How do I calculate my stairs?

Measure the total rise, plumb, from finished floor to finished floor, and divide it by the number of risers: 108 in ÷ 14 = 7.714286 in, every riser the same (7 11/16 in to the nearest 1/16 in). With the upper floor as the top step there is one tread fewer than risers, 13, and the total run is 13 × your going: at 10 1/2 in, 136.5 in (11 ft 4 1/2 in). Starting from your own maximum riser instead, divide and round up: 108 ÷ 7.5 = 14.4, so 15 risers of 7.2 in. Rounding to the nearest count would give 14 risers of 7.714286 in, over the maximum you set.

How do you calculate stair stringers, and how long is a 2x12 for a 5-step or a 14-step stringer?

The notches sit one step, S = √(R² + T²), apart along the top edge, so the pitch line is the number of treads × S; the board for a stringer seated on the floor with its top plumb cut at the back of the last tread adds R × (R − t) ÷ S. “Steps” can mean treads or risers, and with the upper floor as the top step there is one tread fewer than risers, so each length below is given both ways. At example inputs of a 7 1/2 in riser, a 10 1/2 in going and a 1 in tread: S = √(7.5² + 10.5²) = 12.903488 in, and R × (R − t) ÷ S = 7.5 × 6.5 ÷ 12.903488 = 3.778048 in. 5 treads, so 6 risers (a 45 in rise): pitch line 5 × 12.903488 = 64.5174 in (5 ft 4 1/2 in); board 5 × 12.903488 + 3.778048 = 68.2955 in (5 ft 8 5/16 in). 5 risers, so 4 treads (a 37.5 in rise): pitch line 4 × 12.903488 = 51.614 in (4 ft 3 5/8 in); board 4 × 12.903488 + 3.778048 = 55.392 in (4 ft 7 3/8 in). 14 treads, so 15 risers (a 112.5 in rise): pitch line 14 × 12.903488 = 180.6488 in (15 ft 5/8 in); board 14 × 12.903488 + 3.778048 = 184.4269 in (15 ft 4 7/16 in). 14 risers, so 13 treads (a 105 in rise): pitch line 13 × 12.903488 = 167.7453 in (13 ft 11 3/4 in); board 13 × 12.903488 + 3.778048 = 171.5234 in (14 ft 3 1/2 in). The width of the board does not change these lengths, and no stock length is chosen here.

What is the 7–11 rule for stairs?

The pair 7 in and 11 in is the 2024 IBC’s general riser maximum and tread minimum: 1011.5.2 gives risers of “7 inches (178 mm) maximum and 4 inches (102 mm) minimum” and rectangular treads of “11 inches (279 mm) minimum”. Its Exception 3 (Group R-3; dwelling units in Group R-2 not required to be Accessible or Type A; accessory Group U) gives “7 3/4 inches (197 mm)” and “10 inches (254 mm)”, and the 2024 IRC gives 7 3/4 in (196 mm) and 10 in (254 mm) in R318.7.5.1 and R318.7.5.2. A 7 in riser on an 11 in going is atan(7 ÷ 11) = 32.47°. A named “7-11 rule” was not found in the sources reviewed.

What is the ideal rise and run for stairs, and what is 2R + T or the 27 rule?

The codes set limits, not an ideal. England’s Approved Document K (2013 edition, for use in England) says “The normal relationship between the dimensions of the rise and going is: twice the rise plus the going (2R + G) equals between 550mm and 700mm.” That is 21.65 to 27.56 in. NBS Building Science Series 120 (1979) reports two older suggestions: Harper, Florio and Stafford (1958), that “the sum of the height of a riser and the length of a run should not be less than 17, or more than 18 in.” (p. 31); and Grandjean (1973), “2r + t = 63 cm (24.8 in.)” (p. 32). “2R + T = 24 to 25 in” and a “27 rule” were not found in the sources reviewed. The calculator applies none of these.

Is an 8 inch stair riser too high?

This page does not decide; the code your jurisdiction has adopted does. Quoted: the 2024 IRC R318.7.5.1, “The riser height shall be not more than 7 3/4 inches (196 mm).” The 2024 IBC 1011.5.2, “7 inches (178 mm) maximum and 4 inches (102 mm) minimum”, with “7 3/4 inches (197 mm)” under Exception 3. OSHA 29 CFR 1910.25(c)(2), for general-industry workplaces: “Have a maximum riser height of 9.5 inches (24 cm)”. OSHA’s Table D-1, for standard stairs installed before January 17, 2017, prints an angle of 40 deg. 08' for a rise of 8 in and a tread run of 9 ½ in; atan(8 ÷ 9.5) computes to 40.10° (40° 06′), so the printed figure differs. An 8 in riser on a 10 1/2 in going is atan(8 ÷ 10.5) = 37.30°, and on 11 in, 36.03°.

Why is there one fewer tread than risers?

Because the last step up lands on the upper floor, which is the top tread of the stair but not one cut on the stringer. 14 risers therefore need 13 treads on the stringer. If the top tread is set level with the upper floor instead, choose that option: the stringer then carries as many treads as risers, and the total run grows by one going.

How much headroom does a stair need?

Quoted, not applied: the 2024 IRC R318.7.2, “not less than 6 feet 8 inches (2032 mm) measured vertically from the sloped line adjoining the tread nosing”; the 2024 IBC 1011.3, “not less than 80 inches (2032 mm) measured vertically from a line connecting the nosings”. Both measure from the nosing line, so under an opening edge D from the top nosing, with floor depth F, the headroom is D × R ÷ T − F. With the example stair, 120 in from the top nosing to the far edge of the opening and a 10 in floor depth: 120 × 7.714286 ÷ 10.5 − 10 = 78.1633 in. For a headroom you choose, say 82 in, the distance from the top nosing is (82 + 10) × 10.5 ÷ 7.714286 = 125.2222 in. D is measured from the top nosing, not from the header: the framed opening, header to far edge, is D + p where the upper floor is the top step, p being the nosing projection, and D + T + p where the top tread is level with the floor.

