Stair Calculator

How to Calculate Stair Dimensions (Rise, Run, Stringer)

Calculating stairs correctly is one of the most math-intensive parts of any deck or home project. Get the riser height wrong by even a quarter inch and you'll feel it in every step — and your building inspector will fail it. This calculator handles the geometry so you can focus on the build.

The Rise-Run Relationship

Every stair design balances two measurements: the riser (vertical height per step) and the run (horizontal tread depth). The IRC 2021 building code sets clear limits:

• Maximum riser height: 7¾ inches (7.75")
• Minimum riser height: 4 inches
• Minimum tread depth (run): 10 inches
• Riser consistency: All risers in one flight must be within ⅜" of each other

The classic comfort formula is 2R + T = 24–25 inches (where R = riser height, T = tread depth). A 7" riser with an 11" tread gives 2(7)+11 = 25 — perfect. A 7.5" riser with a 10" tread gives 25 as well. Both are comfortable and code-compliant.

Step-by-Step: Calculating Stair Dimensions

1. Measure total rise: Use a level and tape to measure the vertical distance from the bottom landing to the top landing (deck surface, door threshold, etc.). Be precise — a ½" error across 8 risers means each riser is 1/16" off. That's usually fine, but ⅜" total variation is the limit.

2. Determine number of risers: Divide total rise by your target riser height. A 7" target is comfortable for most people. Round to the nearest whole number, then verify the actual riser height (total rise ÷ number of risers) stays between 4" and 7.75". Adjust the count if it doesn't.

3. Calculate treads: Number of treads = number of risers minus 1. The bottom riser uses the ground as the final "tread," so you always have one fewer tread than risers.

4. Calculate total run: Multiply tread count by tread depth. This tells you how far out the stair will project from the structure. Make sure there's enough room on the landing.

5. Calculate stringer length: Stringers are the angled side boards that support the treads and risers. Their length is the hypotenuse of the right triangle formed by the total rise and total run: stringer length = √(rise² + run²). Add 15% for notching cuts at the top and bottom, then round up to the next standard board length (8, 10, 12, 14, 16 ft).

Understanding Stringers

Stringers are cut from 2×12 pressure-treated lumber (dimensional thickness: 1.5" × 11.25"). Each riser/tread notch cut into the stringer removes material, weakening it. The IRC requires at least 3.5 inches of remaining depth below the deepest point of any notch — this is the "effective depth" rule. Exceeding this rule is how older decks fail under load.

For a 7" riser and 10.5" tread, each notch cuts 7" vertical and 10.5" horizontal from a corner of the stringer. A 2×12 has 11.25" of actual depth. After a 7" notch, the remaining depth along the plumb line is 11.25 − 7 = 4.25" — just above the 3.5" minimum. If you use taller risers, check this math or use a deeper board.

Stringer spacing: Stringers must be spaced no more than 16" on center. For a 36"-wide stair, use 3 stringers (at 0", 18", 36"). For 48" width, use 4 stringers (at 0", 16", 32", 48"). A middle stringer is required because tread boards will sag without center support on anything wider than about 30".

Tread Materials and Sizing

Tread boards span the full stair width between stringers. The most common options:

• 5/4×6 pressure-treated decking (1" × 5.5" actual): Two boards side-by-side create a ~11" tread. Light, affordable, resists rot.
• 2×12 PT (1.5" × 11.25" actual): Single board per tread, strong and clean-looking. More expensive but simpler installation.
• Composite decking: Won't rot or splinter; heavier; costs 2–3× more than PT.

Treads typically overhang the stringer face by 1" at the front (the nosing) and should be flush or slightly overhang at the sides. Standard nosing overhang per code: ¾"–1¼" maximum.

Common Stair-Building Mistakes

Not measuring total rise correctly: Always measure from the finished surface to finished surface. If you're adding a landing pad (concrete, gravel) after the stairs, account for its thickness in your rise measurement.

Cutting stringers too deep: Stringer notch depth is cumulative. Verify that the thinnest section (the "throat") of the stringer is ≥ 3.5" after all cuts.

Inconsistent riser heights: The last riser is the hardest to get right. If your total rise doesn't divide evenly, the last riser ends up different. Always recalculate riser height as an even division of total rise by number of risers.

Skipping the footing: Deck stairs exert significant downward and outward force on the landing. Most codes require a concrete footing at least 12" deep (below frost line in cold climates) under the stringer base. Check local code — in some areas, a concrete landing pad is sufficient.

No kickboard at the bottom: A pressure-treated 2×6 kickboard (sill plate) anchored to the footing gives stringers a solid, level base and keeps the bottom from splitting under load.