Stair Calculator - Rise, Run, Stringers & Materials

How to use it

1. Enter the total rise: the vertical distance from the finished lower floor to the finished upper floor or deck surface. This is the one measurement everything is solved from, so measure it carefully.
2. Pick interior or deck stairs. Deck mode loads deck-typical defaults (a 2x tread, open risers) and links our deck calculator; interior mode assumes a finished tread and closed risers.
3. Choose the mount: standard (the stringer drops off the rim and the upper floor is the top step) or flush (the stringer top is level with the floor, adding one tread). This changes the tread count by one and it is the classic point of confusion.
4. Set the target riser height (7 in is the comfortable default) and the tread depth (10 in minimum, 10 1/2 or 11 in for a roomier step). The solver divides the rise into equal risers and never exceeds the 7 3/4 in code max.
5. Set the tread thickness so the bottom riser is dropped to match. Forgetting this is the single most common way a finished stair ends up with an uneven first or last step.
6. Turn on a landing if the rise is tall or the run will not fit. The tool splits the rise into two flights and sizes each one, with the landing counted as its own platform.
7. Set the stair width to size the stringers (36 in gives three) and the tread and riser boards.
8. Pick a tread material to load a starting price, edit any price to your own numbers, and read the step count, stringer length, code check and full cost in the takeoff slip. Watch the diagram redraw as you go.

At a glance

• 55 in interior rise, 7 in target, standard mount: 8 risers at 6 7/8 in, 7 treads at 10 1/2 in, a 73 1/2 in total run, about a 36.8 degree stair, and a stringer 91 3/4 in long that cuts from an 8 ft 2x12.
• 30 in deck rise, flush mount, 5/4 treads: 4 risers at 7 1/2 in, 4 treads (flush adds the top one), a 42 in run, and a stringer near 51 1/2 in from a 6 ft 2x12. A pad or footing carries the base.
• 103 in basement rise with a landing: 15 risers at 6 7/8 in split into two flights of 7 and 8, a landing platform between them, and each flight given its own run and stringer length.

How the math works

Everything starts from the total rise. The tool divides it into equal risers as close as it can to your target height, then bumps the count up if that would push a riser over the 7 3/4 in code maximum, so the risers are always uniform and always within code. The tread count depends on the mount: a standard-mount stringer that drops off the rim has one fewer tread than risers, because the upper floor is the top step, while a flush-mount stringer level with the floor adds a tread at the top. The total run is the tread count times the tread depth. The stringer length is the hypotenuse of a right triangle whose legs are the total rise and the total run, and the stair angle is the arctangent of rise over run. The bottom riser is cut shorter by one tread thickness so that once the tread boards are laid, every riser reads the same height. A landing splits the rise into two flights at equal riser height, with the landing counted as its own platform and each flight given its own run and stringer. Stringers are counted from the width at roughly 16 in spacing (36 in gives three), and each is bought at the next 2x12 stock length past the stringer run. Tread boards are the width long, two per step for a standard tread, and riser boards match the riser count when the risers are closed. Fasteners are estimated per tread and per riser across the stringers, plus a bracket at each stringer top and a tube of adhesive per few steps. Cost prices each group at the numbers you enter and divides by the step count for a cost per step.

1. 1. Measure the total rise

   The total rise is the vertical distance from the finished floor you start on to the finished floor or deck surface you end on. Measure it plumb, over the finished surfaces you will actually walk on, not the subfloor. Say it comes to 55 in. Everything else is solved from this one number, so a 1/2 in error here becomes a 1/2 in error spread across every step.

2. 2. Divide the rise into equal risers

   Divide the rise by a comfortable target riser, around 7 in. 55 / 7 = 7.86, which rounds to 8 risers. Then 55 / 8 = 6.875 in, or 6 7/8 in per riser. Because 6 7/8 in is under the 7 3/4 in code maximum, 8 risers works. If the first divide had left a riser over 7 3/4 in, the tool would add a riser and divide again, so the risers stay equal and legal.

