For a 108 in rise with the IRC's 7 3/4 in maximum riser and 10 in treads, that's 14 risers of 7.71 in, 13 treads, 130 in of run, and a stringer about 14.08 ft long before cutting.
To lay out a staircase the way a stair calculator does, divide the total rise (finished floor to finished floor) by the maximum riser height and round up to get the number of risers. Then divide the rise by that number for the exact riser height. You'll have one fewer tread than risers, and the total run is the number of treads × tread depth.
These results are for planning and ordering materials. Stairs are a safety item: confirm the layout with your local building department, and have a qualified pro build or check any structural stair.
How to measure the total rise
- Measure finished floor to finished floor. Measure from the top of the lower floor to the top of the upper floor. If flooring isn't installed yet, add its thickness at the top and bottom, or your first or last step will come out uneven.
- For deck or porch stairs, measure to the landing spot. Ground slopes, so don't measure straight down at the house. Run a straight board level from the deck surface out to where the bottom step will land, then measure down to the ground there. Planning the deck itself? The deck calculator counts boards and joists.
- Choose your tread depth. The IRC minimum is 10 in. At 11 in or more, no nosing is required.
- Choose a maximum riser. 7 3/4 in is the IRC maximum. Entering a lower number, like 7.5 in, adds a step and makes the stair less steep.
- Check the space. Make sure the total run fits, with room for a landing at the bottom, and that there's at least 6 ft 8 in of headroom along the whole stair. For a concrete landing pad outdoors, the concrete calculator gives cubic yards and bags.
The stair formula
The calculator uses:
- Risers = total rise ÷ maximum riser height, rounded up
- Riser height = total rise ÷ risers
- Treads = risers − 1
- Total run = treads × tread depth
- Stringer length = √(rise² + run²) ÷ 12, in feet
There's one fewer tread than risers because the upper floor or deck surface serves as the top step. Dividing the rise evenly keeps every riser the same height, which matters because the IRC allows no more than 3/8 in of difference between the tallest and shortest riser in a flight.
Worked example (the calculator's default values)
A total rise of 108 in, a 7.75 in maximum riser, and 10 in treads:
- Risers: 108 ÷ 7.75 = 13.94, rounded up to 14
- Riser height: 108 ÷ 14 = 7.714 in, just under 7 3/4 in (about 7 23/32 in)
- Treads: 14 − 1 = 13
- Total run: 13 × 10 = 130 in, or 10.83 ft
- Stringer: √(108² + 130²) = √28,564 = 169.0 in, or 14.08 ft
The calculator shows: "You need 14 risers of 7.71 in and 13 treads. Total run: 130.0 in (10.83 ft). Stringer length: about 14.08 ft before cutting."
Stair angle by riser height and tread depth
37.8 degrees is the steepest stair the IRC allows: a 7 3/4 in riser over a 10 in tread. The angle is the arctangent of riser height ÷ tread depth, so shorter risers or deeper treads make a gentler stair:
| Riser height | 10 in tread | 10 1/2 in tread | 11 in tread | 12 in tread |
|---|---|---|---|---|
| 6 in | 31.0° | 29.7° | 28.6° | 26.6° |
| 6 1/2 in | 33.0° | 31.8° | 30.6° | 28.4° |
| 7 in | 35.0° | 33.7° | 32.5° | 30.3° |
| 7 1/4 in | 35.9° | 34.6° | 33.4° | 31.1° |
| 7 1/2 in | 36.9° | 35.5° | 34.3° | 32.0° |
| 7 3/4 in | 37.8° | 36.4° | 35.2° | 32.9° |
The calculator's default stair (7.71 in risers on 10 in treads) works out to about 37.6 degrees. Trex says a comfortable angle for a staircase is usually between 35 and 37 degrees, which matches risers of about 7 to 7 1/2 in on 10 in treads, and notes that most deck steps are 7 to 7 1/2 in tall. The calculator doesn't show the angle, so read it from this chart using the riser height it gives.
