The Stair Calculator converts a total rise into a full stair layout: riser height, tread depth, step count, stringer length and stair angle. Enter the vertical distance a staircase needs to climb, choose a target riser height or a fixed number of steps, and the calculator distributes the rise evenly across every step. A code-check panel compares the result against common riser, tread, headroom and width limits, flagged as general guidance rather than a citation of a specific local code.
Calculate rise, run and step count
Total rise is the full vertical distance a staircase climbs, from the lower finished floor to the upper one, and every other stair dimension is derived from that single number once a target riser height or step count is chosen. Total run is the horizontal distance the stairs occupy, driven by how many treads are stacked end to end.
Number of risers = Total rise ÷ Target riser height (rounded to a whole number)
Actual riser height = Total rise ÷ Number of risers
Total run = Number of treads × Tread depthRounding the riser count to a whole number changes the actual riser height slightly from the target, since a real staircase cannot have a fractional step. The calculator reports the actual riser height after rounding, not the target, since that adjusted figure is what actually gets built and needs to be checked against code limits.
Set a fixed riser or a fixed step count
A stair layout can be driven from either end: a target riser height that gets rounded to a whole step count, or a fixed step count that determines the riser height directly. Both paths produce the same kind of result and the calculator supports either as a starting point.
Entering a target riser height of 7 in for a 108 in total rise rounds 108 ÷ 7 = 15.43 to 15 risers, then recalculates the actual riser height as 108 ÷ 15 = 7.2 in, evenly distributed across every step. Entering 15 as a fixed step count for the same 108 in rise arrives at the identical 7.2 in riser height directly, without the intermediate rounding step. The fixed-step path suits a job where the number of steps is already constrained, such as fitting a stair between two known floor levels with a specific tread count already framed in.
Apply the stair geometry formulas
Riser height comes directly from dividing total rise by step count; tread depth is chosen or specified separately; stringer length and stair angle both follow from treating the total rise and total run as the two legs of a right triangle. The stringer is the diagonal hypotenuse of that triangle.
Riser height = Total rise ÷ Number of risers
Stringer length = √(Total rise² + Total run²)
Stair angle = atan(Riser height ÷ Tread depth)Standard stringer mount uses one fewer tread than riser, since the top riser lands on the upper floor itself rather than on a tread cut into the stringer. Flush mount uses a tread at every riser level, including the top, which is common where the stair lands on an intermediate platform rather than a finished floor.
Lay out a 108 inch total rise
A staircase climbing a 108 inch total rise, built with 15 risers and a 10 inch tread, needs a run of 140 inches and a stringer roughly 176.8 inches long. Every step below carries the units through. 1. Find the actual riser height. 108 in ÷ 15 risers = 7.2 in
2. Find the tread count (standard mount). 15 risers − 1 = 14 treads
3. Find the total run. 14 treads × 10 in = 140 in
4. Find the stringer length. √(108² + 140²) = √(11,664 + 19,600) = √31,264 ≈ 176.82 in
5. Find the stair angle. atan(7.2 ÷ 10) ≈ 35.8°
A 7.2 inch riser sits comfortably under the 7.75 inch maximum most codes allow, and a 10 inch tread meets the typical 10 inch minimum exactly. The 35.8 degree angle this layout produces is within the comfortable walking range for a residential stair; a steeper angle, from a shorter run or a taller riser, makes a stair feel more like a ladder than a staircase.
Check the design against building codes
Riser height, tread depth, nosing, headroom, width and guard requirements are the dimensions inspected on nearly every residential stair, and the calculator checks the computed layout against common limits for each one. These limits are general guidance, not a citation of a specific local code, and the authority with jurisdiction over the project should confirm every figure before framing begins.
| Check | Common limit | 108 in example |
|---|---|---|
| Maximum riser height | 7.75 in | 7.2 in, passes |
| Minimum tread depth | 10 in | 10 in, meets the minimum exactly |
| Nosing projection | 0.75 to 1.25 in | Not used in this layout |
| Minimum headroom | 80 in | Depends on framing above the stair |
| Minimum stair width | 36 in | Depends on the entered width |
| Guard required | above 30 in total rise | Required; 108 in total rise exceeds the threshold |
A stair that fails the riser or tread check is not just uncomfortable, it is a documented fall hazard, since uneven or oversized steps break the rhythm a person's foot expects from the previous step. This is a safety-adjacent tool: the warnings never block the calculation from completing, but they should never be dismissed without checking the actual local requirement.
Understand stair terminology
Stair terminology stays consistent across residential and light commercial work, and knowing the terms makes it possible to read a code requirement or a supplier's stringer spec without translation. Nine terms cover nearly everything on a standard stair. Tread is the horizontal surface a foot lands on.
Riser is the vertical face between two treads. Nosing is the small overhang where a tread projects past the riser beneath it. Stringer is the diagonal structural board, notched to hold the treads and risers, that carries the load of the whole stair down to the floor. Landing is a flat platform breaking a long run into two shorter ones. Headroom is the clear vertical space above the stair, measured from the nose of each tread straight up to the ceiling or framing above it. Guard is the barrier along an open side of a stair or landing. Handrail is the graspable rail a hand runs along while climbing or descending. Standard mount and flush mount describe whether the top tread lands on the upper floor or on the stringer itself, as covered above.