What is the stringer throat, and how deep should it be?

The throat is the board left under the notches, measured square to its edges: the board width − R × T ÷ S. For the example stair on a 2x12 (11 1/4 in, PS 20-25 minimum dressed dry) it is 5.0332 in. AWC’s DCA 6, a deck guide “Based on the 2015 International Residential Code”, shows “5" min.” on the cut stringer in its Figure 28 and says “All stringers shall be a minimum of 2x12.” Its commentary adds “Cut stringers were analyzed with 5.1" depth which is based on 7.75:10 rise to run ratio”; the same throat formula gives 11.25 − 7.75 × 10 ÷ 12.651581 = 5.1243 in. Those are quoted, not applied: they are for decks, based on the 2015 IRC.

What does OSHA require for stairs?

For general-industry workplaces, 29 CFR 1910.25(c) requires standard stairs to be installed at 30 to 50 degrees from the horizontal, with a maximum riser height of 9.5 in, a minimum tread depth of 9.5 in and a minimum width of 22 in. Under (c)(5), the riser and tread limits do not apply to standard stairs installed before January 17, 2017: OSHA accepts those if they match Table D-1 or use a combination that achieves the 30 to 50 degree angle. For construction workplaces, 29 CFR 1926.1052(a)(3) says “Variations in riser height or tread depth shall not be over ¼-inch (0.6 cm) in any stairway system.” These are workplace rules, quoted, not applied.

How do I measure the total rise?

Plumb, from the finished surface of the lower floor to the finished surface of the upper floor. The IRC (R318.7.5) and the IBC (1011.5.1) take stair dimensions exclusive of carpets, rugs or runners. A hard floor finish laid after you measure changes the total rise by its thickness: one laid on the upper floor adds it, one laid on the lower floor takes it off.

Measurement · Risers, treads and stringer layout

Stair Calculator

Riser height, treads, total run, stair angle and the stringer layout from your total rise, with a cut list in feet, inches and sixteenths and in millimetres.

Use the calculator How it works

Stairs

The working

Risers = your count
= 14 risers
Riser height = Total rise ÷ Risers
= 108 in ÷ 14
= 7.714286 in
Every riser is equal by construction. Lengths are worked in inches, whatever unit they were entered in; 1 in = 25.4 mm exactly.
Riser height in mm = R × 25.4
= 7.714286 × 25.4
= 195.9429 mm
Treads = Risers − 1 (the upper floor is the top step)
= 14 − 1
= 13 treads
The last step up lands on the upper floor, so the stringer carries one tread fewer than there are risers.
Total run = Treads × Going
= 13 × 10.5 in
= 136.5 in (11 ft 4 1/2 in, 3,467.1 mm)
Riser face to riser face, which is also nosing to nosing. A nosing on the bottom tread projects past the bottom riser by its projection.
One step along the stringer, S = √(R² + T²)
= √(7.714286² + 10.5²)
= 13.029206 in
Angle = atan(R ÷ T), per step
= atan(7.714286 ÷ 10.5)
= 36.30°
The slope of the nosing line. Total rise ÷ total run, atan(108 ÷ 136.5) = 38.35°, divides the rise of 14 risers by the run of 13 treads, so it is steeper than any step of this stair.
Pitch line = Treads × S
= 13 × 13.029206
= 169.3797 in (14 ft 1 3/8 in, 4,302.24 mm)
Along the stringer’s top edge, from the top corner of the first riser cut to the back of the last tread. The straight line from the foot of the bottom riser to the top of the top riser, √(108² + 136.5²) = 174.0582 in, is a different line: it takes 14 risers of rise over 13 treads of run.
First riser cut = R − t
= 7.714286 − 0
= 7.7143 in (7 11/16 in, 195.94 mm)
No tread thickness entered, so t = 0: the first riser is cut to the full riser height.
Notch depth = R × T ÷ S
= 7.714286 × 10.5 ÷ 13.029206
= 6.2168 in (6 3/16 in, 157.91 mm)
Measured square to the board edge, from the edge to the inside corner of a notch.
Throat = Board width − R × T ÷ S
Waiting on a board width: enter your own, or choose a 2x10 or 2x12 dressed width, under Stringer board.
Board length = Treads × S + R × (R − t) ÷ S
= 13 × 13.029206 + 7.714286 × (7.714286 − 0) ÷ 13.029206
= 173.9471 in (14 ft 5 15/16 in, 4,418.26 mm)
For this layout only: seated on the lower floor, with the top plumb cut at the back of the last tread, where the top edge is t below the upper floor. Hangers, ledgers and flush tops change it. It is a length along the board, not a stock length to buy.
Floor tip = (R − t) × S ÷ R
= (7.714286 − 0) × 13.029206 ÷ 7.714286
= 13.0292 in (1 ft 1 in, 330.94 mm)
How far down the top edge, from the top corner of the first riser cut, the uncut edge would meet the lower floor: a layout reference, cut away with the first riser.
Check: Risers × R to the nearest 1/16 in
= 14 × 7.6875
= 107.625 in (8 ft 11 5/8 in, 2,733.68 mm)
7.714286 in to the nearest 1/16 in is 7 11/16 in. Stepped off 14 times it ends 3/8 in (0.375 in) short of the 108 in rise, so the marks in the cut list are cumulative: each is k × R from the exact R, rounded once.
Cut list, tread top of tread 13 = k × R
= 13 × 7.714286
= 100.2857 in (8 ft 4 5/16 in, 2,547.26 mm)
One line for each column of the cut list, worked for tread 13. Every row is worked the same way from the exact R and rounded once, so no rounding builds up.
Cut list, along the top edge to tread 13 = (k − 1) × S
= 12 × 13.029206
= 156.3505 in (13 ft 3/8 in, 3,971.3 mm)
Cut list, level from the first riser face to tread 13 = (k − 1) × T
= 12 × 10.5
= 126 in (10 ft 6 in, 3,200.4 mm)
Other counts, 12 risers: R = Total rise ÷ Risers
= 108 ÷ 12
= 9 in (9 in, 228.6 mm)
One line for each column of the table of other riser counts, worked for its first row that is not your stair. Plain arithmetic at your going; no count is filtered, and none is set against a code figure.
Other counts, 12 risers: Total run = Treads × Going
= 11 × 10.5
= 115.5 in (9 ft 7 1/2 in, 2,933.7 mm)
Other counts, 12 risers: Angle = atan(R ÷ T)
= atan(9 ÷ 10.5)
= 40.60°