Stair layouts for common rises
With the 7 3/4 in maximum riser and 10 in treads:
| Total rise | Risers | Riser height | Treads | Total run | Stringer before cutting |
|---|---|---|---|---|---|
| 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 |
| 48 in | 7 | 6.86 in | 6 | 60 in | 6.40 ft |
| 96 in | 13 | 7.38 in | 12 | 120 in | 12.81 ft |
| 105 in | 14 | 7.50 in | 13 | 130 in | 13.93 ft |
| 108 in | 14 | 7.71 in | 13 | 130 in | 14.08 ft |
| 114 in | 15 | 7.60 in | 14 | 140 in | 15.05 ft |
| 120 in | 16 | 7.50 in | 15 | 150 in | 16.01 ft |
Floor-to-floor height is the ceiling height plus the thickness of the floor structure and flooring above it, so always measure rather than assume.
Deck stair stringers by deck height
4 risers and a stringer about 3.54 ft long for a 30 in (2 ft 6 in) deck, and 7 risers with a 6.40 ft stringer for a 48 in (4 ft) deck, with the calculator's 7 3/4 in maximum riser and 10 in treads. Measure the deck height from the deck surface down to the ground where the bottom step will land:
| Deck height | Risers | Treads | Total run | Stringer length | 2 × 12 to buy |
|---|---|---|---|---|---|
| 12 in (1 ft) | 2 of 6.00 in | 1 | 10 in | 1.30 ft | 8 ft |
| 18 in (1 ft 6 in) | 3 of 6.00 in | 2 | 20 in | 2.24 ft | 8 ft |
| 24 in (2 ft) | 4 of 6.00 in | 3 | 30 in | 3.20 ft | 8 ft |
| 30 in (2 ft 6 in) | 4 of 7.50 in | 3 | 30 in | 3.54 ft | 8 ft |
| 36 in (3 ft) | 5 of 7.20 in | 4 | 40 in | 4.48 ft | 8 ft |
| 42 in (3 ft 6 in) | 6 of 7.00 in | 5 | 50 in | 5.44 ft | 8 ft |
| 48 in (4 ft) | 7 of 6.86 in | 6 | 60 in | 6.40 ft | 8 ft |
| 54 in (4 ft 6 in) | 7 of 7.71 in | 6 | 60 in | 6.73 ft | 8 ft |
| 60 in (5 ft) | 8 of 7.50 in | 7 | 70 in | 7.68 ft | 10 ft |
| 66 in (5 ft 6 in) | 9 of 7.33 in | 8 | 80 in | 8.64 ft | 10 ft |
| 72 in (6 ft) | 10 of 7.20 in | 9 | 90 in | 9.60 ft | 12 ft |
The last column is the shortest standard length (8 to 20 ft in 2 ft steps, per the Southern Forest Products Association) that is at least 1 ft longer than the stringer, because Home Depot suggests starting with a board about 12 in longer than the stringer. DCA 6 requires 2 × 12 stringers. Then check the run against the cut-stringer span: up to the 60 in deck, the run stays within the 6 ft (72 in) limit in Simpson Strong-Tie's summary; the 66 in deck's 80 in run fits only the 7 ft that JLC cites for Southern pine 2 × 12s, and the 72 in deck's 90 in run needs a support post or a landing. Above 30 in, the IRC also requires guards on the open sides of the stair, and every row with 4 or more risers needs a handrail.
