothing to the total run — but it does add to the board. A 10-inch tread depth with a 1-inch nosing needs an 11-inch-wide tread board, and the flight still advances only 10 inches per step.

So put the nosing-to-nosing figure in the tread box. Type the board width instead and the run comes back an inch per step too long, which across thirteen treads is more than a foot of floor you do not have.

Why the Riser Count Comes First

Because it is the only quantity in the layout that has to be an integer. Tread depth is yours to choose above the minimum; total rise is not yours to choose at all. So the calculator divides the rise by the maximum riser the chosen standard allows and rounds up, which yields the smallest whole number of risers that keeps every step under the cap.

Rounding up is what makes it work. 106 divided by 7.75 is 13.68, and thirteen risers would be 8.15 inches each — over the residential maximum on every step in the flight, not just the last one. Fourteen risers of 7.57 inches clear it. There is no fractional escape, because the tallest and shortest riser in a flight may differ by no more than ⅜ inch, so you cannot make thirteen normal risers and one short one.

Adding risers beyond that minimum makes the stair gentler — fifteen risers over 106 inches works out at 7.07 inches each — but on 10-inch treads it costs another ten inches of floor, and the calculator will not offer it. It always returns the smallest count that fits. The commercial code puts a floor under this as well as a ceiling: riser heights there are “7 inches maximum and 4 inches minimum”.

One Straight Flight, and Nothing Else

What gets modeled is a single run of parallel treads between two levels. There is no field for a landing, a turn, a winder or a spiral, and no way to split a rise across two flights. If your stair breaks at a landing, run the tool once per flight, because a landing is simply a floor as far as the geometry is concerned.

Working out how much floor the flight and its landing will take out of the room below? Measure the space with the Square Footage Calculator.

That still covers most of what actually gets built: basement stairs, a straight flight to a second story, deck and porch steps. It does not cover the L-shaped stair wrapped around a stairwell, which has to be laid out as two flights meeting at a platform.

How Do You Calculate Stair Risers and Treads?

Four steps, and only the first involves a decision: divide, round up, divide back, then multiply out.

The Stair Formula, Written Out

This is what the page runs, in order:

risers    = ceil( total rise ÷ max riser )     max riser: 7.75″ IRC, 7″ IBC
riser ht  = total rise ÷ risers               every riser identical
treads    = risers − 1
total run = treads × tread depth
stringer  = √( total rise² + total run² )
2R + T    = 2 × riser ht + tread depth       comfort score, target 24–25″

centimeter entries are divided by 2.54 first;
every line of the answer is printed in inches

Two guards sit in front of that arithmetic. The tread depth has to be at least 10 inches on the residential setting and 11 on the commercial one, and the total rise has to be 200 inches or less — 508 centimeters — or the panel declines the run rather than laying out a flight nobody would build in one piece.

Step by Step

• Measure the total rise finished floor to finished floor. If the hardwood is not down yet, add its thickness now; a stringer is cut once, and flooring that arrives afterwards changes the riser it lands on.
• Pick the standard. Residential (IRC) caps the riser at 7¾ inches and asks 10 inches minimum of tread; Commercial (IBC) caps the riser at 7 inches and asks 11. They are radio buttons, and Residential is preselected.
• Choose your units. Inches or Centimeters changes only what you type — every line of the answer comes back in inches either way.
• Enter the tread depth nosing to nosing. Ten inches is the residential floor; eleven gives a noticeably easier stair and, at 11 inches or more, removes the code's nosing requirement altogether.
• Press Calculate. Both measurement boxes start empty and neither is optional, so the panel shows a dash until you fill them both in, and nothing recalculates as you type. Reset returns it to the dash.