Start from

Total rise

Plumb, finished floor to finished floor. The IRC and IBC take stair dimensions without carpets, rugs or runners. A hard floor finish laid after you measure changes the rise by its thickness.

Number of risers

I know how many risersKeep every riser at or under my maximum

Riser height = rise ÷ risers

Risers

Every riser comes out equal: total rise ÷ risers.

Going (tread depth, nosing to nosing)

Measured level, as the IRC measures tread depth: “horizontally between the vertical planes of the foremost projection of adjacent treads”. It is not the depth of the tread board.

At the top

With the upper floor as the top step, the stringer stops under it and carries one tread fewer than risers. A top tread level with the floor adds one tread to the stringer.

Riser height

inches

7 11/16 in to the nearest 1/16 in (7.6875 in); 195.94 mm. Exact: 108 ÷ 14 = 7.714286 in.

Risers: 14risersYour count.
Treads on the stringer: 13treadsOne fewer than risers: the upper floor is the top step.
Total run: 136.5in11 ft 4 1/2 in; 3,467.1 mm. Riser face to riser face.
Stair angle: 36.3°atan(R ÷ T), per step: a rise of 7 11/16 in on a going of 10 1/2 in.
Stringer pitch line: 169.3797in14 ft 1 3/8 in; 4,302.24 mm. 13 × S along the top edge.
Board length, this layout: 173.9471in14 ft 5 15/16 in; 4,418.26 mm. Seated on the lower floor, top plumb cut at the back of the last tread.
First riser cut: 7.7143in7 11/16 in; 195.94 mm. No tread thickness entered, so t = 0.
Notch depth: 6.2168in6 3/16 in; 157.91 mm. Square to the board edge.
Throat: —inEnter your board width, or choose a 2x10 or 2x12 dressed width, for the throat.

Which code and edition apply, and any local amendment, are decided by your jurisdiction. This page does not say whether a stair complies. The ICC states that the IRC is “in use or adopted in 49 states, the District of Columbia, Guam, Puerto Rico and the U.S. Virgin Islands”, and that “some jurisdictions amend the code” in the process. The figures quoted from the 2024 IRC and IBC are in a table with the results, each beside your own number.

Cut list: a mark for each tread, from the exact riser height

Tread top: the top of tread k above the lower floor, k × R. Along the top edge: from the top corner of the first riser cut, (k − 1) × S. Level: from the face of the first riser, (k − 1) × T to k × T. Each mark is worked from the exact R, 7.714286 in, and rounded once, so no rounding builds up.

Tread	Tread top, k × R	Along the top edge, (k − 1) × S	Level from the first riser face
1	7.7143 in (7 11/16 in, 195.94 mm)	0 in (0 in, 0 mm)	0 to 10.5 in (0 in to 10 1/2 in)
2	15.4286 in (1 ft 3 7/16 in, 391.89 mm)	13.0292 in (1 ft 1 in, 330.94 mm)	10.5 to 21 in (10 1/2 in to 1 ft 9 in)
3	23.1429 in (1 ft 11 1/8 in, 587.83 mm)	26.0584 in (2 ft 2 1/16 in, 661.88 mm)	21 to 31.5 in (1 ft 9 in to 2 ft 7 1/2 in)
4	30.8571 in (2 ft 6 7/8 in, 783.77 mm)	39.0876 in (3 ft 3 1/16 in, 992.83 mm)	31.5 to 42 in (2 ft 7 1/2 in to 3 ft 6 in)
5	38.5714 in (3 ft 2 9/16 in, 979.71 mm)	52.1168 in (4 ft 4 1/8 in, 1,323.77 mm)	42 to 52.5 in (3 ft 6 in to 4 ft 4 1/2 in)
6	46.2857 in (3 ft 10 5/16 in, 1,175.66 mm)	65.146 in (5 ft 5 1/8 in, 1,654.71 mm)	52.5 to 63 in (4 ft 4 1/2 in to 5 ft 3 in)
7	54 in (4 ft 6 in, 1,371.6 mm)	78.1752 in (6 ft 6 3/16 in, 1,985.65 mm)	63 to 73.5 in (5 ft 3 in to 6 ft 1 1/2 in)
8	61.7143 in (5 ft 1 11/16 in, 1,567.54 mm)	91.2044 in (7 ft 7 3/16 in, 2,316.59 mm)	73.5 to 84 in (6 ft 1 1/2 in to 7 ft)
9	69.4286 in (5 ft 9 7/16 in, 1,763.49 mm)	104.2336 in (8 ft 8 1/4 in, 2,647.53 mm)	84 to 94.5 in (7 ft to 7 ft 10 1/2 in)
10	77.1429 in (6 ft 5 1/8 in, 1,959.43 mm)	117.2629 in (9 ft 9 1/4 in, 2,978.48 mm)	94.5 to 105 in (7 ft 10 1/2 in to 8 ft 9 in)
11	84.8571 in (7 ft 7/8 in, 2,155.37 mm)	130.2921 in (10 ft 10 5/16 in, 3,309.42 mm)	105 to 115.5 in (8 ft 9 in to 9 ft 7 1/2 in)
12	92.5714 in (7 ft 8 9/16 in, 2,351.31 mm)	143.3213 in (11 ft 11 5/16 in, 3,640.36 mm)	115.5 to 126 in (9 ft 7 1/2 in to 10 ft 6 in)
13	100.2857 in (8 ft 4 5/16 in, 2,547.26 mm)	156.3505 in (13 ft 3/8 in, 3,971.3 mm)	126 to 136.5 in (10 ft 6 in to 11 ft 4 1/2 in)

