Stair Stringer Calculator

How Stair Layout Works

Every stair starts with one fixed number: the total rise, measured from the finished floor at the bottom to the finished floor at the top. Divide it by the tallest riser you will allow, round up to a whole number of risers, and divide the total rise by that count. That gives a riser height that is the same for every step.

A stair always has one fewer tread than risers, because the upper floor acts as the last tread. Multiply the treads by the tread depth (the unit run) to get the total run, the floor space the stair takes up. The stringer is the diagonal of that rise and run.

Rounding the riser count down instead of up is the classic mistake. It gives fewer, taller risers that can exceed the code maximum.

IRC Stair Requirements

Most U.S. homes are built under the International Residential Code (IRC), Section R311.7. Many states and cities amend these numbers, so check the code your jurisdiction adopted.

• Riser height: 7-3/4" maximum (R311.7.5.1).
• Tread depth: 10" minimum, measured nosing to nosing (R311.7.5.2).
• Uniformity: the largest riser or tread in a flight can exceed the smallest by no more than 3/8".
• Nosing: 3/4" to 1-1/4" on stairs with solid risers, not required when treads are at least 11" deep (R311.7.5.3).
• Headroom: 6' 8" minimum, measured from the sloped line of the nosings (R311.7.2).
• Width: 36" minimum. Landings: at least 36" in the direction of travel.
• Rise per flight: 151" maximum between floors or landings (R311.7.3).
• Handrail: required on stairs with four or more risers, 34" to 38" above the nosings (R311.7.8).

Stair Formulas

All measurements are in inches. The throat is the uncut wood left between the inside corner of each notch and the bottom edge of the stringer.

N

Number of risers

R

Riser height (unit rise)

T

Tread depth (unit run)

D

Stringer board depth (11-1/4" for a 2x12)

L

Stringer length along the slope

A common comfort check is rise + run between 17" and 18". A 7-3/4" riser with a 10" tread is 17-3/4".

Worked Example: 9-Foot Basement Stair

Total rise is 108" (9 ft) from the basement slab to the finished floor above. Treads are 10" deep and 1" thick.

1. 108 ÷ 7.75 = 13.94, rounded up to 14 risers.
2. Riser height: 108 ÷ 14 = 7.714", or 7-11/16".
3. Treads: 13. Total run: 13 × 10 = 130" (10' 10").
4. Stringer length: √(108² + 130²) = 169.0" (14' 1"), so buy 16 ft stock.
5. Throat on a 2x12: 11.25 − 7.714 × 10 ÷ 12.63 = 5-1/8".
6. Bottom riser cut: 7.714 − 1 = 6-11/16".

Result: 14 risers at 7-11/16" and 13 treads at 10", with 10' 10" of run. Leave at least 36" of clear landing at the bottom.

Worked Example: Short Stair, 30-1/2" Rise

A short run between two floor levels, 30-1/2" finished floor to finished floor, with 10" treads.

1. 30.5 ÷ 7.75 = 3.94, rounded up to 4 risers.
2. Riser height: 30.5 ÷ 4 = 7-5/8".
3. Treads: 3. Total run: 3 × 10 = 30".
4. Comfort check: 7-5/8 + 10 = 17-5/8".

Result: 4 risers at 7-5/8" and 3 treads, matching the worked example in JLC’s stringer layout guide. With four risers, it needs a handrail.

Worked Example: Deck Stairs, 40" Rise

A deck surface 40" above the landing pad, with 11" treads made from two deck boards and 2x12 cut stringers.

1. 40 ÷ 7.75 = 5.16, rounded up to 6 risers at 6-11/16".
2. Treads: 5. Total run: 5 × 11 = 55" (4' 7").
3. Stringer length: √(40² + 55²) = 68.0" (5' 8").
4. Throat: 5-9/16", more than a steeper 7-3/4" by 10" stair leaves.

Result: 6 risers at 6-11/16" over 4' 7" of run. AWC’s DCA 6 deck guide calls for 2x12 stringers and at least three cut stringers on a 36" stair, with stringers no more than 18" apart on wider stairs.

Stair Riser Chart by Total Rise

Risers needed at the IRC maximum of 7-3/4", with the total run at 10" treads.

Field Tips

Practical advice from JLC, Fine Homebuilding, This Old House and the American Wood Council.

1. 1

   Measure rise where the stair lands

   Don’t measure straight down from the top. Level out from the upper floor to where the bottom step will land, then adjust for flooring: subtract finish flooring that will go down at the bottom and add flooring that will go on at the top.

2. 2

   Drop the stringer for the tread

   The first tread adds its thickness to the bottom step, so cut the bottom riser that much shorter. If flooring goes in around the stringer later, add its thickness back: 1-1/4" treads over 3/4" flooring drop the stringer 1/2".

3. 3

   Cut one, test it, then copy it

   Lay out the first stringer on the straightest 2x12 you have, crown up toward the notches. Set it in place and check the steps with a level before using it as a pattern for the rest.

4. 4

   Don’t overcut the notches

   Stop the circular saw short of the inside corner and finish with a handsaw or reciprocating saw. An overcut at the corner weakens the stringer right where the throat is thinnest.

5. 5

   Keep the throat thick enough

   AWC’s deck guide sizes cut 2x12 stringers assuming about 5.1" of remaining wood, the throat a 7-3/4" by 10" step leaves. Steeper steps, smaller lumber or overcut notches leave less, so add stringers or support.

Sources: JLC: Stair stringers, calculation and layout, Fine Homebuilding: Laying out basic stair stringers, Fine Homebuilding: How to cut stair stringers, This Old House: Cutting stair stringers, American Wood Council: DCA 6 deck construction guide