Worked Example: a 106-Inch Rise on 10-Inch Treads

Residential, inches, total rise 106, tread depth 10. A wall framed 96 inches from subfloor to top plate, carrying 2×10 joists and a ¾-inch subfloor above it, arrives at exactly that: 96 + 9¼ + ¾ = 106. Press Calculate and the panel reads:

• 14 risers of 7.57″
• 13 treads at 10″ = total run 130.0″ (10′ 10.0″)
• Stringer length: 167.7″ (13′ 11.7″)
• Comfort check (2R + T): 25.1″ — target 24–25″
• Max riser used: 7.75″ (IRC residential)

Trace it through. 106 ÷ 7.75 = 13.68, rounded up to 14 risers. 106 ÷ 14 = 7.5714 inches, printed as 7.57. Thirteen treads at 10 inches make a 130-inch run, and √(106² + 130²) = 167.7 inches of stringer. Every line is computed from the unrounded 7.5714 rather than the 7.57 on your screen, so arithmetic you redo off the display can land a hair away from the panel.

Look closely at the stringer line. 167.7 inches is 13 feet 11.7 inches, which is why it prints that way rather than rounding itself up to 14 feet — and why a 14-foot board will not do the job. Allow for the plumb cut at the top and the level cut at the bottom and the cut list wants a 16-foot 2×12 per stringer.

Worked Example: the Same Rise Under the Commercial Standard

Switch the standard to Commercial (IBC) and the tread to 11, the commercial minimum, leaving the rise at 106. Now the panel returns:

• 16 risers of 6.63″
• 15 treads at 11″ = total run 165.0″ (13′ 9.0″)
• Stringer length: 196.1″ (16′ 4.1″)
• Comfort check (2R + T): 24.3″ — target 24–25″
• Max riser used: 7″ (IBC commercial)

Two more risers, nearly an inch shorter each, and 35 inches more floor. That is the difference between the two codes in a single comparison: the commercial layout runs at 31.1 degrees off horizontal against the residential layout's 37.1 — an angle the panel never prints, though arctan(riser ÷ tread) gives it — and it takes 13 feet 9 inches of the room instead of 10 feet 10.

The comfort score moves the other way. 24.3 sits inside the 24–25 target where the residential layout's 25.1 sits just outside it, and that is the arithmetic behind the reputation commercial stairs have for feeling easy underfoot.

Working in Centimeters

The Centimeters setting converts what you type at 2.54 and then works in inches for everything after that, including every line of the answer. A 280-centimeter rise on a 25.4-centimeter tread returns:

• 15 risers of 7.35″
• 14 treads at 10″ = total run 140.0″ (11′ 8.0″)
• Stringer length: 178.2″ (14′ 10.2″)
• Comfort check (2R + T): 24.7″ — target 24–25″
• Max riser used: 7.75″ (IRC residential)

25.4 centimeters was not picked at random: it is exactly 10 inches, which is the residential tread minimum. Type 25 instead and the run is refused with “Tread depth must be at least 10″ for this code standard”, because 25 centimeters is 9.84 inches. Under the commercial setting the equivalent floor is 27.94 centimeters.

A tread that is not a whole number of inches shows its conversion in full in the second line — 28 centimeters prints as 11.023622047244094″ — and the riser heights, run and stringer are all inches, so convert them back yourself. The 140-inch run above is 355.6 centimeters.

Checking It Without the Calculator

Three things fall straight out of the formula and survive on a job site.

• The riser count only changes as the rise crosses a multiple of the maximum riser. Residentially those thresholds are 93, 100.75, 108.5, 116.25 and 124 inches, so any rise between two of them shares a count — which is why 96 and 100 both come back as 13 risers.
• Multiply the count by the maximum riser and check the product clears your rise. 14 × 7.75 = 108.5, comfortably over 106, so fourteen is enough; 13 × 7.75 = 100.75, under 106, so thirteen is not.
• Total run depends on the tread count alone once the tread depth is chosen — riser height never enters it. Two rises that share a riser count therefore share a run: 96 and 100 inches both give 120 inches of run on 10-inch treads.

None of it replaces measuring the real rise on site. Half an inch of subfloor is enough to push a rise across one of those thresholds, and the whole layout shifts with it.

Stair Chart: Risers, Treads and Stringers by Rise

Every figure below came out of this calculator rather than off another chart. Rises are the finished floor-to-floor measurement, and the run carries the panel's own feet-and-inches conversion alongside it.

