Stair Calculator

This stair calculator tells you how many steps you need, how tall each riser is, how far the staircase reaches across the floor, and how long the stringer boards must be. Enter the total rise, your maximum riser height, and your tread depth. The calculator finds the fewest equal risers that stay at or under your limit, then works out every other dimension from that single number.

The default 7.75-inch maximum riser matches the International Residential Code (IRC) limit used in most US jurisdictions, so the results start out code-compliant on height.

The stair formulas

Every staircase is a right triangle broken into equal steps. The calculator uses five formulas, in this order:

1. Number of risers (steps) = total rise ÷ max riser, rounded up to the next whole number
2. Riser height = total rise ÷ number of risers
3. Number of treads = number of risers − 1
4. Total run = number of treads × tread depth
5. Stringer length = √(total rise² + total run²) ÷ 12, in feet

It also reports a comfort check: 2 × riser + tread, which should land between 24 and 25 inches.

Rounding up in step 1 keeps each riser at or under your maximum. Rounding down would leave them taller. The cost is one more step, which adds one more tread of run.

Worked examples

These numbers come straight from the calculator’s formulas, so you can check them against the tool above.

Example 1: a 44-inch deck stair (the default)

Total rise 44 in, max riser 7.75 in, tread 10 in.

• Risers: 44 ÷ 7.75 = 5.68 → round up to 6 steps
• Riser height: 44 ÷ 6 = 7.33 in
• Treads: 6 − 1 = 5 treads
• Total run: 5 × 10 = 50 in
• Stringer: √(44² + 50²) = 66.6 in = 5.55 ft
• Comfort: 2 × 7.33 + 10 = 24.67 in, right in the sweet spot

An 8-foot 2×12 covers that stringer with room for the end cuts.

Example 2: a full floor-to-floor stair

Total rise 108 in (a typical 9-foot floor-to-floor height), max riser 7.75 in, tread 10 in.

• Risers: 108 ÷ 7.75 = 13.94 → 14 steps
• Riser height: 108 ÷ 14 = 7.71 in
• Treads: 13
• Total run: 13 × 10 = 130 in (10 ft 10 in)
• Stringer: 14.08 ft
• Comfort: 2 × 7.71 + 10 = 25.43 in, slightly steep

This stair is legal but near the limit on every count. The next example makes it gentler.

Example 3: the same stair, built more comfortably

Total rise 108 in, max riser lowered to 7.5 in, tread 10.5 in.

• Risers: 108 ÷ 7.5 = 14.4 → 15 steps
• Riser height: 108 ÷ 15 = 7.20 in
• Treads: 14
• Total run: 14 × 10.5 = 147 in (12 ft 3 in)
• Stringer: 15.20 ft
• Comfort: 2 × 7.20 + 10.5 = 24.90 in

The gentler stair costs 147 − 130 = 17 more inches of floor space. Both stairs still fit on 16-foot stringer stock. If you have the floor space, it is the easier stair to climb.

How many steps do I need? Riser count by total rise

Results from this stair calculator using a 7.75-inch maximum riser and 10-inch treads:

Total rise	Risers (steps)	Riser height	Treads	Total run	Stringer
24 in	4	6.00 in	3	30 in	3.20 ft
30 in	4	7.50 in	3	30 in	3.54 ft
36 in	5	7.20 in	4	40 in	4.48 ft
42 in	6	7.00 in	5	50 in	5.44 ft
48 in	7	6.86 in	6	60 in	6.40 ft
60 in	8	7.50 in	7	70 in	7.68 ft
72 in	10	7.20 in	9	90 in	9.60 ft
84 in	11	7.64 in	10	100 in	10.88 ft
96 in	13	7.38 in	12	120 in	12.81 ft
108 in	14	7.71 in	13	130 in	14.08 ft
120 in	16	7.50 in	15	150 in	16.01 ft
144 in	19	7.58 in	18	180 in	19.21 ft

In the 24-inch row, 24 ÷ 7.75 = 3.1, which rounds up to 4 risers of 6 inches. Three risers of 8 inches would break the 7.75-inch code limit.