The same rise at other riser counts, at your going

Two fewer to three more risers than yours, never below one, at your 10 1/2 in going and with the same top layout. Plain arithmetic: no count is filtered, and none is set against a code figure.

Risers	Riser height, H ÷ n	Treads	Total run, treads × T	Angle, atan(R ÷ T)
12	9 in (9 in, 228.6 mm)	11	115.5 in (9 ft 7 1/2 in, 2,933.7 mm)	40.60°
13	8.3077 in (8 5/16 in, 211.02 mm)	12	126 in (10 ft 6 in, 3,200.4 mm)	38.35°
14 (yours)	7.7143 in (7 11/16 in, 195.94 mm)	13	136.5 in (11 ft 4 1/2 in, 3,467.1 mm)	36.30°
15	7.2 in (7 3/16 in, 182.88 mm)	14	147 in (12 ft 3 in, 3,733.8 mm)	34.44°
16	6.75 in (6 3/4 in, 171.45 mm)	15	157.5 in (13 ft 1 1/2 in, 4,000.5 mm)	32.74°
17	6.3529 in (6 3/8 in, 161.36 mm)	16	168 in (14 ft, 4,267.2 mm)	31.18°

Figures quoted from model codes, beside your own

Each figure is quoted with its edition and section, and your own number is set beside it as a plain number. Nothing is coloured or ticked. Which code and edition apply, and any local amendment, are decided by your jurisdiction. This page does not say whether a stair complies.

Dimension	Quoted	Your stair
Riser	2024 IRC R318.7.5.1 (R311.7.5.1 in the 2021 IRC): “The riser height shall be not more than 7 3/4 inches (196 mm).” 2024 IBC 1011.5.2: “7 inches (178 mm) maximum and 4 inches (102 mm) minimum”; its Exception 3 (Group R-3; dwelling units in Group R-2 not required to be Accessible or Type A; accessory Group U): “7 3/4 inches (197 mm)”.	7.7143 in (7 11/16 in, 195.94 mm), every riser the same.
Tread depth (going)	2024 IRC R318.7.5.2: “The tread depth shall be not less than 10 inches (254 mm).” 2024 IBC 1011.5.2: “11 inches (279 mm) minimum”; Exception 3: “10 inches (254 mm)”.	10.5 in (10 1/2 in, 266.7 mm).
Uniformity	“3/8 inch (9.5 mm)” between the greatest and the smallest riser, and tread, in a flight: 2024 IRC R318.7.5.1 and R318.7.5.2; 2024 IBC 1011.5.4.	the calculated risers are all 7.714286 in, a difference of 0 in. The quoted figure is a tolerance on what gets built.
Headroom	2024 IRC R318.7.2: “not less than 6 feet 8 inches (2032 mm) measured vertically from the sloped line adjoining the tread nosing”. 2024 IBC 1011.3: “not less than 80 inches (2032 mm) measured vertically from a line connecting the nosings”.	Not calculated: switch on the headroom inputs under Space and headroom.
Vertical rise of one flight	2024 IRC R318.7.3: “12 feet 7 inches (3835 mm)”. 2024 IBC 1011.8: “12 feet (3658 mm)”.	108 in (9 ft, 2,743.2 mm) in one flight.
Nosing projection	2024 IRC R318.7.5.3: “not less than 3/4 inch (19 mm) and not more than 1 1/4 inches (32 mm)”; Exception 1: “A nosing projection is not required where the tread depth is not less than 11 inches (279 mm).” Exception 2: “Where risers are open, the maximum nosing projection shall be permitted to exceed 1 1/4 inches (32 mm).” 2024 IBC 1011.5.5.1: “not more than 1 1/4 inches (32 mm)”; its exception permits a larger projection where solid risers are not required. IBC 1011.5.2 Exception 3 gives 3/4 to 1 1/4 in on solid risers where the tread is under 11 in.	Not entered.

Enter the total rise and either how many risers you want or your own maximum riser height, then your going. The calculator makes every riser equal, counts the treads on the stringer, and lays out the stringer: pitch line, first riser cut, notch depth, throat, board length for one drawn layout, and a mark for every tread worked from the exact riser height. Headroom under a floor opening is optional. The figures of the 2024 IRC and IBC are quoted beside your numbers; this page does not say whether a stair complies.

How this calculator works

Only your inputs and exact unit conversions. Where a figure comes from anywhere else, it is recorded below with its source.