Residential (IRC), 10-Inch Treads

Three different rises share the 14-riser row and therefore share a 130-inch run, because the run answers to the tread count and never to how tall the risers are. What moves instead is the riser height, from 7.43 inches at a 104-inch rise to 7.71 at 108 — and at 124 inches it lands exactly on the 7.75 maximum, with nothing in hand.

Every layout in that table sits between 36.3 and 37.8 degrees off horizontal, a much narrower band than the rises suggest. The riser is pinned close to its legal ceiling and the tread is pinned on its legal floor, so there is very little room left to vary.

Commercial (IBC), 11-Inch Treads

The same job under the 7-inch riser cap and the 11-inch tread minimum:

All five commercial rows land inside the 24–25 comfort band. Only five of the twelve residential rows above do. That is a consequence of the code rather than a coincidence: 2R + T at the commercial limits is 2 × 7 + 11 = 25 exactly, so any riser under the 7-inch cap on an 11-inch tread has to score below it.

Deck and Porch Steps

Short outdoor flights under residential limits, on 11-inch treads — two 2×6 deck boards laid side by side measure 11 inches of board:

Watch the 24-inch and 30-inch rows. Both take four risers and both run 33 inches, because the tread count did not change — all that moved was the riser height, from 6.00 inches to 7.50. Six extra inches of deck height cost nothing at all in ground space.

The tread count on a deck stair reads low for a reason. A 36-inch rise gets five risers and four treads, because the deck surface is what you step onto at the top rather than a fifth tread. The same logic is why a single 7-inch step comes back with “0 treads”: there is nothing between the ground and the platform.

Four risers is also where the handrail requirement begins. The residential code asks for a handrail on at least one side of any continuous run of four or more risers, so the 24-inch rise in that table needs one and the 18-inch rise above it does not.

What Changing the Tread Depth Does

The same 106-inch rise, residential, with the tread depth swept upward from the 10-inch minimum. The riser count and riser height never budge — tread depth cannot reach them:

Deepening the tread makes the comfort score worse, not better, which surprises most people the first time they see it. 2R + T is scoring a stride, and a 7.57-inch riser wants roughly a 10-inch tread to sit in the 24–25 band; pair it with 12 inches and the score reaches 27.1. The only way back down is a shorter riser, which means more risers — and at this rise the residential setting will not give you any.

How to Read Your Result

Five lines come back on every successful run, always in the same order. Here they are from the residential 106-inch layout, written the way the formula returns them — the panel then splits each of the last four at its “=” or “:” into a label on the left and a value right-aligned against it, and drops the separator:

• 14 risers of 7.57″
• 13 treads at 10″ = total run 130.0″ (10′ 10.0″)
• Stringer length: 167.7″ (13′ 11.7″)
• Comfort check (2R + T): 25.1″ — target 24–25″
• Max riser used: 7.75″ (IRC residential)

The first line is the big readout; the other four become breakdown rows beneath it. “Copy result” puts all five on the clipboard as plain text.

The Riser Line Is the One to Check First

It carries both numbers you cut to: how many risers to lay out, and how tall each one is. That height is the rise divided exactly by the count, so it almost never lands on a tape-measure fraction — 7.57 inches is a hair over 7 and 9/16, about nine thousandths of an inch over.

Which is why stringers are laid out with a framing square and stair gauges set to the rise and the run, or stepped off with a story pole, rather than measured riser by riser. Measuring 7 and 9/16 fourteen times accumulates error in one direction, and the ⅜-inch variation limit is unforgiving of it.

Read the count as risers, not as steps you walk on. Fourteen risers means thirteen treads plus the upper floor.

Run, Stringer and the Lumber Order

The run tells you how much floor the flight eats; the stringer tells you what to buy. 167.7 inches is 13 feet 11.7 inches of straight-line diagonal before either end is cut. A 14-foot board is 168 inches, about a quarter of an inch longer than that, which leaves nothing for the plumb cut at the top or the level cut at the bottom — so the flight wants a 16-foot 2×12.

