Stair Calculator: Risers, Treads and Stringer Length

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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.

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.

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 many stairs do you need?

Enter the total rise from finished floor to finished floor. We work out the risers, treads, and stringer length.

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The IRC (residential code) allows a maximum riser of 7 3/4 in and a minimum tread of 10 in. Always confirm with your local building department.

How to measure the total rise

  1. 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.
  2. 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.
  3. Choose your tread depth. The IRC minimum is 10 in. At 11 in or more, no nosing is required.
  4. 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.
  5. 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.
Parts of a stair: riser, tread and stringerClose-up of three steps: the riser height of 7.71 inches is the vertical rise of each step, the tread depth of 10 inches is the horizontal run, and the notched stringer carries the treads. The IRC allows a maximum riser of 7 3/4 inches and a minimum tread of 10 inches.PARTS OF A STAIRRiser7.71 in10 inTread depth (run)Stringernotched board thatcarries the treadsIRC limitsRiser: 7 3/4 in maxTread: 10 in minLocal codes can differ;check before you build.This stair: 7.71 in risers and 10 in treads, within those limits
Riser height is the vertical step and tread depth the horizontal run; the IRC allows risers up to 7 3/4 in and treads of at least 10 in, so check your local code.

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:

  1. Risers: 108 ÷ 7.75 = 13.94, rounded up to 14
  2. Riser height: 108 ÷ 14 = 7.714 in, just under 7 3/4 in (about 7 23/32 in)
  3. Treads: 14 − 1 = 13
  4. Total run: 13 × 10 = 130 in, or 10.83 ft
  5. 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 math for a 108 inch total riseSide view of a straight stair with a total rise of 108 inches: 14 risers of 7.71 inches and 13 treads of 10 inches give a total run of 130 inches, and the stringer is about 14.08 feet long.STAIRS: RISE, RUN, AND STRINGER108 intotal riseTotal run 130 in (10.83 ft)Stringer ≈ 14.08 ft14 risersof 7.71 in13 treadsof 10 in (run)Risers: 108 in ÷ 7.75 in max = 13.9 → 14 risersRiser height: 108 ÷ 14 = 7.71 inTreads: 14 − 1 = 13 treads × 10 in = 130 in of runStringer: √(108² + 130²) = 169 in ÷ 12 ≈ 14.08 ftEstimates only. Confirm riser and tread limits with your local building department.
Divide the total rise by the maximum riser height and round up for 14 risers; 13 treads at 10 in give a 130 in run and a stringer of about 14.08 ft.

Stair layouts for common rises

With the 7 3/4 in maximum riser and 10 in treads:

Total riseRisersRiser heightTreadsTotal runStringer before cutting
24 in46.00 in330 in3.20 ft
30 in47.50 in330 in3.54 ft
36 in57.20 in440 in4.48 ft
48 in76.86 in660 in6.40 ft
96 in137.38 in12120 in12.81 ft
105 in147.50 in13130 in13.93 ft
108 in147.71 in13130 in14.08 ft
114 in157.60 in14140 in15.05 ft
120 in167.50 in15150 in16.01 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.

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.

ItemIRC requirement
Maximum riser height7 3/4 in
Minimum tread depth10 in
Variation within a flightNo more than 3/8 in between largest and smallest riser (same for treads)
Nosing3/4 to 1 1/4 in projection when treads are under 11 in deep
Headroom6 ft 8 in minimum
Stair width36 in minimum clear width
Handrail34 to 38 in high, on at least one side when there are 4 or more risers
GuardsRequired 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.

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.

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.

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.

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.