Specification

Formula version: 1.0.0
Last reviewed: 2026-09-29
External data: 9 sources
Category: Measurement

Manufacturer, standard or trade figureMinimum dressed dry widths of 2x10 and 2x12 lumber — NIST / American Lumber Standard Committee. Inches, the units of record: nominal 12 is 11-1/4 in dressed dry (285.8 mm) and 11-1/2 in green; nominal 10 is 9-1/4 in dressed dry (235.0 mm) and 9-1/2 in green; nominal 2 thick is 1-1/2 in dressed dry. Verified 2026-09-29. Source
Candidate reference, not appliedResidential stair figures (IRC) — International Code Council (ICC). Inches, feet and inches, with the code’s own millimetres in parentheses: riser not more than 7 3/4 in (196 mm); tread not less than 10 in (254 mm); 3/8 in (9.5 mm) between the greatest and smallest; headroom 6 ft 8 in (2032 mm); vertical rise of a flight 12 ft 7 in (3835 mm); nosing 3/4 in (19 mm) to 1 1/4 in (32 mm). Verified 2026-09-29. Source
Candidate reference, not appliedBuilding code stair figures (IBC) — International Code Council (ICC). Inches and feet, with the code’s own millimetres: riser 7 in (178 mm) maximum and 4 in (102 mm) minimum, tread 11 in (279 mm) minimum; Exception 3, 7 3/4 in (197 mm) and 10 in (254 mm); 3/8 in (9.5 mm) tolerance; headroom 80 in (2032 mm); vertical rise of a flight 12 ft (3658 mm); nosing not more than 1 1/4 in (32 mm). Verified 2026-09-29. Source
Candidate reference, not appliedWhere the IRC is in use, and local amendment — International Code Council (ICC). No figure applied: two sentences quoted. Verified 2026-09-29. Source
Candidate reference, not appliedWorkplace stairs, general industry (OSHA 1910.25) — US Department of Labor, Occupational Safety and Health Administration (OSHA). Degrees from horizontal and inches (centimetres as printed): 30 to 50 degrees; maximum riser height 9.5 in; minimum tread depth 9.5 in; minimum width 22 in; clearance 6 ft 8 in from the leading edge of the tread. Verified 2026-09-29. Source
Candidate reference, not appliedStairways in construction workplaces (OSHA 1926.1052) — US Department of Labor, Occupational Safety and Health Administration (OSHA). Degrees from horizontal (30° to 50°) and inches: variation in riser height or tread depth not over 1/4 in (0.6 cm) in any stairway system. Verified 2026-09-29. Source
Candidate reference, not appliedDeck stair stringers (AWC DCA 6) — American Wood Council (AWC). Inches and feet-inches as printed. Verified 2026-09-29. Source
Candidate reference, not appliedRise and going relationship (England) — UK Government, Approved Document K to the Building Regulations 2010. Millimetres: private stair rise 150 to 220 and going 220 to 300, maximum pitch 42°; 2R + G between 550 and 700 mm. Verified 2026-09-29. Source
Candidate reference, not appliedStair dimension suggestions reported in 1979 (NBS) — National Bureau of Standards (now NIST), prepared for the US Consumer Product Safety Commission. Inches, and centimetres as printed: Harper, Florio and Stafford (1958), riser plus run not less than 17 or more than 18 in (p. 31); Grandjean (1973), 2r + t = 63 cm (24.8 in) (p. 32). Verified 2026-09-29. Source

What this calculates

From the total rise and either your riser count or your own maximum riser height, the riser height, the treads on the stringer, the total run and the stair angle; then the stringer layout: the pitch line, the first riser cut, the notch depth, the throat, the board length for one drawn layout and a mark for every tread. Lengths are given in inches, in feet, inches and sixteenths, and in millimetres (1 in = 25.4 mm exactly). With the headroom inputs, the headroom at the edge of the floor opening, and the opening length for a headroom you choose.

Risers and treads

Riser height R = total rise H ÷ risers n, exactly, so every riser is equal by construction. With your own maximum instead of a count, n = H ÷ your maximum, rounded up: the fewest risers that keep every riser at or under it. Rounding to the nearest count can put every riser over it: 108 ÷ 7.5 = 14.4 rounds to 14 risers of 7.714286 in, where rounding up gives 15 of 7.2 in.

With the upper floor as the top step, the last riser lands on the floor itself, so the stringer carries one tread fewer than there are risers: m = n − 1. With a top tread level with the upper floor, m = n.

Run, step and angle

The going T is measured level, nosing to nosing: the 2024 IRC measures tread depth “horizontally between the vertical planes of the foremost projection of adjacent treads” (R318.7.5.2). The total run, m × T, is from the face of the top riser to the face of the bottom riser, which is also nosing to nosing. A nosing on the bottom tread projects past the bottom riser by its projection.

One step along the stringer is S = √(R² + T²). The stair angle is atan(R ÷ T), the slope of the nosing line. Dividing the total rise by the total run instead takes the rise of n risers over the run of n − 1 treads: at 108 in, 14 risers and a 10 1/2 in going it gives atan(108 ÷ 136.5) = 38.35°, against 36.30° for every step of the stair.

The stringer

The notches are laid out along the top edge of the board, one S apart. The pitch line, m × S, runs along that edge from the top corner of the first riser cut to the back of the last tread. The first riser is cut to R − t, where t is the tread thickness, so that the first finished riser equals the others; a blank tread thickness counts as 0.

The notch depth, measured square to the edge, is R × T ÷ S. The throat, the board left under the notches, is the board width − R × T ÷ S.

For a stringer seated on the lower floor with its top plumb cut at the back of the last tread, where its top edge is t below the upper floor, the board spans m × S + R × (R − t) ÷ S along its length. That figure is for this layout only: hangers, ledgers and flush tops change it, and it is not a stock length to buy. With a top tread level with the upper floor no board length is given.

Rounding and the cut list

Every mark is worked from the exact riser height and rounded once, to the nearest 1/16 in. Stepping off a rounded riser adds its rounding at every step: 7.714286 in rounds to 7 11/16 in, and 14 of those come to 8 ft 11 5/8 in, 3/8 in short of 108 in.