Staircase length for 8 to 12 ft rises, and when you need a landing
10.83 ft of floor length for the 108 in default with 10 in treads, or 11.92 ft with 11 in treads. The total run is the staircase's length on the floor and the stringer is its length along the slope, both with the 7 3/4 in maximum riser:
| Total rise | Risers | Treads | Floor length, 10 in treads | Floor length, 11 in treads | Stringer, 11 in treads |
|---|---|---|---|---|---|
| 96 in (8 ft) | 13 of 7.38 in | 12 | 10.00 ft | 11.00 ft | 13.60 ft |
| 108 in (9 ft) | 14 of 7.71 in | 13 | 10.83 ft | 11.92 ft | 14.93 ft |
| 120 in (10 ft) | 16 of 7.50 in | 15 | 12.50 ft | 13.75 ft | 17.00 ft |
| 126 in (10 ft 6 in) | 17 of 7.41 in | 16 | 13.33 ft | 14.67 ft | 18.04 ft |
| 132 in (11 ft) | 18 of 7.33 in | 17 | 14.17 ft | 15.58 ft | 19.07 ft |
| 138 in (11 ft 6 in) | 18 of 7.67 in | 17 | 14.17 ft | 15.58 ft | 19.37 ft |
| 144 in (12 ft) | 19 of 7.58 in | 18 | 15.00 ft | 16.50 ft | 20.40 ft |
| 151 in (12 ft 7 in) | 20 of 7.55 in | 19 | 15.83 ft | 17.42 ft | 21.49 ft |
151 in (12 ft 7 in) is the most a single flight may rise between floor levels or landings under IRC R311.7.3, as quoted in the City of Albany, GA code-check handout, so a taller stair needs a landing partway up. For deck stairs, DCA 6 requires an intermediate landing once the total height of the stairway is over 12 ft. Each landing needs at least 36 in in the direction of travel, so leave at least that much clear floor at the bottom of the stair too. The calculator lays out one straight flight: for a stair with a landing, run it once for each flight, using the rise from the floor or landing to the next level.
Residential stair code at a glance
These limits come from the International Residential Code (IRC) as summarized by Viewrail for the 2021 edition and by the City of Saint Paul's stair handout. Your jurisdiction may have adopted a different edition or local amendments.
| Item | IRC requirement |
|---|---|
| Maximum riser height | 7 3/4 in |
| Minimum tread depth | 10 in |
| Variation within a flight | No more than 3/8 in between largest and smallest riser (same for treads) |
| Nosing | 3/4 to 1 1/4 in projection when treads are under 11 in deep |
| Headroom | 6 ft 8 in minimum |
| Stair width | 36 in minimum clear width |
| Handrail | 34 to 38 in high, on at least one side when there are 4 or more risers |
| Guards | Required on open sides more than 30 in above the floor or grade below |
Deck stairs: stringer rules
- DCA 6 requires stringers of at least 2 × 12 lumber.
- Stringer spans are limited. Simpson Strong-Tie's summary puts the maximum horizontal span at 6 ft for a cut (notched) stringer and 13 ft 3 in for a solid stringer. DCA 6 shows the limits in its stringer figure, and JLC notes that Southern pine cut stringers are allowed 7 ft, so check the figure for your lumber.
- If you use only cut stringers, DCA 6 requires at least three.
- For stairs wider than 36 in, DCA 6 limits stringer spacing to 18 in on center.
- DCA 6 requires every rectangular landing to measure at least 36 in in the direction of travel and to be no narrower than the stairs.
The 108 in default is an indoor, floor-to-floor example. Its 130 in (10.83 ft) run is far beyond the roughly 6 ft limit for a cut stringer, so an outdoor stair that size needs intermediate support or a landing, designed by someone qualified.
How many stair stringers do I need?
Count the spaces, then add one: stringers = stair width ÷ maximum spacing, rounded up, + 1. For deck stairs, DCA 6 requires at least three stringers when they are all cut stringers, and for stairs wider than 36 in it limits stringer spacing to 18 in on center. Trex says to space stringers to the specifications of your tread material, which usually means 12 in on center or less.
Worked example: a deck surface 36 in above the landing spot. With the calculator's 7 3/4 in maximum riser and 10 in treads, that's 5 risers of 7.20 in, 4 treads, 40 in of run, and a stringer about 4.48 ft long (the 36 in row in the chart above), well within the roughly 6 ft limit for a cut stringer.
- 36 in wide, wood treads: 36 ÷ 18 = 2 spaces, + 1 = 3 stringers, the DCA 6 minimum.
