Stair calculator
This stair calculator turns the total rise of your stairs into the number of risers and treads, the exact riser height, the total run, the stair angle and the stringer length, then checks the result against the residential code limits.
- Risers, treads and total run in 1/16 inch fractions
- Stringer length, throat depth and how many stringers
- Checks against the IRC riser, tread and nosing limits
Last updated
How to use the stair calculator
- Measure the total rise: from the top of the finished floor or deck straight down to the finished ground, slab or floor where the stairs will land. Use a level and a tape, because the ground is rarely flat.
- Enter the highest riser you will accept. 7 3/4 inches is the IRC maximum; a lower number gives more, gentler steps.
- Enter the tread depth (run) and the nosing overhang. With treads under 11 inches, the code asks for a 3/4 to 1 1/4 inch nosing.
- Pick the stringer board and stair width, then read the risers, treads, stringer length and the code checks. Mark the riser and tread on a framing square to lay out each stringer.
How stair rise and run are calculated
Divide the total rise by the highest riser you want and round up. That gives the number of risers. Then divide the total rise by that whole number to get the exact, equal riser height.
risers = total rise ÷ max riser, rounded up
riser height = total rise ÷ risers
treads = risers − 1
There is one fewer tread than risers, because the upper floor or deck is the top step. The rest follows from the right triangle the stair makes:
total run = treads × tread depth
stair angle = arctan(riser ÷ tread)
stringer length = √(total rise² + total run²)
The throat is the wood left under the notches, measured square to the edge of the board: board width − (riser × tread ÷ √(riser² + tread²)). The board to buy is the next even length that covers the stringer length plus one more step, to leave room for the top and bottom cuts.
Worked example
A deck 4 ft (48 inches) above a patio, risers no higher than 7 3/4 inches, 10 1/2 inch treads, a 1 inch nosing, stairs 36 inches wide on 2x12 stringers.
- Risers: 48 ÷ 7.75 = 6.19, so 7 risers.
- Riser height: 48 ÷ 7 = 6.857 inches, about 6 7/8 inches.
- Treads: 7 − 1 = 6. Total run: 6 × 10.5 = 63 inches (5 ft 3 in).
- Angle: arctan(6.857 ÷ 10.5) = 33.1 degrees.
- Stringer length: √(48² + 63²) = 79.2 inches, or 6 ft 7 3/16 in. Adding one step (12.5 in) gives 91.7 inches, so buy 8 ft boards.
- Throat: 6.857 × 10.5 ÷ 12.54 = 5.74 inches of cut, so 11.25 − 5.74 = 5.51 inches (5 1/2 in) of wood is left.
- Stringers: 36 ÷ 18 = 2 spaces, so 3 stringers. Tread boards: 10.5 + 1 = 11 1/2 inches deep.
Every number passes the IRC checks. With 7 risers the stair needs a handrail, and with 48 inches of rise a deck stair needs a guard.
What are the code limits for residential stairs?
The International Residential Code (IRC) sets the maximum riser height at 7 3/4 inches and the minimum tread depth at 10 inches, with no more than 3/8 inch of difference between the largest and smallest riser or tread in a flight. These are the figures quoted in Boise’s IRC handout and Mesa County’s stair guide (last checked 6 November 2026). Your city may amend them: Baltimore’s adopted code allows 8 1/4 inch risers and 9 inch treads, so check with your building department.
| Rule (IRC R311.7) | Limit |
|---|---|
| Riser height | 7 3/4 in max; risers in a flight within 3/8 in of each other |
| Tread depth | 10 in min, nosing to nosing; treads within 3/8 in of each other |
| Nosing | 3/4 to 1 1/4 in; not required when treads are 11 in or deeper |
| Open risers | Openings must stop a 4 in sphere |
| Headroom | 6 ft 8 in min |
| Width | 36 in min |
| Handrail | Required with 4 or more risers, 34 to 38 in above the nosings |
| Rise of one flight | 151 in (12 ft 7 in) max between floor levels or landings |
Put together, the steepest stair the IRC allows is a 7 3/4 inch riser on a 10 inch tread: arctan(7.75 ÷ 10) = 37.8 degrees. Many carpenters also check comfort with an old rule of thumb that adds two risers and one tread; it is a habit of the trade, not a code rule, so this page does not score your stair against it.