Each row of the cut list gives the top of tread k above the lower floor, k × R; the level seat cut on the stringer, k × R − t; the distance along the top edge from the top corner of the first riser cut, (k − 1) × S; and the level distance from the face of the first riser, (k − 1) × T to k × T. The uncut edge would meet the lower floor (R − t) × S ÷ R further down the edge. The cut list is a table with the result. Beside it, a second table works the same rise at two fewer to three more risers, at your going, as plain numbers. The working shows one line for each column of both tables.

Headroom

Both codes measure headroom from the nosing line: the 2024 IRC “not less than 6 feet 8 inches (2032 mm) measured vertically from the sloped line adjoining the tread nosing” (R318.7.2), the 2024 IBC “not less than 80 inches (2032 mm) measured vertically from a line connecting the nosings” (1011.3). At a level distance D from the top nosing the nosing line is D × R ÷ T below the upper floor, so under an opening edge with floor depth F the headroom is D × R ÷ T − F. That holds to n × T from the top nosing, where the nosing line reaches the lower floor; past it the headroom is H − F, measured from the lower floor. For a headroom you choose, the distance from the top nosing is (target + F) × T ÷ R; when target + F is more than the total rise, no distance along the stair gives it, and the page says so instead of printing a length. Measured from the back of a tread instead, the figure is up to one riser more.

D is measured from the top nosing, not from the header. Where the upper floor is the top step, the header is taken at the top riser face, as in the drawn layout, and the nosing at the edge of the upper floor projects p in front of it, so the framed opening, header to far edge, is D + p. Where the top tread is level with the upper floor, that tread runs one going from the header to its riser face, so the framed opening is D + T + p. A blank nosing counts as 0.

Board widths

The 2x12 and 2x10 options apply PS 20-25 Table 3’s minimum dressed dry widths, 11 1/4 in and 9 1/4 in; the standard gives inches as its units of record. Green lumber is dressed to 11 1/2 and 9 1/2 in, and the standard’s footnote b sets other green sizes for Redwood, Western Red Cedar and Northern White Cedar. The width enters the throat only. Your own measured width is the default.

Codes: quoted, never applied

The riser, tread, uniformity, headroom, flight and nosing figures of the 2024 IRC (Section R318.7; R311.7 in the 2021 IRC) and the 2024 IBC (Section 1011) are quoted in a table with the result, each beside your own number, as plain numbers. No option fills one in, nothing is coloured or ticked, and the calculator does not say whether a stair complies.

Which code and edition apply, and any local amendment, are decided by your jurisdiction. This page does not say whether a stair complies. The ICC states that the IRC is “in use or adopted in 49 states, the District of Columbia, Guam, Puerto Rico and the U.S. Virgin Islands”, and that “some jurisdictions amend the code” when they adopt it. Winders, spiral stairs, landings, handrails, guards, stair width and existing stairs are not modelled.

Pouring concrete steps

This page lays out the steps. The volume of concrete for poured steps is on the concrete calculator, in its stairs mode, linked under Where people go next at the foot of this page.

A 108 in rise in 14 risers, with the stringer cut from a 2x12

The rise, the risers, the 10 1/2 in going, the 1 in tread, the 2x12, the 120 in from the top nosing to the far edge of the opening and the 10 in floor depth are example inputs, not recommendations. The upper floor is the top step.

Given

Total rise: 108 in (9 ft)
Risers: 14
Going: 10 1/2 in
Tread thickness: 1 in
Stringer board: 2x12, 11.25 in (PS 20-25 minimum dressed dry)
From the top nosing to the far edge; floor depth: 120 in; 10 in

Step by step

01Riser height R = Total rise ÷ Risers= 108 in ÷ 14= 7.714286 in
02Treads = Risers − 1= 14 − 1= 13 treads
03Total run = Treads × Going= 13 × 10.5= 136.5 in
04S = √(R² + T²)= √(7.714286² + 10.5²)= 13.029206 in
05Angle = atan(R ÷ T)= atan(7.714286 ÷ 10.5)= 36.30°
06Pitch line = Treads × S= 13 × 13.029206= 169.3797 in
07First riser cut = R − t= 7.714286 − 1= 6.7143 in
08Notch depth = R × T ÷ S= 7.714286 × 10.5 ÷ 13.029206= 6.2168 in
09Throat = Board width − R × T ÷ S= 11.25 − 7.714286 × 10.5 ÷ 13.029206= 5.0332 in
10Board length = Treads × S + R × (R − t) ÷ S= 13 × 13.029206 + 7.714286 × (7.714286 − 1) ÷ 13.029206= 173.355 in (14 ft 5 3/8 in)
11Headroom = D × R ÷ T − F= 120 × 7.714286 ÷ 10.5 − 10= 78.1633 in
12Check: Risers × R to the nearest 1/16 in= 14 × 7.6875= 107.625 in (8 ft 11 5/8 in, 3/8 in short of 108 in)

Risers, run and stringer board

14 risers of 7.714286 in (7 11/16 in to the nearest 1/16), 13 treads, 11 ft 4 1/2 in run; board 14 ft 5 3/8 in for this layout

Stair angle by riser and going, in degrees

Every cell is atan(riser ÷ going) in degrees, to one decimal: the angle of the nosing line. A 7 in riser on an 11 in going is 32.5°. The rows and columns are a range for reading, not a limit: no cell is marked and no figure is applied.