3. 3. Count the treads from the mount type

   A standard-mount stringer drops off the rim and the upper floor becomes the top step, so there is one fewer tread than riser: 8 risers gives 7 treads. A flush-mount stringer sits level with the upper floor, which adds a tread at the top, so 8 risers gives 8 treads. Getting this wrong by one tread is the classic mistake, which is why the diagram shows the top of the stair as you switch it.

4. 4. Find the total run

   The total run is the tread count times the tread depth measured nosing to nosing. With 7 treads at a 10 1/2 in depth, the run is 7 x 10.5 = 73 1/2 in. A deeper tread makes a longer, gentler stair and eats more floor space; a shallower one is steeper and must still clear the 10 in minimum.

5. 5. Solve the stringer length and the angle

   The stringer follows the hypotenuse of a right triangle: rise and run are the legs. Stringer = square root of (55^2 + 73.5^2) = square root of (3025 + 5402.25) = 91.8 in, near 91 3/4 in. The stair angle is arctangent of 55 / 73.5 = 36.8 degrees, a comfortable slope. That 91.8 in is 7.65 ft, so each stringer cuts from an 8 ft 2x12 with a little to spare.

6. 6. Drop the bottom riser by the tread thickness

   If you cut every notch to 6 7/8 in and then lay a 1 in tread on each step, the first step ends up 1 in too tall and the top step 1 in too short. The fix is to cut the bottom riser shorter by one tread thickness: 6 7/8 in minus 1 in leaves a 5 7/8 in bottom cut. Once the treads are on, every riser reads 6 7/8 in. This one adjustment is the difference between a stair that passes and one that trips people.

7. 7. Take off the lumber

   A 36 in wide stair takes three 2x12 stringers at roughly 16 in spacing. Treads are the width long, usually two 2x6 boards per step: 7 treads is 14 boards, 42 linear ft. Closed risers add a board per riser face, 8 boards and 24 linear ft here. Add structural screws (about four per tread per stringer), a bracket at each stringer top, and a tube of construction adhesive every few steps to stop squeaks.

8. 8. Price it and read the cost per step

   Each group is priced on the quantity you need: stringers by the board, treads and risers by the linear foot, hardware and any labor as an allowance per step. Sum them for the total and divide by the step count for a cost per step, which is the quickest way to compare a plain pressure-treated flight against oak treads or a longer, gentler run.

Worked scenarios, start to finish

Real jobs with the numbers carried all the way through, so you can see how the estimate is built and check your own figures against them.

The judgement calls a pro makes

Decisions the tool cannot make for you, and how someone who does this for a living thinks them through.

Get the design checked, do not trust the numbers alone

This tool sizes a stair to prescriptive IRC values. It does not certify that a given stringer, its throat, or its connection carries your load, and codes vary by jurisdiction and can be stricter. Pull a permit where one is required, and let the inspector confirm the riser, tread, handrail, guard and stringer details before you build. A stair is where falls happen, so treat every number here as a starting point for that conversation, not a green light.

A 7 in comfortable riser versus the 7 3/4 in maximum

The code lets a riser reach 7 3/4 in, but that does not make it comfortable. Around 7 in is the sweet spot for daily use, and 6 1/2 to 7 in reads as gracious on a main stair. Push toward the maximum only when the run is genuinely tight, because steeper risers combined with a minimum tread wear people out and catch heels. The solver defaults to a 7 in target and only climbs when the rise forces it.

Standard mount or flush mount

A standard-mount stringer hangs off the rim joist and drops one tread height below the upper floor, so the upper floor itself is the top step and you get one fewer tread than risers. A flush-mount stringer sits with its top cut level with the floor and adds a tread there. Deck stairs are often flush to the framing; interior stairs are commonly standard. Pick the one that matches how your stringer meets the upper structure, and let the diagram confirm the top step looks right.

Cut stringers or solid cleated stringers

A cut (sawtooth) stringer is notched for each tread and riser and is the common choice, but every notch removes material and the throat, the wood left behind the cut, must stay at least about 5 in or the stringer is weak. A solid stringer with cleats or housed dados keeps the full 2x12 depth and is stronger for long or heavily loaded flights. On a tall exterior stair, a solid or doubled outer stringer is cheap insurance.