- 48 in wide, wood treads: 48 ÷ 18 = 2.67, rounded up to 3 spaces, + 1 = 4 stringers.
- 48 in wide, composite treads at 12 in on center: 48 ÷ 12 = 4 spaces, + 1 = 5 stringers.
Spacing is measured center to center, so working from the full stair width keeps the count on the safe side. Each stringer is a 2 × 12 cut from a board longer than 4.48 ft. Confirm the count with the tread maker's instructions and your local code.
Stringers by stair width: 3 to 8 ft wide stairs
3 stringers for a 36 in wide stair and 4 for a 48 in stair with wood treads, using DCA 6's 18 in maximum spacing. Composite treads need more, because Trex spaces stair stringers 9 to 12 in apart depending on the board:
| Stair width | Wood treads, 18 in on center | Composite, 12 in on center | Composite, 9 in on center |
|---|---|---|---|
| 36 in (3 ft) | 3 | 4 | 5 |
| 42 in (3 ft 6 in) | 4 | 5 | 6 |
| 48 in (4 ft) | 4 | 5 | 7 |
| 60 in (5 ft) | 5 | 6 | 8 |
| 72 in (6 ft) | 5 | 7 | 9 |
| 96 in (8 ft) | 7 | 9 | 12 |
Each count is the stair width ÷ spacing, rounded up, + 1, the method in the section above. JLC gives the same counts for wood treads: three stringers for a 3 ft stair and four for one 3 ft 6 in wide. A stair built only with cut stringers needs at least 3 under DCA 6 however narrow it is, and every stringer is a 2 × 12 cut to the length in the deck height chart above. For composite, use the spacing in your tread maker's installation instructions.
Tips and common mistakes
- Measuring to the subfloor. If finished flooring goes on later, the top or bottom riser ends up taller or shorter than the rest. Measure finished surface to finished surface.
- Forgetting the tread thickness on cut stringers. When treads sit on top of the stringer cuts, every tread adds its thickness, so the bottom of the stringer is usually trimmed by one tread thickness to keep the first riser the same height as the others.
- Buying stringer stock too short. The stringer length is the straight line from bottom to top. The plumb cut at the top and the level cut at the bottom need extra board, so buy the next longer length (a 16 ft board for the 14.08 ft example).
- Rounding each riser to a nearby fraction. 14 risers at a full 7 3/4 in would add up to 108.5 in, half an inch too tall. Lay out with the exact figure, or round to the nearest 1/16 in and check the total.
- Confusing run with tread board depth. The run is measured nosing to nosing. The tread board itself is deeper when it has a nosing overhang.
- Spacing stringers for wood treads under composite. Composite treads usually need stringers closer together. Trex says stair stringers are usually 12 in on center or less, depending on the tread material.
Frequently asked questions
How many steps do I need for a 108 inch rise?
With the IRC maximum riser of 7 3/4 in, 108 inches needs 14 risers of about 7.71 in each and 13 treads. With 10 in treads, the stairs run 130 in (10.83 ft) horizontally.
How many stairs do I need?
Measure the total rise from finished floor to finished floor in inches, divide it by 7.75, the IRC maximum riser height, and round up. That gives the risers, the steps you climb; you build one fewer tread, because the upper floor is the top step. A 108 in rise takes 14 risers of 7.71 in and 13 treads, and a 96 in rise takes 13 risers of 7.38 in and 12 treads. Confirm the layout with your local building department.
How many steps do I need for a 4 foot deck?
7 risers of about 6.86 in and 6 treads for a 48 in rise, with the 7 3/4 in maximum riser and 10 in treads, since the deck surface is the top step. The stairs run 60 in (5 ft) out from the deck, within the 6 ft span for a cut stringer, and each stringer is about 6.40 ft long, so an 8 ft 2 × 12 is enough. Measure the 48 in from the deck surface to the ground where the bottom step lands, since the ground often slopes.
What is the maximum stair riser height?