Riser	Going 8 in	Going 9 in	Going 10 in	Going 11 in	Going 12 in	Going 13 in	Going 14 in
4 in	26.6	24.0	21.8	20.0	18.4	17.1	15.9
4 1/4 in	28.0	25.3	23.0	21.1	19.5	18.1	16.9
4 1/2 in	29.4	26.6	24.2	22.2	20.6	19.1	17.8
4 3/4 in	30.7	27.8	25.4	23.4	21.6	20.1	18.7
5 in	32.0	29.1	26.6	24.4	22.6	21.0	19.7
5 1/4 in	33.3	30.3	27.7	25.5	23.6	22.0	20.6
5 1/2 in	34.5	31.4	28.8	26.6	24.6	22.9	21.4
5 3/4 in	35.7	32.6	29.9	27.6	25.6	23.9	22.3
6 in	36.9	33.7	31.0	28.6	26.6	24.8	23.2
6 1/4 in	38.0	34.8	32.0	29.6	27.5	25.7	24.1
6 1/2 in	39.1	35.8	33.0	30.6	28.4	26.6	24.9
6 3/4 in	40.2	36.9	34.0	31.5	29.4	27.4	25.7
7 in	41.2	37.9	35.0	32.5	30.3	28.3	26.6
7 1/4 in	42.2	38.9	35.9	33.4	31.1	29.1	27.4
7 1/2 in	43.2	39.8	36.9	34.3	32.0	30.0	28.2
7 3/4 in	44.1	40.7	37.8	35.2	32.9	30.8	29.0
8 in	45.0	41.6	38.7	36.0	33.7	31.6	29.7
8 1/4 in	45.9	42.5	39.5	36.9	34.5	32.4	30.5
8 1/2 in	46.7	43.4	40.4	37.7	35.3	33.2	31.3
8 3/4 in	47.6	44.2	41.2	38.5	36.1	33.9	32.0
9 in	48.4	45.0	42.0	39.3	36.9	34.7	32.7
9 1/4 in	49.1	45.8	42.8	40.1	37.6	35.4	33.5
9 1/2 in	49.9	46.5	43.5	40.8	38.4	36.2	34.2

Which riser and going a stair may have is set by the code your jurisdiction has adopted. The figures of the 2024 IRC and IBC are quoted in a table with the result and in the answers below, not in this table.

What it assumes

01Every riser is equal, the total rise ÷ the risers, and every going is equal.
02The total rise is measured plumb between finished walking surfaces.
03One straight flight: no landing, winder or spiral.
04The notches are laid out along the stringer’s top edge, and its two edges are parallel.
05Board length: seated on the lower floor, top plumb cut at the back of the last tread, top edge t below the upper floor.
06Headroom is measured plumb from the nosing line, at the far edge of the opening, a level distance D from the top nosing.
07The header is at the top riser face where the upper floor is the top step, and one going behind the top riser face where the top tread is level with the floor.

What it does not do

It does not say whether a stair complies with any code. The quoted figures are not applied; local adoption and amendment decide which, if any, apply.
No landings, winders, spiral stairs, handrails, guards, stair width, or provisions for existing stairs.
No structural check: stringer size, span, spacing and fastening are not calculated. AWC DCA 6’s deck figures are quoted in one answer only.
The board length is for the drawn layout only. Hangers, ledgers and flush tops change it, and no stock length is chosen.
Accessibility rules (the ADA Standards, ICC A117.1) and codes outside the US, apart from England’s Approved Document K quoted in one answer, were not reviewed.

Common questions.