Stair rise and run: IRC code limits

IRC section R311.7 sets the rules most US homes are inspected against:

Element	IRC requirement	Section
Riser height	7¾ in maximum	R311.7.5.1
Tread depth	10 in minimum, nosing to nosing	R311.7.5.2
Riser / tread variation	⅜ in max between largest and smallest in a flight	R311.7.5.1, R311.7.5.2
Nosing	¾ to 1¼ in, required where treads are under 11 in	R311.7.5.3
Stair width	36 in minimum clear above the handrail	R311.7.1
Headroom	6 ft 8 in minimum, measured from the nosing line	R311.7.2
Handrail height	34 to 38 in above nosings, on flights of 4+ risers	R311.7.8
Landing	At top and bottom, at least as wide as the stair and 36 in deep	R311.7.6
Open risers	Opening must not pass a 4 in sphere when total rise exceeds 30 in	R311.7.5.1

Local codes can amend these numbers, and commercial stairs fall under the IBC, which is stricter (7-inch maximum risers and 11-inch minimum treads). Always confirm with your local building department before you cut.

The ⅜-inch variation rule is why the calculator divides the rise into perfectly equal risers. The most common inspection failure is a bottom or top step that differs from the rest because the finished floor was not accounted for.

How to measure total rise

Total rise is the vertical distance from the finished lower surface to the finished upper surface. Measure to the finished surfaces, not the subfloor.

1. Set a straight board or level on the upper floor so it projects out past the edge.
2. Measure straight down from the underside of the level to the lower surface.
3. Add the thickness of any flooring that is not installed yet, and subtract it at the bottom if the bottom surface will be raised (tile, a concrete pad, pavers).
4. For outdoor stairs, measure where the bottom step will actually land. Ground usually slopes away from a deck, so a reading taken right at the rim joist can be 1–2 inches short.

If you are 1 inch off on a 14-riser stair, every riser is off by 1 ÷ 14 = 0.07 inches, which is fine. But if you measure to the subfloor and then add ¾-inch hardwood upstairs, the top step alone gets ¾ inch taller, which breaks the ⅜-inch variation limit.

Tread depth, nosing, and the comfort rule

Tread depth in this calculator is the horizontal run of each step, measured nosing to nosing. The board you buy is usually wider: a 10-inch run with a 1-inch nosing needs an 11-inch tread, which is why two 5½-inch deck boards (11 inches total) are a common deck stair tread.

The 2R + T rule ties riser and tread together. Taller risers need shallower treads and the reverse. Use the comfort readout to tune your design:

• Under 24 in: steps feel short and choppy. Increase the tread depth.
• 24–25 in: a natural stride.
• Over 25 in: steps feel like a reach. Lower the max riser to add a step, or shorten the tread if code still allows.

When floor space is the limit

If the run is too long for your floor space, you have three choices:

• Raise the max riser toward 7.75 inches. This removes risers, and each removed riser removes one tread of run.
• Shorten treads toward the 10-inch minimum.
• Add a landing and turn the stair 90° or 180°. The IRC allows a single flight to climb up to 151 inches (12 ft 7 in) between landings under the 2018 and later editions.

Do not solve a space problem by going over the riser limit. A 10-inch run with an 8-inch riser will fail inspection.

Common stair mistakes

• Counting treads as steps. Steps means risers. A stair with 6 risers has 5 treads.
• Forgetting the finished floor. Measure finished-to-finished, as described above.
• Ignoring headroom. On an interior stair, check that the ceiling opening is long enough for 6 ft 8 in of clearance along the whole flight. Measure the clearance at the nosing of every step that sits under the floor opening’s edge.
• Cutting the bottom riser full height. When you lay out a stringer, the bottom riser is cut shorter by one tread thickness, because the tread adds that height back. Skip this and the first step is too tall.
• Undersizing stringers. Use 2×12 lumber. After notches, a 2×12 cut for a 7¼-inch riser and 10-inch tread keeps only about 5⅜ inches of solid wood below the notches. The AWC’s DCA 6 deck guide limits cut stringers to roughly 6 feet of horizontal span for common species, so longer stairs need a mid-span support.

Related calculators

• Lay out the notches on each board with the stair stringer calculator, which also counts how many stringers your stair width needs.
• Pouring steps instead of framing them? The concrete stairs calculator finds the volume and bag count.
• Building the deck the stairs lead to? Size the framing with the deck joist calculator and the surface with the decking board calculator.
• Need a step-free route? The ramp calculator works out the length for a given rise at an accessible slope.

This stair calculator gives geometry, not engineering. Stringer size, fastening, footing, and guard design must follow your local building code. Confirm the plan with your building inspector before you cut lumber.