Stair Calculator finds risers, step height, first step, total run, stringer length and angle using rise, tread depth and tread thickness. Formula: stringer length = √(stringer rise² + run²).
Why the Best Framers Still Blow a Stringer Layout
Every carpenter knows the formula: total rise divided by desired step height equals number of risers. But between that napkin math and a cut stringer that actually fits lie a handful of decisions that the formula alone doesn’t capture. If you measure total rise from rough framing instead of finished floors, the stair will settle a half inch low after flooring goes down. If you forget to account for tread thickness on the bottom cut, the first step ends up taller than the rest by the exact thickness of your stock.
And if you choose flush mount without realizing it adds a tread to the stringer, you’ll cut the wrong number of steps and the top won’t land on the deck. This calculator bakes in every one of those real-world adjustments — tread thickness, mount type, whole-riser rounding, and code compliance — so the numbers you get back match what you need to mark and cut.
Formulas
Riser Count and Actual Rise
Steps (risers) = round( Total Rise ÷ Target Step Height )
(minimum 1)
Actual Rise (F) = Total Rise ÷ Steps
First Step Adjustment
First Step (E) = F − Tread Thickness
(valid only when Tread Thickness < F)
Number of Treads and Total Run
Standard Mount (below deck):
Treads (D) = Steps − 1
Flush Mount (even with deck):
Treads (D) = Steps
(minimum 1)
Total Run (G) = D × Tread Depth
Stringer Geometry
Stringer Rise = E + (D − 1) × F
Stringer Length = √( Stringer Rise² + G² )
Angle and Slope
θ (degrees) = arctan( F ÷ Tread Depth ) × (180 / π)
Slope Ratio = F ÷ Tread Depth
Placement Drop (mounting offset from top of deck)
Standard Mount: Drop (H) = F
Flush Mount: Drop (H) = Tread Thickness
Code‑Reference Thresholds (used only for the warning)
US: max riser 7.75 in, min tread 10 in
Metric: max riser 197 mm, min tread 254 mm
How the Calculation Works
The tool begins by rounding Total Rise ÷ Target Step Height to the nearest whole number. That single rounding decision sets the riser count — and once it’s locked, the actual uniform rise (F) becomes Total Rise ÷ risers, no exceptions. This means the actual rise can differ noticeably from your target, especially when the division lands near a half-integer. The calculator then checks that the tread thickness is less than F; if not, it halts, because a bottom cut of F minus thickness would be zero or negative.
With a valid rise, the first step height (E) is calculated as F minus tread thickness. This is the foundational field trick that keeps every finished step height identical after tread boards are installed. The number of treads depends on the mount: Standard Mount treats the deck surface as the final step, so D = Steps − 1. Flush Mount requires a tread at the deck level, so D = Steps.
Total run (G) follows directly, and stringer length comes from the Pythagorean theorem applied to the stringer’s vertical rise (E + (D−1)×F) and total run. The stair angle is derived from arctan(F ÷ Tread Depth), classified into four pitch ranges, and the placement drop tells you exactly how far the top of the stringer sits below the deck surface.
Field-Level Gotchas That Cost Lumber
1. The Bottom Cut Must Be Shortened — Every Time
If you cut all risers to the full uniform rise, the first step becomes one tread thickness taller than the rest after the tread is attached. That’s a trip hazard. The correction — subtracting tread thickness from the bottom riser — is simple, but skipping it is the single most common stringer cutting error. The calculator enforces it automatically.
2. Flush Mount Adds a Tread, Changing the Entire Geometry
In standard mount, the stringer hangs below the deck rim; the last “step” is the deck itself, so you cut one fewer tread than there are risers. In flush mount, the stringer top sits even with the deck, requiring a tread at that elevation — giving you exactly as many treads as risers. Switching mount type without recalculating total run and stringer length will leave you with a stair that is either one tread too short or too long to meet the deck.