Account for tread thickness and mount type
Tread thickness changes the actual height a foot climbs on the first step, and skipping this adjustment produces a first step that measures differently from every other step on the same staircase, even though the framing itself was cut evenly. This is one of the most common finish-carpentry errors on an otherwise correctly framed stair.
In a standard stringer mount, each tread sits on top of a notch cut into the stringer, meaning the first riser's finished height is effectively increased by the thickness of the tread that will be added later, unless the stringer layout compensates for it in advance. A stringer cut for a clean 7.2 in riser at every step, with a 1 in thick tread added after the fact, produces a first step that measures 8.2 in from the finished lower floor to the top of that first tread, a full inch taller than every step above it, unless the bottom of the stringer is trimmed down by that same 1 in before installation. Flush mount avoids this specific issue because every tread, including the first, sits at the same relationship to its riser.
Convert fractions to decimals for layout
Stair layout marks are usually written as fractions of an inch on site, but the arithmetic behind a stringer layout is easier and less error-prone in decimal form, so converting between the two in both directions is a routine part of laying out a stair by hand.
| Fraction | Decimal |
|---|---|
| 1/16 in | 0.0625 in |
| 1/8 in | 0.125 in |
| 1/4 in | 0.25 in |
| 1/2 in | 0.5 in |
A riser height of 7 3/16 in converts to 7.1875 in for calculation, and a computed riser of 7.2 in converts back to the nearest sixteenth, 7 3/16 in, for marking on the stringer with a square. Rounding to the nearest sixteenth is standard precision for stair layout; finer fractions rarely make a practical difference once a tread and riser are nailed and finished.
Frequently asked questions
How many steps do I need for a 108 inch rise?
At a target riser height of 7 in, 108 ÷ 7 = 15.43 rounds to 15 steps, giving an actual riser height of 7.2 in once evenly distributed. A different target riser height changes the step count; a taller target riser, such as 7.5 in, would round to 14 steps instead.
What is the maximum riser height allowed by code?
7.75 inches is the commonly cited maximum for residential stairs in most US model codes. This is general guidance rather than a specific local citation, and the authority with jurisdiction over the project should confirm the exact figure that applies.
What is the minimum tread depth?
10 inches is the commonly cited minimum tread depth for residential stairs, measured from the nose of one tread to the nose of the next. A tread shallower than this shortens the safe landing area for a foot descending the stairs.
How do I calculate stringer length?
Treat the total rise and total run as the two legs of a right triangle, and find the stringer length as the hypotenuse: the square root of the rise squared plus the run squared. A stair with a 108 in rise and a 140 in run has a stringer length of about 176.8 in.
What is the difference between a standard mount and a flush mount stringer?
Standard mount uses one fewer tread than riser, since the top riser lands directly on the upper floor rather than on a tread cut into the stringer. Flush mount places a tread at every riser level, including the top, which suits a stair landing on an intermediate platform instead of a finished floor.
Do I need a handrail or guard on my stairs?
A guard is commonly required along any open side of a stair or landing where the total rise exceeds about 30 inches, and a handrail is commonly required on stairs with more than a small number of risers. Both figures are general guidance; confirm the exact threshold with the local building authority before finalising a design.
How much headroom do stairs need?
80 inches of clear vertical space is the commonly cited minimum, measured from the nose of each tread straight up to the ceiling or framing above. Existing structures with limited floor-to-floor height sometimes cannot achieve this without redesigning the stair's run or angle.
How do I convert a fraction of an inch to a decimal for stair layout?
Divide the fraction's numerator by its denominator: 3/16 becomes 3 ÷ 16 = 0.1875. Stair layout is normally worked in decimal inches for the arithmetic, then converted back to the nearest sixteenth for marking the stringer with a square.
Why does the first riser need to be adjusted for tread thickness?
On a standard stringer mount, each tread sits on top of the stringer's notch, adding the tread's thickness to the effective height of the step beneath it. Without compensating for that thickness at the bottom of the stringer, the first step ends up measurably taller than every step above it, even though the stringer itself was cut with even risers.
What is nosing, and how much should it overhang?
Nosing is the small lip where a tread projects past the riser below it, commonly specified between 0.75 and 1.25 inches. It increases the usable tread depth slightly and gives a descending foot a visual cue for where the edge of the step actually is.
Summary
The Stair Calculator turns a total rise into riser height, tread depth, run, stringer length and angle, distributing the rise evenly across a target riser height or a fixed step count. A 108 inch total rise built with 15 risers produces a 7.2 inch riser, a 140 inch run and a stringer of roughly 176.8 inches.
Riser, tread, headroom, width and guard requirements are checked against common limits as general guidance, and tread thickness needs a first-riser adjustment on a standard stringer mount to keep every step even. Confirm every code figure with the local authority before cutting a stringer.