Stair Stringer Calculator

Sizing and cutting stair stringers requires calculating both the geometric hypotenuse of the stair flight and the additional board length needed for t

Construction

Total Vertical Rise

Finished floor-to-floor vertical distance

Tread Depth (Unit Run)

Horizontal depth per cutout on the stringer (excluding nosing)

Target Maximum Riser

Maximum allowed riser height to determine step count

Stair Width

Total staircase width across stringers

Plumb & Seat Cut Board Allowance

Extra board length needed for top plumb cut and bottom landing seat cut

Stringer Spacing (On-Center)

Maximum spacing between stringers (16" standard for wood; 12" for composite)

Formula & Methodology

Net Hypotenuse = √(Total Rise² + Total Run²) Required Board Length = Net Hypotenuse + Plumb/Seat Cut Allowance Commercial Board Size = Next Even Foot Length (Ceiling in 2-ft increments) Number of Stringers = Ceiling(Stair Width ÷ Spacing Limit) + 1

The net stringer travel length is calculated using the Pythagorean theorem from total rise and total run. However, carpenters must make an angled plumb cut at the upper floor header and a horizontal seat cut at the bottom landing, consuming 8 to 14 inches of timber. Adding this cut allowance yields total board length, which is rounded up to commercial 2-foot increments (e.g. 14', 16'). Stringer count is determined by dividing stair width by on-center spacing limits (typically 16 inches for wood treads, 12 inches for composite).

Stringer Board Length Specification

169" Net (16-ft Boards Needed) stringer

Overview

Sizing and cutting stair stringers requires calculating both the geometric hypotenuse of the stair flight and the additional board length needed for top plumb cuts and bottom seat cuts. Ordering lumber boards based solely on the bare diagonal hypotenuse invariably results in stringers that are too short to securely mount to floor joist headers.

Estimates and calculations are for preliminary planning and layout purposes only. This calculator does not provide structural engineering, load design, or official building code compliance certification. Stair dimensions, maximum riser heights, minimum tread depths, handrail requirements, and minimum vertical headroom clearances are strictly governed by local building codes and municipal ordinances. Always verify measurements with a local building inspector or licensed general contractor before cutting stringers or beginning construction.

Worked Examples

Example 1: 108" Total Rise with 130" Run (Check Case)

Inputs: Total Rise = 108 in, Tread Depth = 10 in (Run = 130 in), Width = 36 in, Cut Allowance = 12 in, Spacing = 16 in

Calculate net hypotenuse: √(108² + 130²) = √(11,664 + 16,900) = √28,564 ≈ 169.01 in (14.08 ft).
Add 12" cut allowance: 169.01 + 12.0 = 181.01 in (15.08 ft).
Determine commercial lumber board: 15.08 ft requires a standard 16-foot board.
Calculate stringer count: Ceiling(36 ÷ 16) + 1 = 3 + 1 = 4 stringers (spaced at 12" on-center to keep within 16" limit).

Final Answer: 169.0" net hypotenuse (16-foot boards required; 4 stringers for 36" width at 16" max spacing)

Example 2: Wide Deck Stair (48" Width with 12" Composite Spacing)

Inputs: Total Rise = 48 in, Run = 60 in, Width = 48 in, Cut Allowance = 12 in, Spacing = 12 in

Net hypotenuse: √(48² + 60²) = √(2,304 + 3,600) = √5,904 ≈ 76.84 in (6.40 ft).
Board length needed: 76.84 + 12 = 88.84 in (7.40 ft) → 8-foot board.
Stringer count: Ceiling(48 ÷ 12) + 1 = 4 + 1 = 5 stringers.

Final Answer: 76.8" net hypotenuse (8-foot boards; 5 stringers for composite deck)

Example 3: Basement Flight (96" Rise with 120" Run)

Inputs: Total Rise = 96 in, Run = 120 in, Width = 36 in, Cut Allowance = 12 in, Spacing = 16 in

Net hypotenuse: √(96² + 120²) = √(9,216 + 14,400) = √23,616 ≈ 153.67 in (12.81 ft).
Board length: 153.67 + 12 = 165.67 in (13.81 ft) → 14-foot board.
Stringers needed: 3 stringers.

Final Answer: 153.7" net hypotenuse (14-foot boards; 3 stringers)

Reference Table

Total Rise	Total Run	Net Hypotenuse	Board Req (+12" Allowance)	Commercial Lumber Board
72 in	90 in	115.3 in (9.6 ft)	127.3 in (10.6 ft)	12-foot board
84 in	100 in	130.6 in (10.9 ft)	142.6 in (11.9 ft)	12-foot board
96 in	120 in	153.7 in (12.8 ft)	165.7 in (13.8 ft)	14-foot board
108 in	130 in	169.0 in (14.1 ft)	181.0 in (15.1 ft)	16-foot board
114 in	140 in	180.5 in (15.0 ft)	192.5 in (16.0 ft)	16-foot board
120 in	150 in	192.1 in (16.0 ft)	204.1 in (17.0 ft)	18-foot board

Frequently Asked Questions

Why does the stringer lumber board need to be longer than the hypotenuse?

The diagonal hypotenuse measures strictly from the tip of the bottom step to the tip of the top step. When cutting timber stringers, the top must be cut vertically (plumb cut) to mount to the header joist, and the bottom must be notched horizontally (seat cut) to rest on the landing pad, consuming 8 to 14 inches of extra lumber.

How many stringers are required for a 36-inch wide staircase?

Standard residential wooden stairs require a minimum of 3 stringers for a 36-inch wide flight (one on each side plus one center support stringer, spaced roughly 16 to 18 inches on-center). Composite decking treads are more flexible and require stringers spaced at 12 inches on-center (4 stringers for 36 inches).

What is the "bottom riser deduction" during stringer installation?

When cutting the bottom seat cut of a stringer, the carpenter must slice off the exact thickness of one tread board from the bottom riser. If this deduction is forgotten, adding the tread board later makes the bottom step too tall by the thickness of the tread.

What lumber size is commonly used for cutting stringers?

Stringers are traditionally cut from wide dimension lumber to ensure at least 3.5 to 5 inches of solid wood (throat depth) remains uncut behind the notches. Consult an engineer or local code for minimum allowable throat depth.

What is the difference between cut stringers and closed stringers?

A cut (open) stringer has sawtooth notches where treads rest on horizontal cuts. A closed (routed) stringer has full flat edges with internal routed grooves into which the treads and risers slide.