3. Total Rise Must Be Finished Floor to Finished Floor
Measure from the top of the finished deck surface to the top of the finished landing below. If you measure from framing to raw ground before pavers or a landing pad, the stair will end up a fraction of a step too short or too tall once final surfaces are in place. This calculator expects that finished-floor total rise; add the thickness of any future landing material to your measurement.
4. The Rounding Trap Can Land You Near Code Limits
Because the tool rounds the number of risers to the nearest whole value, a small shift in target rise can bounce the actual rise by nearly a quarter inch per step. For example, a 107‑inch total rise with a 7.5‑inch target gives 14.27 → 14 risers, producing a 7.64‑inch actual rise, just under the 7.75‑inch IRC maximum. A 7.7‑inch target with the same total rise rounds to 14 risers and hits 7.64 inches as well, but a 7.8‑inch target rounds to 14 risers too, resulting in 7.64 inches — the rounding buffered the target. Always check the computed actual rise after rounding, not your target, against local code.
5. Minimum Throat Depth on a 2×12 Stringer
After cutting notches for treads and risers, the remaining uncut width of the stringer (the throat) must typically be at least 5 inches per IRC R311.7.5. This calculator doesn’t draw the stringer cross-section, so it’s on you to verify that your chosen lumber depth — usually a 2×12 — leaves sufficient throat after the deepest cut. For a 2×12 (11¼″ actual), if you cut a 7.5″ rise and a 10″ tread, the diagonal throat can drop dangerously close to 5″. Consider upgrading to a 2×14 or adding intermediate support if throat is marginal.
Worked Example: Deck Stair in US Customary
A carpenter frames a deck whose finished surface is 105 inches above the finished patio slab. Target step height is 7½ inches, tread depth (going) is 10 inches, using 1‑inch thick tread stock, standard mount.
Inputs:
Total Rise = 105 in
Target Step Height = 7.5 in
Tread Depth = 10 in
Tread Thickness = 1 in
Mount = Standard
Outputs:
Hero card: 14 Risers, typical step height 7.50 in.
Typical Step [F] card: 7.50 in actual rise, First Step [E] 6.50 in, Tread Depth 10.00 in.
Stringer Length card: 161.90 in (13 ft 6 in), 13 Steps on Stringer, Placement Drop 7.50 in.
Total Run [G] card: 130.00 in horizontal footprint, 13 Treads.
Angle card: 36.87°, Slope Ratio 0.75, Pitch Status Optimal.
Insight alert: “Advanced Framing Note” — the bottom cut is shortened by tread thickness to keep all finished rises equal.
Frequently Asked Questions
What happens if tread thickness is greater than or equal to the actual step rise?
The calculation stops and shows a warning. Subtracting tread thickness from the rise would yield zero or a negative first step, which is impossible to cut. Use a thinner tread material or increase the total rise.
Why does Flush Mount give one extra tread?
Standard mount treats the deck as the final step, so the stringer carries one fewer tread board. Flush mount brings the stringer top level with the deck, so you need a tread there — the tread count matches the riser count. This affects total run and stringer length directly.
Does the calculator include nosing overhang?
No. Tread Depth [B] is the horizontal going from riser face to riser face. If your tread design includes a nosing (e.g., 1¼″ overhang), you must add that to your input if you want the total run to reflect the nosing projection. Otherwise, the total run is strictly D × (going measurement).
What building code drives the compliance warning?
The warning uses IRC R311.7.5.1: maximum riser height 7¾ inches (197 mm) and minimum tread depth 10 inches (254 mm). The alert triggers when either limit is exceeded, regardless of the stair angle classification.
How do I account for a landing or multiple flights?
This calculator handles a single straight flight. For stairs with a landing, break the total rise into two segments, treat each as a separate stair, and ensure the landing itself is built to meet minimum depth requirements. Run two calculations separately.
Why doesn’t the stringer length match my measuring tape after cutting?
Stringer length is the diagonal measurement from the bottom of the first riser notch to the top of the last riser notch. It does not include any tail extensions for ground contact or attachment to the deck ledger. Add your required top and bottom bearing lengths to this dimension when laying out your board.