How do I calculate my stairs?: Measure the total rise, plumb, from finished floor to finished floor, and divide it by the number of risers: 108 in ÷ 14 = 7.714286 in, every riser the same (7 11/16 in to the nearest 1/16 in). With the upper floor as the top step there is one tread fewer than risers, 13, and the total run is 13 × your going: at 10 1/2 in, 136.5 in (11 ft 4 1/2 in). Starting from your own maximum riser instead, divide and round up: 108 ÷ 7.5 = 14.4, so 15 risers of 7.2 in. Rounding to the nearest count would give 14 risers of 7.714286 in, over the maximum you set.
How do you calculate stair stringers, and how long is a 2x12 for a 5-step or a 14-step stringer?: The notches sit one step, S = √(R² + T²), apart along the top edge, so the pitch line is the number of treads × S; the board for a stringer seated on the floor with its top plumb cut at the back of the last tread adds R × (R − t) ÷ S. “Steps” can mean treads or risers, and with the upper floor as the top step there is one tread fewer than risers, so each length below is given both ways. At example inputs of a 7 1/2 in riser, a 10 1/2 in going and a 1 in tread: S = √(7.5² + 10.5²) = 12.903488 in, and R × (R − t) ÷ S = 7.5 × 6.5 ÷ 12.903488 = 3.778048 in. 5 treads, so 6 risers (a 45 in rise): pitch line 5 × 12.903488 = 64.5174 in (5 ft 4 1/2 in); board 5 × 12.903488 + 3.778048 = 68.2955 in (5 ft 8 5/16 in). 5 risers, so 4 treads (a 37.5 in rise): pitch line 4 × 12.903488 = 51.614 in (4 ft 3 5/8 in); board 4 × 12.903488 + 3.778048 = 55.392 in (4 ft 7 3/8 in). 14 treads, so 15 risers (a 112.5 in rise): pitch line 14 × 12.903488 = 180.6488 in (15 ft 5/8 in); board 14 × 12.903488 + 3.778048 = 184.4269 in (15 ft 4 7/16 in). 14 risers, so 13 treads (a 105 in rise): pitch line 13 × 12.903488 = 167.7453 in (13 ft 11 3/4 in); board 13 × 12.903488 + 3.778048 = 171.5234 in (14 ft 3 1/2 in). The width of the board does not change these lengths, and no stock length is chosen here.
What is the 7–11 rule for stairs?: The pair 7 in and 11 in is the 2024 IBC’s general riser maximum and tread minimum: 1011.5.2 gives risers of “7 inches (178 mm) maximum and 4 inches (102 mm) minimum” and rectangular treads of “11 inches (279 mm) minimum”. Its Exception 3 (Group R-3; dwelling units in Group R-2 not required to be Accessible or Type A; accessory Group U) gives “7 3/4 inches (197 mm)” and “10 inches (254 mm)”, and the 2024 IRC gives 7 3/4 in (196 mm) and 10 in (254 mm) in R318.7.5.1 and R318.7.5.2. A 7 in riser on an 11 in going is atan(7 ÷ 11) = 32.47°. A named “7-11 rule” was not found in the sources reviewed.
What is the ideal rise and run for stairs, and what is 2R + T or the 27 rule?: The codes set limits, not an ideal. England’s Approved Document K (2013 edition, for use in England) says “The normal relationship between the dimensions of the rise and going is: twice the rise plus the going (2R + G) equals between 550mm and 700mm.” That is 21.65 to 27.56 in. NBS Building Science Series 120 (1979) reports two older suggestions: Harper, Florio and Stafford (1958), that “the sum of the height of a riser and the length of a run should not be less than 17, or more than 18 in.” (p. 31); and Grandjean (1973), “2r + t = 63 cm (24.8 in.)” (p. 32). “2R + T = 24 to 25 in” and a “27 rule” were not found in the sources reviewed. The calculator applies none of these.
Is an 8 inch stair riser too high?: This page does not decide; the code your jurisdiction has adopted does. Quoted: the 2024 IRC R318.7.5.1, “The riser height shall be not more than 7 3/4 inches (196 mm).” The 2024 IBC 1011.5.2, “7 inches (178 mm) maximum and 4 inches (102 mm) minimum”, with “7 3/4 inches (197 mm)” under Exception 3. OSHA 29 CFR 1910.25(c)(2), for general-industry workplaces: “Have a maximum riser height of 9.5 inches (24 cm)”. OSHA’s Table D-1, for standard stairs installed before January 17, 2017, prints an angle of 40 deg. 08' for a rise of 8 in and a tread run of 9 ½ in; atan(8 ÷ 9.5) computes to 40.10° (40° 06′), so the printed figure differs. An 8 in riser on a 10 1/2 in going is atan(8 ÷ 10.5) = 37.30°, and on 11 in, 36.03°.
Why is there one fewer tread than risers?: Because the last step up lands on the upper floor, which is the top tread of the stair but not one cut on the stringer. 14 risers therefore need 13 treads on the stringer. If the top tread is set level with the upper floor instead, choose that option: the stringer then carries as many treads as risers, and the total run grows by one going.
How much headroom does a stair need?: Quoted, not applied: the 2024 IRC R318.7.2, “not less than 6 feet 8 inches (2032 mm) measured vertically from the sloped line adjoining the tread nosing”; the 2024 IBC 1011.3, “not less than 80 inches (2032 mm) measured vertically from a line connecting the nosings”. Both measure from the nosing line, so under an opening edge D from the top nosing, with floor depth F, the headroom is D × R ÷ T − F. With the example stair, 120 in from the top nosing to the far edge of the opening and a 10 in floor depth: 120 × 7.714286 ÷ 10.5 − 10 = 78.1633 in. For a headroom you choose, say 82 in, the distance from the top nosing is (82 + 10) × 10.5 ÷ 7.714286 = 125.2222 in. D is measured from the top nosing, not from the header: the framed opening, header to far edge, is D + p where the upper floor is the top step, p being the nosing projection, and D + T + p where the top tread is level with the floor.
What is the stringer throat, and how deep should it be?: The throat is the board left under the notches, measured square to its edges: the board width − R × T ÷ S. For the example stair on a 2x12 (11 1/4 in, PS 20-25 minimum dressed dry) it is 5.0332 in. AWC’s DCA 6, a deck guide “Based on the 2015 International Residential Code”, shows “5" min.” on the cut stringer in its Figure 28 and says “All stringers shall be a minimum of 2x12.” Its commentary adds “Cut stringers were analyzed with 5.1" depth which is based on 7.75:10 rise to run ratio”; the same throat formula gives 11.25 − 7.75 × 10 ÷ 12.651581 = 5.1243 in. Those are quoted, not applied: they are for decks, based on the 2015 IRC.
What does OSHA require for stairs?: For general-industry workplaces, 29 CFR 1910.25(c) requires standard stairs to be installed at 30 to 50 degrees from the horizontal, with a maximum riser height of 9.5 in, a minimum tread depth of 9.5 in and a minimum width of 22 in. Under (c)(5), the riser and tread limits do not apply to standard stairs installed before January 17, 2017: OSHA accepts those if they match Table D-1 or use a combination that achieves the 30 to 50 degree angle. For construction workplaces, 29 CFR 1926.1052(a)(3) says “Variations in riser height or tread depth shall not be over ¼-inch (0.6 cm) in any stairway system.” These are workplace rules, quoted, not applied.
How do I measure the total rise?: Plumb, from the finished surface of the lower floor to the finished surface of the upper floor. The IRC (R318.7.5) and the IBC (1011.5.1) take stair dimensions exclusive of carpets, rugs or runners. A hard floor finish laid after you measure changes the total rise by its thickness: one laid on the upper floor adds it, one laid on the lower floor takes it off.

Where people go next

All measurement tools

Ordered by what usually comes next in the same job, not by keyword.

01Roof pitchPitch, angle, rafter, squaresPitch as X in 12, the angle, grade and pitch factor from a rise and run, a pitch or an angle, plus the rafter line length with overhang and the roof area in squares.02Board feetBoard feet, linear feet and costBoard feet from the thickness, width and length of each piece, for up to four lumber sizes, with the linear feet and, at your own price, the cost.03ConcreteCubic yards, and bag countCubic yards and cubic feet for slabs, footings, walls, round piers, stairs and curb and gutter — with a bag count from the yield on your bag, not a guessed constant.04SlopeGrade, ratio, angle, lengthRise, run, percent grade, ratio and angle — enter any one and get the others.