Stair Stringer Calculator: Exact Rise, Run, Throat Depth, and Stringer Cuts

Q: Why do I have to cut the bottom of the stringer shorter than the rest?

When you install a tread at the base of a staircase, that tread adds its own thickness to the floor. Without adjustment, the first step would be higher than all the others by exactly one tread thickness. To compensate, you trim the bottom riser cut shorter by the tread thickness. This is called dropping the stringer, and the result is that every finished step is exactly the same height.

Q: How many stringers do I need for my staircase width?

As a general rule, you need one stringer for every 16 inches of staircase width, with a minimum of two stringers (one on each side). A 36-inch wide staircase typically uses three stringers: two on the outside edges and one in the middle. Always check your local building code for exact requirements.

Q: What happens if my throat depth is too small?

The throat depth is the remaining wood below each step notch, measured perpendicular to the bottom edge of the stringer. If throat depth falls below 3.5 inches, the stringer is considered structurally unsafe and may crack or fail under load. Most building codes require a minimum of 3.5 inches. If your stringer is too narrow, switch to a wider board (2x14), reduce the rise height, or increase the run.

Stair Stringer Calculator

Compute Your Stringer Cuts

All results update in real time as you type. No button needed.

Units:

Total Rise - floor to floor height

Tread Thickness - board thickness

Target Step Dimensions

Enter a total rise above to see your stringer calculations.

Exact Step Dimensions (Lay Out Each Notch to These)

-- Rise x -- Run

Total Run

horizontal span

Risers / Treads

steps total

Bottom Riser Cut

dropped stringer

Raw Stringer Length

diagonal board length needed

Lumber to Buy

includes 15% buffer

Throat Depth (2x12 Stringer, 11.25" actual) -- --

0" 3.5" min 10"

Structural Warning: This throat depth is below the 3.5" code minimum. The stringer may fail under load. Use a 2x14 board, reduce the rise, or increase the run.

Key Terms Explained

Stringer The diagonal structural board (usually a 2x12) that runs from the lower floor to the upper floor and supports all the treads and risers. Most staircases use two or three stringers.

Rise The vertical height of a single step. The "total rise" is the full floor-to-floor height. Each individual unit rise is the total rise divided evenly by the number of risers.

Run The horizontal depth of a single step, measured from the nosing of one tread to the nosing of the next. Also called the tread run. This does not include the nosing overhang itself.

Tread The horizontal board you step on. For exterior and deck stairs, 5/4 deck boards (actual 1" thick) are most common. Interior stairs typically use 1-inch nominal boards (actual 3/4").

Riser Board The vertical board that closes the face of each step. Not all staircases have riser boards - open-riser designs skip them - but the riser height is still a critical layout dimension regardless.

Throat Depth The minimum remaining depth of material in a cut stringer, measured perpendicular from the inside corner of a step notch to the bottom edge of the board. Building codes require at least 3.5 inches.

Dropping the Stringer Trimming the bottom riser cut shorter by exactly one tread thickness so that all finished steps are equal in height. Without this adjustment, the bottom step would be taller than every other step by one board thickness.

Headroom The clear vertical distance between any stair tread and the ceiling, soffit, or framing directly above it. Most building codes require a minimum of 80 inches (6 ft 8 in) of headroom along the full stair run.

The Complete Guide to Cutting Stair Stringers

Building a staircase that is safe, comfortable, and code-compliant starts with getting the stringer math right before you make a single saw cut. This guide walks through every number this calculator produces, explains the carpentry logic behind each one, and answers the questions that come up most often on the job site.

How to Use This Calculator

Start by measuring the total rise - the vertical distance from the finished floor below to the finished floor above. Enter that number in the "Total Rise" field. Then select your tread thickness (5/4 deck boards are 1 inch actual; standard interior treads are 3/4 inch). Finally, choose a step dimension preset or enter a custom target rise and run. Every result updates instantly as you type.

The "Exact Step Rise" and "Exact Step Run" are the two numbers you will transfer to your speed square or rafter square when laying out cuts on the stringer board. All other outputs flow from those two dimensions.

Why the Rise and Run Are Never Round Numbers

You choose a target rise and run, but the calculator divides your actual floor-to-floor height by the number of risers and gives you the precise rise per step. If your total rise is 109 inches and your target is 7.5 inches per step, you get 14.53 risers, which rounds to 15. Divided evenly, each step is exactly 7.267 inches - not 7.5. The run stays at your target (10 or 11 inches, or whatever you entered), so only the rise gets adjusted. This is normal and expected: every step must be identical, and the total rise must add up perfectly.

