Stair Stringer Calculator

How to Measure Total Stair Rise

The total rise is the vertical distance from the finished lower surface, where the bottom of the stair will stand, to the finished upper surface, such as the top of the deck boards or the finished floor. Everything else in the layout comes from this one number, so it is worth measuring carefully.

1. Lay a straight board or long level on the upper surface so it extends past the edge where the stairs will start.
2. Level it, then measure straight down from the underside of the board to the lower surface at the exact spot where the stair will land.
3. If the ground is sloped or uneven, measure where the foot of the stringers will actually bear, not at the nearest high or low point.
4. Measure to the finished surfaces. If the decking, pavers or flooring are not installed yet, add their thickness to the measurement.

Where a deck stair meets the ground, DCA 6 has its own bearing and footing requirements (its Figure 34). This calculator does not evaluate them. If your project will cover or change either surface later, recalculate with the final heights.

How to Calculate Stair Risers and Treads

Every stair calculator starts from the tallest riser you will accept. A stair riser calculator divides the total rise by it and rounds up, then divides the rise by that whole number so every riser is the same.

• Number of risers: N = ceiling(total rise ÷ maximum riser height)
• Riser height: R = total rise ÷ N
• Number of treads: N − 1
• Horizontal run: G = treads × tread depth

The tread count is one less than the riser count because the upper floor or deck is the last step. The top riser rises from the last tread to that surface, so a flight of six risers has five treads and a run of five tread depths, not six. This is the most common mistake, whether you use a stair tread calculator or work the numbers by hand.

Example: a 42 in rise with a 7¾ in maximum riser gives 42 ÷ 7.75 = 5.42, which rounds up to 6 risers of 42 ÷ 6 = 7 in each. With 10 in treads there are 5 treads and a run of 50 in.

The riser and tread limits are yours to choose and your local code to set. The IRC and DCA 6 (2015 edition) use a 7¾ in maximum riser, a 10 in minimum tread and no more than ⅜ in variation between risers or between treads in a flight. Some jurisdictions amend these figures. Because every riser here is calculated as the same height, the variation is zero by construction. Building the stair to match is up to you.

Stair landings are not part of this version of the calculator. If you are searching for a stair stringer calculator with a landing, note that a landing splits the stair into separate straight flights, and the landing itself needs its own framing. DCA 6 requires an intermediate landing when a deck stair's total rise is more than 12 ft.

How to Calculate Stair Stringer Length

The stringer layout length is the straight-line distance between two reference points:

• A, the lower reference point: the finished lower surface at the face of the first riser, taken as the origin (0, 0).
• B, the upper reference point: the finished upper surface at the face of the last riser, at (run, total rise).

Point B is the total rise above A and one run away horizontally, so the length is the hypotenuse of that triangle: L = √(total rise² + run²). For the example, L = √(42² + 50²) = √4264 = 65.299 in.

The run is treads × tread depth, not risers × tread depth. Using the riser count would add a tread that does not exist and overstate the length.

Line A to B is not parallel to the stair. Because the first tread is one riser above the lower surface, A to B is steeper than the line through the tread edges, which is the line that sets the stair angle. The results also show the length along that line from the front edge of the first tread to the front edge of the deck, which is treads × √(riser² + tread²), or 5 × √149 = 61.033 in in the example, so you can see both.

Layout length is not purchase length. Neither figure is the length of board to buy. The board has to contain the whole cut layout, including the plumb and level end cuts and the depth of the board itself, and how much extra that needs depends on how you lay out and cut it. The calculator does not invent an allowance. Lay the stair out full size on the board before cutting, and choose a standard length that holds it.

The stair stringer angle is the angle of the line through the tread edges: arctangent(riser height ÷ tread depth). In the example, arctangent(7 ÷ 10) = 34.99°.

Stair Stringer Throat Depth Explained

A cut stringer is a board with notches cut into its top edge. The throat is the smallest amount of board left under a notch, measured at right angles to the underside of the stringer. It is found by subtracting the notch depth, measured the same way, from the actual depth of the board:

throat = actual board depth − (unit rise × unit run ÷ √(unit rise² + unit run²))

Use the actual dressed size of the lumber. A nominal 2×12 is about 11¼ in deep, not 12, so a 2×12 stair stringer calculator that used 12 in would overstate the throat by ¾ in.

For a 7 in rise and 10 in run the notch depth is 7 × 10 ÷ √149 = 5.735 in. The table shows the throat that leaves for each board size:

DCA 6 shows a 5 in minimum throat for cut stringers (its Figure 28), and the calculator warns when your result is below that. Passing the throat check does not show that a stringer is strong enough, because strength also depends on the lumber species and grade, the span, the loads and the connections. A solid stringer is not notched, so no throat applies to it.