The American Wood Council's deck guide sets the stock and the count: “All stringers shall be a minimum of 2x12,” and “If only cut stringers are used, a minimum of three are required” on a 36-inch stair, with cut and solid stringers together spaced no more than 18 inches on center on anything wider.

Pricing the stringers, treads and riser boards as lumber once the cut list is settled is a job for the Board Foot Calculator.

There is a structural reason the 2×12 is the floor. Notch a 7¾-inch riser and a 10-inch tread out of an 11¼-inch board and 5.12 inches of solid wood is left behind the cut, which matches the guide's own commentary: cut stringers “were analyzed with 5.1″ depth which is based on 7.75:10 rise to run ratio.” Cut the identical notches into a 2×10 and only 3.12 inches remains to carry the flight.

The Comfort Check (2R + T)

The fourth line scores your layout against a rule of thumb far older than any code on this page: two risers plus one tread should total between 24 and 25 inches, on the reasoning that a person's stride shortens as it rises. The panel prints the score and the target and then leaves the judgment to you. Nothing is rejected for failing it.

Sibling rules exist, and the calculator runs none of them: riser plus tread around 17 to 18 inches, and riser times tread around 70 to 75. The 106-inch residential layout scores 17.6 on the first, comfortably inside its band, and 75.7 on the second, a fraction above the top of it. Its 25.1 on 2R + T overshoots as well. That is a fair picture of how much these rules actually agree with one another.

Below 24 the stair is shallow for its rise; above 25 it is steep. Neither is a code failure, and 2R + T appears in none of the code sections quoted further down this page. For scale, every residential row in the chart above scores between 24.7 and 25.5.

The Angle, Which the Panel Does Not Print

There is no degrees line anywhere in the result. If you need the pitch it is arctan(riser ÷ tread): the 106-inch residential layout runs at 37.1 degrees, a 75.7 percent slope, and the same rise under the commercial standard eases to 31.1 degrees. The steepest a residential flight can legally get is 7.75 over 10, which is 37.8 degrees.

The same rise-over-run geometry, expressed as a pitch rather than as steps, is what you get from the Roof Pitch Calculator.

Treat that as a cross-check rather than a design input. If you have entered a rise and a tread and the arctangent comes back at 45 degrees, one of the two measurements is wrong: the steepest thing any code quoted on this page allows is Michigan's 8¼-inch riser on a 9-inch tread, and that is 42.5 degrees.

When You See the Amber Notice

Eight messages can replace the result, and they come from two places. The page checks for an empty required box before the formula is ever called; the rest are the formula's own refusals.

Both measurement boxes are required and both start empty, which is why the panel opens on a dash rather than a worked example: the on-load calculation is skipped whenever a required field is blank. Press Calculate with one still empty and the page stops there — it does not read the empty box as a zero and it does not hand it to the formula. It names the field instead, taking the name from the label above the box with the parenthetical trimmed off, so “Total Rise (floor to floor)” comes back as “Enter a value for Total Rise.”

A zero or a negative number is a different case. Both are values, so they clear the page's own check and reach the formula, which turns them away with a message of its own — the last five rows of that table are all the formula talking. Order matters there too: the formula tests the rise before the tread, so zeros in both boxes return the rise message by itself, while blanks in both boxes are named together in a single line.

Nothing else is refused. There is no maximum tread depth, no minimum rise, and no check that the riser height handed back is sensible — a 3.5-inch rise on the commercial setting comes back as “1 risers of 3.50″” without mentioning that the IBC's minimum riser is 4 inches.

Stair Code Limits: IRC, IBC and Local Amendments

The two figures behind the calculator's standard buttons are the two that the codes actually cap. Everything else about a stair is governed as well, and none of the rest is in the panel.