Understanding the Dropped Stringer

When you place the first tread on the ground at the base of the staircase, that tread raises the first "landing" surface by one tread thickness. If you did nothing about this, the first step up would be shorter than all the others by exactly one tread thickness - a tripping hazard and a code violation. The fix is simple: cut the very bottom riser (the first notch at the base of the stringer) shorter by that same tread thickness. All higher steps stay at the full unit rise. The "Bottom Riser Cut" output above is the dimension you use for that first cut only.

How Throat Depth Is Calculated

Every notch you cut into the stringer removes material. The throat depth is the closest point between the inside corner of a step notch and the bottom edge of the stringer board, measured perpendicular to the board's long axis. For a 2x12 stringer (actual width 11.25 inches) with a given rise and run, the formula is: Throat = (Rise x Run) / square root of (Rise squared + Run squared). A shallower staircase pitch - wide treads and small risers - actually produces a smaller throat depth than a steep pitch, which surprises most people. If your throat depth falls below 3.5 inches, the stringer will likely split or crack under load. Switch to a 2x14 board, which gives you an extra two inches of depth to work with.

How to Figure Out How Many Stringers You Need

The number of stringers required depends on the total width of your staircase. As a practical rule, place one stringer per 16 inches of width, with no fewer than two (one on each side). A standard 36-inch exterior deck stair uses three stringers: two on the outside edges and one centered. Always verify against your local residential building code - some jurisdictions require closer spacing, particularly for stairs over a certain total height or that serve a primary egress path.

Stringer Length and What Lumber to Buy

The raw stringer length is the hypotenuse of the right triangle formed by the total rise and total run - calculated with the Pythagorean theorem. To this number the calculator adds a 15% buffer to account for the plumb cut at the top and the seat cut at the bottom, which eat into the board length. The "Lumber to Buy" output rounds up to the next standard framing lumber length (8, 10, 12, 14, 16, or 18 feet) so you can go straight to the lumber yard. For a typical single-story deck stair, a 12-foot 2x12 is usually sufficient for each stringer.

Frequently Asked Questions

What is the 7-11 rule in stair building?

The 7-11 rule is a carpenter's guideline stating that a comfortable stair step has a riser height of approximately 7 inches and a tread run of approximately 11 inches. The broader principle is that one rise plus one run should add up to between 17 and 18 inches for a natural, comfortable gait. At 7 + 11 = 18, the deck/exterior preset in this calculator hits right at the upper end of that range. Residential interior stairs are often built to the "7.5 + 10 = 17.5" ratio instead. Both are code-compliant in most jurisdictions, but check your local requirements for the exact allowable rise and run limits.

Why do I have to cut the bottom of the stringer shorter than the rest?

When you install the bottom tread board on the ground floor, that board adds its own thickness to the floor surface. If you did not adjust for this, the very first step up from the floor would be taller than every other step by one tread thickness - a significant and dangerous height discrepancy. The fix is called "dropping the stringer." You trim the bottom riser notch shorter by exactly the tread thickness (1 inch for 5/4 deck boards, 3/4 inch for standard interior lumber). Every other step on the stringer stays at the full unit rise. The result: once the treads are installed, every finished step is exactly the same height from bottom to top.

How many stringers do I need for my staircase width?

The standard rule is one stringer per 16 inches of staircase width, with a minimum of two stringers regardless of width. So a 36-inch wide stair needs three stringers (two sides plus one center), and a 48-inch wide stair needs three to four. Always place a stringer on each outside edge of the stair. For interior staircases over a certain width, some codes require the center stringer to be a solid-sawn piece rather than a cut stringer - check your local residential building code. For deck stairs, the International Residential Code (IRC) requires that treads have no more than 18 inches of unsupported span between stringers.

What happens if my throat depth is too small?

The throat depth is the minimum remaining wood left in the stringer after cutting the step notches. When that depth drops below 3.5 inches, the stringer has too little material to safely carry the load of people walking on the stairs. A stringer with inadequate throat depth can crack at the notch corners or split along the grain under repeated loading - often without warning. Building codes (including the IRC) set 3.5 inches as the minimum. If your calculation shows a warning, your options are: switch to a wider board (a 2x14 gives you 13.25 inches of actual width instead of 11.25), reduce the unit rise height to lower the pitch, increase the unit run to steepen the pitch angle (counterintuitive but effective), or use a structural metal stringer instead of a cut wood stringer.

Estimating tool only. All outputs are calculated from the dimensions you enter and are intended to assist planning. Always verify your final cuts against your actual site measurements. Stair construction must comply with local building codes. Consult a licensed contractor or building inspector before framing structural staircases.