Open risers or closed risers

Closed risers, a board on each riser face, look finished, stiffen the stair and stop objects sliding through, and are usual indoors. Open risers drain and lighten a deck stair but must not let a 4 in sphere pass on many codes, which limits the riser height, and some jurisdictions require closed risers on certain stairs. Decide early, because it changes the riser board count and the fastener total.

When a landing is required

Beyond comfort, code caps the vertical rise of a single flight at 12 ft (147 in), so anything taller needs an intermediate landing. Landings also give a place to turn a stair in a tight footprint and a spot to rest on a long climb. If your rise is near or over 12 ft, or the straight run will not fit the space, split it: the tool keeps the riser height identical across both flights so the walk stays even.

Common mistakes, and the fix

• × Forgetting the tread thickness on the bottom riser.

  ✓ Cut the bottom riser shorter by one tread thickness. If you notch every riser the same and then add the treads, the first step comes out too tall and the top too short by exactly the tread thickness, an uneven-riser fail. The tool shows the dropped bottom cut for you.

• × Measuring the total rise to the wrong surface.

  ✓ Measure finished floor to finished floor, over the surfaces you walk on. Measuring to the subfloor, or to the top of the deck framing instead of the decking, throws every riser off and can push the stair out of code once the finish goes down.

• × Mixing up standard and flush mount, so the step count is off by one.

  ✓ Decide how the stringer meets the upper floor first. Standard mount drops below the floor and has one fewer tread than risers; flush mount is level and adds a tread. The diagram redraws the top step as you toggle, so use it to check.

• × Uneven risers, especially the top one in a flush mount.

  ✓ Keep every riser within 3/8 in of the others, which code requires. Uniform risers come from dividing the rise into equal parts and applying the bottom-riser correction, not from eyeballing the last step. The tool solves equal risers by design.

• × Over-notching the stringer and leaving a thin throat.

  ✓ Keep at least about 5 in of solid wood behind the deepest notch. A 2x12 barely allows a full 7 3/4 in riser and 11 in tread notch while holding the throat, so on deep cuts step up to a wider stringer or go solid and cleated.

• × Ordering a stringer board exactly the hypotenuse length.

  ✓ Buy the next stock length past the stringer run so you have material for the plumb and level cuts at the top and bottom. A 91.8 in (7.65 ft) stringer wants an 8 ft board at least, and a 10 ft board gives comfortable cutting room.

Material and unit specifics

The 2x12 stringer

Stringers are almost always cut from 2x12 stock because a smaller board cannot hold the minimum 5 in throat once the tread and riser notches are cut. Use pressure-treated 2x12 outdoors and a straight, sound board indoors. The stringer length is the diagonal, so a stair rising 55 in over a 73 1/2 in run needs a 91.8 in board, cut from an 8 ft or 10 ft 2x12.

Tread material

Deck stairs commonly use two 2x6 pressure-treated or composite boards per tread; interior stairs use a 1 in finished hardwood tread such as oak, often sold cut to length. 5/4 deck board is thinner and lighter. The tread depth is measured nosing to nosing, and the nosing overhang (around 1 in) adds to the board depth, not to the run.

Riser boards

Closed risers use a board on each riser face, typically a 1x8 indoors or a 2x or composite board on a deck. They stiffen the stair and give a finished face. Open risers skip the boards, which lightens a deck stair and lets it drain, but many codes limit the open gap to under 4 in, which caps the riser height.

Exterior fasteners and hardware

Outdoors everything is galvanized or stainless: structural or deck screws for treads and risers, a stair or angle bracket to tie each stringer to the rim at the top, and hangers or a ledger at the base. Construction adhesive under the treads kills squeaks. Never use plain steel fasteners with treated lumber, since the treatment corrodes them.

The base: pad or footing

The bottom of an exterior stringer should land on concrete, not soil, so it does not wick moisture or settle. A poured pad or a footing keeps the bottom step level and solid over time. Size it with our concrete calculator, and set the stringer on a treated sleeper or a bracket rather than directly on the slab.

