Free Calculator · Published November 2026
Stair Stringer Calculator for the Board
A stair stringer calculator divides total rise by the maximum riser and rounds up. Unit rise is total rise divided by that count. Treads are one fewer than risers. Stringer length is the square root of total rise squared plus total run squared. A nosing is not part of the run.
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The stringer is the long side of a right triangle. One leg is the total rise. The other leg is the total run. The board length is the square root of the sum of those squares.
7.75 and 10 are the 2021 excerpt limits, and you can change them. Nosing is not added to the run. Tread thickness of 1 inch is an example for the bottom drop, not a code figure.
14 risers at 7.714 in. 13 treads. Run 130.000 in. Stringer length 169.009 in (14.084 ft).
Angle 39.72 degrees. Bottom riser after the drop: 6.714 in.
- Unit rise is within 7.75 inches, the excerpt maximum.
- Unit run is at least 10 inches, the excerpt minimum.
- Width is at least 36 inches, the excerpt clear width above the handrail.
- Nosing meets the excerpt rule for this tread depth.
All calculations are estimates based on historical information and should be verified by the user.
Important: confirm the local stair rule
All calculations are estimates based on historical information and should be verified by the user. This tool is provided as a free service for planning purposes only and is not a substitute for a professional assessment, a supplier quote, or applicable local code requirements.
What This Stair Stringer Page Adds
The stair calculator lays out riser count, comfort checks, and a stringer length. This stair stringer calculator stays on the board: the square root, the bottom drop, and the nosing kept out of the run. Headroom of 6 feet 8 inches is a measurement from the nosing line. This page does not compute it from rise and run, because the floor opening is not in those two numbers.
Worked example
Total rise 108 inches. Maximum riser 7.75 inches. 108 ÷ 7.75 = 13.935, so the count rounds up to 14 risers. Unit rise is 108 ÷ 14 = 7.714 inches at three decimals. Treads are 13. At a 10 inch unit run the total run is 130 inches. Length is the square root of 108 squared plus 130 squared, which is 169.009 inches, or 14.084 feet, both at three decimals. The angle is 39.72 degrees at two decimals.
| Step | Figure |
|---|---|
| Risers | 14 |
| Unit rise at three decimals | 7.714 in |
| Treads | 13 |
| Total run | 130 in |
| Stringer length at three decimals | 169.009 in |
| Bottom riser after a 1 in example drop | 6.714 in |
The excerpt limits
The SMA visual interpretation of the 2021 IRC reprints excerpts with ICC permission. R311.7.5.1 says the riser height shall be not more than 7 3/4 inches, measured vertically between the leading edges of adjacent treads. The greatest riser in a flight shall not exceed the smallest by more than 3/8 inch. R311.7.5.2 says the tread depth shall be not less than 10 inches, with the same 3/8 inch limit. Equal risers from one division meet the variation rule by arithmetic. A finished floor that changes one end does not. Measure both floors before you cut.
R311.7.5.3 calls for a nosing not less than 3/4 inch and not more than 1 1/4 inches, and says a nosing is not required where the tread depth is not less than 11 inches. R311.7.1 says the clear width shall be not less than 36 inches above the handrail height. R311.7.2 says headroom shall be not less than 6 feet 8 inches. Spiral stairs point at R311.7.10.1. This page does not check them. South Carolina's adopted riser text, fetched the same day, allows 8 inches on masonry stairs. A local amendment can differ. The boxes start at the model excerpt so you can change them.
Level cut, plumb cut, and the drop
Each notch is a level cut of the unit run and a plumb cut of the unit rise. Those two cuts meet at a right angle. The nosing is extra tread past the level cut. Leave it out of the triangle.
After the notches are marked, many crews shorten the bottom plumb cut by the tread thickness. The top landing is already the finished floor, so the treads add thickness to every step except that top one. The example thickness is 1 inch. 7.714 minus 1 is 6.714 inches at three decimals. That trim does not shrink the stock you need. The board still has to cover 14.084 feet before you allow for a crooked end. This page does not add a fixed waste length.
How should you mark the stringer?
- Total rise, finished floor to finished floor, in inches.
- Riser count, and the unit rise to three decimals.
- Tread count, unit run, and total run. State that the nosing was left out.
- Stringer length from the square root, in inches and in feet.
- Tread thickness used for the bottom drop, or a note that the drop was 0.
- Which limit you checked, and that headroom was measured on site, not computed here.
Birdsmouth is the rafter word
A stair notch can look like a small seat, but the name birdsmouth belongs to the cut where a rafter sits on a wall plate. The level seat and the plumb heel of that cut are on the rafter calculator. Deck framing quantities stay on the deck cost calculator. This page does not price the lumber and does not say how many stringers a span needs. That spacing was not in the excerpt that was fetched.
Frequently Asked Questions
How does the stair stringer calculator get the length?
Divide total rise by the maximum riser and round up. That count is the number of risers. Unit rise is total rise divided by the count. Treads are one fewer than risers. Total run is treads times unit run. Stringer length is the square root of total rise squared plus total run squared. A 108 inch rise with a 7.75 inch maximum and a 10 inch unit run is 14 risers, a unit rise of 7.714 inches, 13 treads, a 130 inch run, and a length of 169.009 inches.
Does a nosing change the stair stringer length?
No. Unit run is the going from nosing to nosing, or the level cut on the stringer. The nosing sticks past that cut on the tread. It is not added to the run, and it is not added inside the square root.
What is the bottom drop on a stair stringer?
If the tread has thickness, the first riser would be tall by that thickness unless the bottom of the stringer is cut shorter by the tread thickness. The example uses 1 inch, which is an example thickness, not a code figure. The board you buy still has to cover the full square-root length.
Is a stair notch a birdsmouth?
The stair notch is a level tread cut and a plumb riser cut. They meet at a right angle. A birdsmouth is the rafter name for the level seat and the plumb cut that land on a wall plate. That cut is on the rafter calculator. This page does not compute a rafter seat.
Save the Stair Stringer Length
The rise, the run, the square-root length, and the drop belong on the cut list.
Get a Free DemoAll calculations are estimates based on historical information and should be verified by the user. This tool is provided as a free service for planning purposes only and is not a substitute for a professional assessment, a supplier quote, or applicable local code requirements.