Deck stair stringers: what the deck guide asks for
The American Wood Council’s Prescriptive Residential Wood Deck Construction Guide (DCA 6, based on the 2015 IRC) gives these stair details for wood decks. Many building departments hand it out as their deck standard.
- Stringer size: 2x12 minimum, with at least 5 inches of wood left below the notches of a cut stringer.
- Span: a cut stringer may span up to 6 ft 0 in horizontally, a solid stringer (treads on ledgers) up to 13 ft 3 in. Past that, add a 4x4 post on a footing or an intermediate landing.
- Spacing: stringers no more than 18 inches apart on center, and at least three when only cut stringers are used.
- Landings: at least 36 inches deep in the direction of travel and as wide as the stair.
- Guard: a stair guard is needed when the stair’s total rise is 30 inches or more.
Rules vary by town and code edition, so treat this as a planning check and confirm with your permit office before cutting.
Common questions
How do I calculate stair rise and run?
Divide the total rise by 7.75 inches and round up to get the number of risers, then divide the total rise by that number for the riser height. Treads are one fewer than risers. A 48 inch rise gives 7 risers of 6 7/8 inches and 6 treads; at 10 1/2 inches each, the total run is 63 inches.
How many steps do I need for a 3 foot rise?
A 36 inch rise needs 5 risers: 36 ÷ 7.75 = 4.6, rounded up to 5, so each riser is 7.2 inches (about 7 3/16 in). That is 4 treads, and with 10 1/2 inch treads the stair runs 42 inches.
What is the maximum riser height and minimum tread depth?
Under the IRC, risers can be at most 7 3/4 inches and treads must be at least 10 inches deep, with no more than 3/8 inch of variation in a flight. Some cities amend these numbers, so confirm with your local building department.
How long should a stair stringer be?
Use the Pythagorean theorem: √(total rise² + total run²). For a 48 inch rise and a 63 inch run, the stringer is 79.2 inches (6 ft 7 3/16 in) along the slope. Buy a board with room for the end cuts, here an 8 ft 2x12.
How many stringers do I need for deck stairs?
The AWC deck guide spaces stringers no more than 18 inches apart and calls for at least three cut stringers. A 36 inch wide stair needs 3 stringers; a 48 inch wide stair needs 4.
When do stairs need a landing?
When the total rise is more than 151 inches (12 ft 7 in), the IRC requires a landing to break the flight. A landing must be at least 36 inches deep in the direction of travel and at least as wide as the stairs.
Related calculators
Sources
- City of Boise Planning and Development Services, IRC Code Handout #437: Stair Treads and Risers (IRC R311.7.5). Riser max 7 3/4 in, tread min 10 in, 3/8 in variation, nosing 3/4 to 1 1/4 in (not required with treads of 11 in or more), 6 ft 8 in headroom, handrail 34 to 38 in. Last checked 6 November 2026
- Mesa County Building Division, Residential Stair and Handrail Guidelines. 36 in min width, 7 3/4 in max rise, 10 in min run, handrail with 4 or more risers, 151 in max vertical rise between floor levels or landings. Last checked 6 November 2026
- American Wood Council, DCA 6 Prescriptive Residential Wood Deck Construction Guide (2015 IRC). Stair requirements and Figure 28: 2x12 minimum stringers, 5 in min throat, 6 ft cut stringer span, 13 ft 3 in solid stringer span, 18 in max stringer spacing, 36 in landings, stair guard at 30 in total rise. Last checked 6 November 2026
- Baltimore City Building, Fire and Related Codes, Part X (IRC) Section 311. Example of a local amendment: 8 1/4 in max riser, 9 in min tread. Last checked 6 November 2026
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