How to Use a Framing Square

A framing square marks the notches. The two numbers it needs are the unit rise (your riser height) and the unit run (your tread depth).

1. Read the unit rise and unit run from the results. In the example they are 7 in and 10 in.
2. Hold the square with the unit rise on the tongue and the unit run on the blade both touching the edge of the board. Stair gauges or clamps fixed at those two marks make it repeatable.
3. Trace the rise and the run, slide the square along so the rise mark meets the end of the line you just drew, and repeat for each step.
4. For a cut stringer whose treads sit on the notches, lay out the first notch one tread thickness lower, so the first walking surface is still one riser above the lower surface. The bottom riser adjustment in the results is that thickness, and the first riser as cut is the riser height minus it.

The calculator shows the unit rise to three decimals and to the nearest sixteenth, because a square is marked in sixteenths. Rounding adds up. For a 96 in rise the riser is 7.385 in, about 7⅜ in on the square. Thirteen risers of exactly 7⅜ in would total 95.875 in, ⅛ in short, so check the total as you step off the board and use the decimal figure with a tape where you can.

Sequences differ between builders. The calculator documents one arrangement (shown in the diagram) and does not decide how the top of the stringer connects to your deck framing, which depends on the framing and the decking thickness.

Cut Stringers vs Solid Stringers

DCA 6 asks for a minimum 2×12 for all stair stringers, and gives minimum tread sizes for cut and solid stringers in its Table 6. These are the guide's figures for its own scope, residential wood decks, and are not a design for your project.

The span is measured horizontally. The calculator compares your run with the DCA 6 span for the stringer type you choose and warns when it is longer. A longer span needs intermediate support, which this calculator does not design.

How Many Stair Stringers Do You Need?

The calculator spaces stringers evenly, from the center of the stringer at one edge to the center of the stringer at the other, with no gap wider than the maximum spacing you enter. It assumes the outer stringers sit flush with the edges of the stair, so the centerline span is the stair width minus one stringer thickness (1½ in for 2× lumber):

stringers = ceiling((stair width − stringer thickness) ÷ maximum spacing) + 1

A 36 in wide stair at 18 in spacing has a centerline span of 34.5 in, which needs two gaps and so three stringers, 17.25 in apart, with the outer ones centered ¾ in from each edge. A 48 in stair gets four stringers (15.5 in apart), a 60 in stair five (14.625 in) and a 72 in stair five (17.625 in). This matches the DCA 6 statement that a stair with only cut stringers needs a minimum of three. For stairs wider than 36 in, DCA 6 allows a combination of cut and solid stringers at no more than 18 in on center, so the calculator compares a solid-stringer spacing on a wider stair with 18 in, not 36 in. What the treads are made of also matters, so check the tread span against DCA 6 Figure 29 and Table 6.

This is a quantity estimate from geometry and a spacing you choose. It is not a structural design, and it does not show that the number of stringers is adequate for any lumber, load or jurisdiction.

Residential Stair Dimensions and Code References

The reference profile in this deck stair stringer calculator uses figures from the American Wood Council's Prescriptive Residential Wood Deck Construction Guide (DCA 6, 2015 edition, based on the 2015 International Residential Code). It is a 2015 guide. It is not the code in force where you live, which may be a newer edition of the IRC and may be amended locally, and the guide itself says that building to it does not assure that the requirements of any particular jurisdiction are met.

Its scope is narrow. DCA 6 applies to single-level residential wood decks attached to the house, and it excludes, for example, decks carrying hot tubs or other large concentrated loads and decks with snow loads above 40 psf. Its stair details are for stairs serving such decks. They are not rules for interior stairs, other buildings, or commercial or workplace stairs, which follow different requirements that this calculator does not cover. Local codes vary and are often amended, so check yours.

The guide brackets the IRC sections it restates, says that provisions not found in the IRC are recommended good practice, and says that where it differs from the IRC, the IRC applies. In the table, the riser, tread, nosing and width figures correspond to IRC R311.7. The stringer size, throat, span, spacing and landing figures are DCA 6's own prescriptive details and the guide gives them without an IRC section reference, so do not treat them as IRC requirements.

Showing a value as within one of these figures is not a statement that your stair meets code, and showing it outside is not a ruling that it does not. The calculator does not check handrails, guards, lighting, footings, connections, lumber grade or loads. For measurements and unit conversions while you plan, the Length Converter covers feet, inches, millimeters and centimeters.

Frequently Asked Questions

Sources

• Prescriptive Residential Wood Deck Construction Guide (DCA 6, 2015 edition), American Wood Council: stair requirements, Figures 27 to 34 and Table 6. Check awc.org for any newer edition.
• International Residential Code, section R311.7 (stairways), International Code Council. Editions and local amendments vary.
• American Softwood Lumber Standard, PS 20: dressed sizes of dimension lumber. Actual sizes vary with the product, so measure your boards.