The Residential Numbers (IRC R311.7)

Quoted from the City of Boise's treads-and-risers handout and Placer County's residential stair guide, which between them reprint R311.7 down to R311.7.7, plus Otsego County's handout for the handrail section neither of them carries:

• Riser: “The riser height shall be not more than 7 ¾ inches (196 mm)”, measured vertically between the leading edges of adjacent treads.
• Riser variation: “The greatest riser height within any flight of stairs shall not exceed the smallest by more than 3/8 inches (9.5 mm).”
• Tread: “The tread depth shall be not less than 10 inches (254 mm)”, measured between the vertical planes of the foremost projections of adjacent treads.
• Tread variation: the same ⅜-inch limit governs the deepest and shallowest tread in a flight.
• Nosing: a projection of not less than ¾ inch and not more than 1¼ inches is required, with one exception — “A nosing projection is not required where the tread depth is not less than 11 inches (279 mm).”
• Width: “Stairways shall not be less than 36″ (914 mm) in clear width at all points above the permitted handrail height and below the required headroom height.”
• Headroom: “not less than 6′ 8″ (2032 mm) measured vertically from the sloped line adjoining the tread nosing.”
• Vertical rise: a flight may not have a vertical rise larger than 151 inches — 12 feet 7 inches — between floor levels or landings.
• Landings: required top and bottom, at least as wide as the flight, and on a straight run “the depth in the direction of travel shall be not less than 36″ (914 mm).”
• Handrail (R311.7.8, from the Otsego reprint): “Handrails shall be provided on at least one side of each continuous run of treads or flight with four or more risers,” at a height “not less than 34 inches (864 mm) and not more than 38 inches (965 mm)” measured vertically from the sloped plane adjoining the tread nosing.

All of those dimensions are “exclusive of carpets, rugs or runners” — the code is measuring the stair, not what gets laid on top of it. Note too that the 200-inch guard in this calculator is its own invention and not a code figure: at 151 inches the IRC already wants an intermediate landing, so a rise between 152 and 200 inches will calculate here quite happily and will not pass inspection as one flight.

The Commercial Numbers (IBC Chapter 10)

From a building-department reprint of the means-of-egress chapter:

• “Stair riser heights shall be 7 inches maximum and 4 inches minimum. Stair tread depth shall be 11 inches minimum” (1011.5.2). The minimum riser is the part residential stairs do not have.
• “The tolerance between the largest and smallest riser or between the largest and smallest tread shall not exceed 3/8 inch in any flight of stairs” (1011.5.4).
• Width: “the minimum width shall not be less than 44 inches”, dropping to 36 inches where the stairway serves an occupant load of 50 or fewer (1011.2).
• Headroom: “a minimum headroom clearance of 80 inches measured vertically from a line connecting the edge of the nosings” (1011.3).
• Landings: “Every landing shall have a minimum dimension measured in the direction of travel equal to the width of the stairway. Such dimension need not exceed 48 inches” (1011.6).
• Handrails on each side (1011.11), where a residential flight needs only one.

The 7-and-11 combination is also what an accessible stair has to hit. The US Access Board's guidance is that every step in a flight must have “uniform riser heights within a range of 4 inches to 7 inches” and “uniform tread depths that are 11 inches minimum”, with nosings projecting no more than 1½ inches over the tread below.

Local Amendments Move These Numbers

The IRC is a model code. What binds you is whatever your jurisdiction adopted and however it amended the text on the way, and stair geometry is one of the sections that gets amended.

Otsego County's handout reprints the 2015 Michigan Residential Code with a maximum riser of 8¼ inches, a minimum tread of 9 inches and a maximum flight rise of 147 inches — a steeper stair and a shorter flight than the model numbers. A 106-inch rise divides into 13 risers of 8.15 inches there, inside Michigan's cap and outside the 7¾-inch one this calculator applies, so the residential setting hands you 14 risers and, on the same 10-inch treads, ten more inches of run than Michigan would require.

The direction of an amendment is not predictable either. Placer County reprints the model figures unchanged, Michigan is more permissive, and other jurisdictions are stricter still. Confirm with your building department before you cut stringers.

Limits: What This Calculator Does Not Check

The arithmetic is exact. What it is exact about is a straight flight between two levels, and a stair that passes here can still fail for several reasons the panel never sees.

Headroom and the Stairwell Opening

This is the check that kills more layouts than riser height ever does, and there is no field for it. Headroom is measured vertically from the sloped line joining the tread nosings up to whatever is overhead, and it has to hold 80 inches the whole way — including under the header at the far end of the floor opening the stair climbs through.