Nosing and tread depth

The tread depth that matters for code and for the run is measured nosing to nosing, so a 10 1/2 in tread depth with a 1 in nosing means a board about 11 1/2 in deep. Nosing gives the foot a little extra landing without lengthening the stair. Open-tread stairs without a nosing usually need a deeper tread to feel safe.

Reading your result

Read the riser height and step count first: those two numbers, plus the mount, define the whole stair. The riser height is shown as a decimal and as the nearest 1/16 in fraction, because that is what you set a story pole and a framing square to. The total run tells you how much floor the stair eats, and the stringer length is the board you buy, rounded up to a stock size. The stair angle is a comfort read: roughly 30 to 37 degrees is easy, and pushing past the high 30s feels steep. Use the code panel as a checklist, not a certificate: green means the number sits inside the IRC prescriptive range, but your local department has the final say and can be stricter. The takeoff and cost slip are a shopping list priced at the numbers you enter, so the total is only as good as your prices, and the structural figures are a starting point to confirm before you cut.

Limitations

• This is a layout and materials estimate, not a structural design or an engineered plan. Every code figure is IRC-style prescriptive guidance to confirm with your local building department, and is not a substitute for a permit or inspection.
• It sizes a single straight flight, or a straight run split by one landing. It does not model winders, spiral stairs, curved flights, or an L or U turn other than through the single-landing split.
• It does not design the handrail or the guard, the stringer connection, or the landing framing. Those follow their own code sections and must be detailed separately.
• It does not size the stringer for load. It assumes a cut 2x12 with an adequate throat and standard spacing; a long, wide or heavily loaded flight may need solid, doubled or more closely spaced stringers.
• The comfort formulas (2R + T and R + T) are guides to a pleasant stair, not code requirements, and a stair can be code-legal while sitting just outside them.
• Cost uses only the prices you enter, so delivery, taxes, finish, handrail, guard and hardware beyond the listed allowances are not included unless you fold them in.

Frequently asked questions

How many steps do I need for a given rise?

Divide the total rise by a comfortable riser height around 7 in and round to a whole number of risers, then divide the rise by that count for the exact riser height. For a 55 in rise, 55 / 7 = 7.9, so 8 risers at 6 7/8 in each. The number of treads is one fewer than the risers for a standard mount, or the same as the risers for a flush mount. If the exact riser would top 7 3/4 in, add a riser and divide again.

What is the maximum riser height and minimum tread by code?

Under the IRC the maximum riser height is 7 3/4 in and the minimum tread depth is 10 in, measured nosing to nosing, with risers uniform to within 3/8 in across the flight. These are prescriptive figures and your local building department can amend them, so confirm before you build. This tool keeps risers equal and never lets the solved riser exceed 7 3/4 in, but it cannot know your local amendments.

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

The stringer length is the diagonal of the rise and run: the square root of (rise squared plus run squared). A stair rising 55 in over a 73 1/2 in run needs a stringer about 91.8 in, or 7.65 ft, long, so you buy the next stock length past that, an 8 ft or a 10 ft 2x12, to leave material for the top and bottom cuts. Stringers use 2x12 because smaller stock cannot keep the required throat behind the notches.

Do deck stairs need a landing or a pad at the bottom?

Code caps a single flight at 12 ft (147 in) of vertical rise, so a taller deck stair needs an intermediate landing; shorter flights do not. The bottom of an exterior stringer should land on concrete, not soil, so a poured pad or footing at the base is strongly recommended to keep the bottom step level and stop it settling. Size that pad with our concrete calculator, and set the stringer on a bracket or treated sleeper.

What angle should stairs be?

A comfortable stair runs roughly 30 to 37 degrees from horizontal. The angle is the arctangent of the total rise over the total run, so a gentler stair has a deeper tread and a shorter riser. Around 32 to 35 degrees suits most homes; past the high 30s a stair starts to feel steep and tiring, and building codes effectively cap the slope through the 7 3/4 in riser maximum and 10 in tread minimum.