Deck Stair Stringer Calculator
Calculate unit rise, tread count, total run, and stringer length for a deck stair from total rise and riser count.
Stringer length
89.64 in
227.7 cm
What is a stair stringer?
A stair stringer is the inclined board or beam, typically a 2x12, that runs from the bottom landing to the deck frame and supports the treads. The stringer must be long enough to span the diagonal from the bottom of the stair to the top, and it must be laid out so the notches for treads and risers are evenly spaced and code-compliant.
Stringer geometry flows from two inputs: total rise and riser count. Total rise is the vertical distance from the lower finished surface to the upper finished surface of the deck. Dividing total rise by the number of risers gives the unit rise per step, which must fall within the code limit (7-3/4 inches maximum under the IRC). The number of treads is always one fewer than the number of risers: the deck surface itself serves as the top landing.
Stringer length is the hypotenuse of the right triangle formed by total rise and total run. Total run equals the number of treads multiplied by the tread depth. These two dimensions determine the length of stock you need and the saw angles for the cuts at top and bottom.
How to calculate stair stringer length
Formula
stringer length = sqrt(total run^2 + total rise^2)
How the formula works
Unit rise = total rise / number of risers. Number of treads = number of risers - 1. Total run = number of treads x tread depth. Stringer length = sqrt(total run^2 + total rise^2). This is the Pythagorean theorem applied to the stair triangle: the stringer is the hypotenuse, total run is the horizontal leg, and total rise is the vertical leg.
Risers and treads
There is always one more riser than there are treads. Each riser is a vertical face; each tread is a horizontal surface you step on. The lowest riser lifts from the bottom landing; the highest riser lifts to the deck surface, which itself is the top landing. Counting up: if you take 8 riser steps, you walk across 7 treads before arriving at the deck.
Adding stock length for cuts
The stringer length from this formula is the diagonal span from bottom corner to top corner of the stair opening. In practice, you need additional length for the plumb cut at the top (where the stringer attaches to the deck rim), the level cut at the bottom (where the stringer rests on the footing or concrete pad), and any overhang. Add 6 to 12 inches to the calculated length before selecting stock.
Code limits
IRC Section R311.7 limits unit rise to 7-3/4 inches maximum and tread depth to 10 inches minimum. If the unit rise from this calculator exceeds 7-3/4 inches, add a riser until it falls within the limit. Verify with your local building department; local amendments to the IRC may impose stricter limits.
Rounding
Results are shown to two decimal places. Stringer lengths are typically rounded up to the nearest inch when selecting lumber.
Example
- 1Unit rise56 / 8 = 7 in per riser
- 2Treads (risers minus 1)8 - 1 = 7 treads
- 3Total run7 x 10 = 70 in
- 4Stringer lengthsqrt(70^2 + 56^2) = sqrt(4900 + 3136) = sqrt(8036) = 89.64 in
FAQ
Why are there one fewer treads than risers?
Each tread is a horizontal landing between two risers. The first riser lifts you from the lower floor to the first tread. The last riser lifts you to the upper floor, which itself is the landing. So a stair with 8 risers has 7 intermediate treads and lands on the deck surface as the eighth step. This is sometimes called the 'one-less rule' in stair layout.
What are the IRC code limits for rise and run?
The International Residential Code (IRC) Section R311.7 limits the maximum unit rise to 7-3/4 inches and the minimum tread depth to 10 inches. The sum of two risers plus one tread (the 2R+T rule) should fall between 24 and 25 inches for comfortable stairs. Local jurisdictions may adopt modified versions of the IRC; verify with your local building department before building. This calculator does not validate code compliance.
How do I use the stringer length?
The stringer length is the diagonal hypotenuse from the bottom of the stringer at grade to the top of the stringer where it connects to the deck frame. This is the minimum length of lumber you need to cut the stringer from. Add several inches for the plumb cut at the top and the level cut at the bottom, and for any overhang at the footings. Most residential deck stringers are cut from 2x12 lumber.
What if the rise doesn't divide evenly?
If the total rise divided by the number of risers does not produce a whole number, that is normal. The IRC allows the largest and smallest risers to differ by no more than 3/8 inch. If you are planning a stair and have flexibility in riser count, try incrementing or decrementing by one riser to find a cleaner unit rise. The calculator shows the exact division; you adjust the number of risers until you get a comfortable result.
Sources
1. International Residential Code (IRC), Section R311.7 Stairways
International Code Council
R311.7 specifies maximum riser height (7-3/4 in), minimum tread depth (10 in), and other dimensional requirements for residential stairways. Local jurisdictions adopt and amend the IRC; verify with your local building department.
https://codes.iccsafe.org/content/IRC2021P1/chapter-3-building-planning2. Prescriptive Residential Wood Deck Construction Guide (DCA 6-23)
American Wood Council
AWC DCA 6 section on stair framing covers stringer sizing, attachment to deck framing, and riser/tread requirements for residential deck stairs.
https://www.awc.org/publications/dca6/
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