You can work it out from the panel's own numbers. Add the floor assembly depth to 80 inches for the vertical drop needed below the upper floor, divide by the riser height, then multiply by the tread depth. For the 106-inch example on a ¾-inch subfloor, 9¼-inch joists and ½-inch ceiling drywall — 10½ inches of assembly — that is 90.5 ÷ 7.5714 = 11.95 risers of descent, and 11.95 × 10 = 119.5 inches of horizontal opening.

Ten feet of floor opening, for a flight whose entire run is 130 inches: twelve of the thirteen treads sit under open air. Where exactly the header lands depends on how it is framed, so treat 119.5 as a first-pass figure and draw the section properly. But if the opening on your framing plan is six feet long, this layout is already dead.

Landings, and Splitting a Rise Across Two Flights

The calculator will lay out any rise up to 200 inches as one flight. The IRC stops at 151 inches and Michigan at 147, and the American Wood Council's deck guide, written to the 2015 IRC, is stricter still: “If the total vertical height of a stairway exceeds 12’-0”, then an intermediate landing shall be required.”

When a landing does break the flight, run the tool twice. A landing is a floor: measure from the lower finished floor to the landing surface for the first flight, and from the landing to the upper finished floor for the second. The ⅜-inch variation rule reads “within any flight of stairs”, so the two flights are governed separately — though whether a change of riser height across a landing is a good idea is a different question, and most builders keep them equal.

The footprint grows by the landing too. That 106-inch residential flight needs 130 inches of run plus a bottom landing at least 36 inches deep, which is 166 inches — 13 feet 10 inches — of floor before anyone opens a door at either end of it.

Nosing, Finish Flooring and the Stringer Drop

Three adjustments happen between the calculator and the saw, and none of them is in the result.

• Tread boards are wider than the tread depth. A 10-inch tread depth with a 1-inch nosing wants an 11-inch board, because the nosing overhangs the riser below and contributes nothing to the run. Enter the nosing-to-nosing figure and buy the wider board.
• Finish flooring changes the rise. If the lower floor receives ¾ inch of hardwood after the stringers are cut and nothing is adjusted, the bottom riser finishes ¾ inch shorter than the other thirteen — double the ⅜-inch variation the code permits, from a single flooring decision.
• The bottom of the stringer gets dropped by one tread thickness. Every riser cut on a stringer is identical, but the lowest one lands on the floor with no tread board over it while all the others land on top of a tread. Cutting the stringer's bottom down by the thickness of one tread is what makes the first step match the rest.

None of that touches the riser count, the run or the stringer length. It changes the cut list, which is why the panel's figures are where a layout starts rather than where it finishes.

Winders, Spirals and Anything That Turns

A winder tread is a wedge, so it has two depths: one at the walkline 12 inches in from the narrow side, one at the narrow edge itself. The IRC asks for at least 10 inches at the walkline and 6 inches anywhere within the clear width; the IBC asks for 11 and 10. There is one tread field here and it models parallel treads, so a winder cannot be laid out with it.

Spiral stairs are a separate section of code entirely, with their own riser maximum and a tread rule measured at a fixed distance from the column. Alternating tread devices and ships ladders are separate again. None of them is what this page computes.

One part still transfers. The riser count for a turning stair is the same rise divided by the same maximum and rounded up, because the risers stay equal whether the treads turn or not. It is the run and stringer lines that stop describing your stair.

What the Layout Leaves Out

• Structure. This sizes geometry, not members. Stringer span, tread thickness, the connection at the top and the footing at the bottom are all outside it.
• Open risers. Where the gap between treads sits more than 30 inches above the floor or grade below, it must not pass a 4-inch sphere — which decides whether you can build the flight without riser boards at all.
• Walking surface. Treads and landings may not slope more than one unit in 48, a 2 percent fall, and no tolerance for that is anywhere in the result.
• Cost. There is no price field: no lumber, no treads, no hardware, no labor.

None of these argue against the numbers the panel gives you. They are the reasons those numbers are a drawing to be checked rather than a permit to start cutting.