The IRC, the model residential code many state and local codes are based on, sets the maximum at 7 3/4 in, and the tallest and shortest risers in a flight can't differ by more than 3/8 in. Some local codes differ, so check with your building department.
What is the minimum stair tread depth?
10 in under the IRC, measured from nosing to nosing. Treads less than 11 in deep need a nosing that projects 3/4 to 1 1/4 in. At 11 in or deeper, no nosing is required.
How long should my stair stringers be?
Use the Pythagorean theorem: the square root of (total rise squared + total run squared). For a 108 in rise and 130 in run, that's 169 in, or about 14.08 ft. Buy the next longer board to leave room for the top and bottom cuts.
What size lumber do you use for stair stringers?
2 × 12 at least: DCA 6 requires 2 × 12 stringers for deck stairs. A 2 × 12 is 11 1/4 in deep, and cutting 7.71 in risers and 10 in treads takes about 6.1 in out of it, leaving about 5.1 in of solid wood below the notches. A 2 × 10 (9 1/4 in) would keep only about 3.1 in. For the length, buy the shortest standard board at least 1 ft longer than the stringer: an 8 ft board for a 48 in deck, a 16 ft board for the 108 in default.
How many stringers do I need for deck stairs?
DCA 6 requires at least three if you use only cut stringers, and a maximum spacing of 18 in on center for stairs wider than 36 in. Composite treads often need closer spacing, which Trex says is usually 12 in on center or less.
How many stringers do I need for 48 inch wide stairs?
4 with wood treads: 48 ÷ 18 = 2.67, rounded up to 3 spaces, + 1, since DCA 6 limits stringer spacing to 18 in on center on stairs wider than 36 in. With composite treads at 12 in on center it's 5 (48 ÷ 12 = 4 spaces, + 1), and at 9 in on center, 7. A 36 in wide stair takes 3 with wood treads, the DCA 6 minimum for cut stringers.
What angle is a standard staircase?
It depends on the riser and tread. The default example (7.71 in risers, 10 in treads) works out to about 37.6 degrees. Shorter risers or deeper treads make the stair less steep.
How many steps do I need for a 10 ft ceiling?
Measure instead of assuming: floor-to-floor height is the ceiling height plus the thickness of the floor structure and flooring above it. As a reference, a 120 in total rise with the 7 3/4 in maximum riser needs 16 risers of 7.50 in and 15 treads, and 10 in treads give a 150 in run.
How much headroom and width does a staircase need?
The IRC calls for at least 6 ft 8 in of headroom along the whole stair and a minimum clear width of 36 in. Your jurisdiction may have adopted a different edition or local amendments, so confirm with your building department.
What is the maximum height of stairs without a landing?
151 in (12 ft 7 in) of vertical rise for one flight under IRC R311.7.3, measured between floor levels or landings, which takes 20 risers of 7.55 in at the 7 3/4 in maximum. Deck stairs under DCA 6 need an intermediate landing once the stairway is more than 12 ft tall. A landing must be at least 36 in deep in the direction of travel and at least as wide as the stairs.
Do stairs need a handrail?
Under the IRC, a handrail 34 to 38 in high is required on at least one side when there are 4 or more risers. Guards are required on open sides more than 30 in above the floor or grade below.
Sources
- Viewrail: Tread Depth and Risers, IRC 2021 Section R311.7.5
- City of Saint Paul: Residential Stairs and Handrails (PDF)
- American Wood Council: DCA 6, Prescriptive Residential Wood Deck Construction Guide (PDF)
- Trex: How to Space and Install Deck Joists (stair stringer spacing)
- Simpson Strong-Tie: Building Safe and Sturdy Stairs for Your Deck
- JLC: Building and Installing Deck Stairs
- City of Albany, GA: Residential Code Check Illustrations, Stairs and Guards (PDF)
- Trex: How to Calculate and Cut Stair Stringers
- The Home Depot: How to Measure Stair Stringers
- Southern Forest Products Association: Standard Sizing
- Southern Forest Products Association: Specification Guidelines
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