A stair stringer calculator finds the stringer length, throat depth and material for a notched stair stringer. Enter the total rise, riser height, tread run and board size, and the tool computes the cut geometry. A 108-inch rise with 7.2-inch risers and 10.5-inch run on a 2×12 gives a 5.31-inch throat and 182-inch stringer.
Lumber, Framing and Carpentry
Vertical distance from the top of the lower finished floor to the top of the upper finished floor.
The height of each riser. IRC max is 7.75 inches. If you have not calculated this yet, use the stair calculator first.
The horizontal depth of each tread from nosing to nosing. IRC min is 10 inches.
Three stringers is standard for a 36-inch stair. Add a fourth for wider stairs or heavy loads.
Cost per linear foot of stringer stock. Leave blank to skip the cost estimate.
Stringer summary
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How to Use the Stair Stringer Calculator
- Enter the total rise from finished floor to finished floor in inches.
- Enter the unit rise (riser height) and unit run (tread depth) from your stair layout.
- Select the stringer board size (2×12 is standard).
- Enter the number of stringers (3 is typical for a 36-inch stair).
- Optionally enter a price per linear foot for a cost estimate.
- Read the stringer length, throat depth, adequacy check and total material.
Here is what each result line means:
| Result | What it means |
|---|---|
| Stringer length | The hypotenuse length of the stringer from bottom to top cut. |
| Throat depth | The narrowest remaining board width after the notch, measured perpendicular to the board edge. |
| Throat adequacy | Whether the throat is structurally adequate, marginal or inadequate. |
| Total linear feet | Total stringer stock needed, based on the count and length. |
| Estimated cost | Material cost if a price per linear foot is entered. |
For riser and tread layout, see the stair calculator.
What Is a Stair Stringer Calculator?
A stair stringer calculator computes the length, throat depth and material quantity for notched (cut) stair stringers. It takes the unit rise, unit run and board width, and returns the cut geometry that a framer needs to lay out and cut the stringers.
Framers, carpenters and DIY builders use it to confirm that the stringer stock is large enough for the rise and run, and to estimate how much lumber to order.
How the Stair Stringer Calculator Works
The stringer length is the hypotenuse of the stair triangle. The throat depth is the remaining board width after the triangular notch is cut, measured perpendicular to the long edge of the board.
- Round the total rise by the unit rise to get the number of risers; compute the actual riser.
- Multiply treads (risers minus 1) by the unit run to get the total run.
- Compute the stringer length as the hypotenuse of the total rise and total run.
- Compute the throat depth from the board width, actual riser and unit run.
- Multiply the stringer length by the count for total material.
Stair Stringer Worked Example
You have a floor-to-floor rise of 108 inches, a unit rise of 7.2 inches, a unit run of 10.5 inches, and plan to use three 2x12 stringers.
Result: The calculator gives 15 risers at 7.20 inches each. The total run is 14 treads at 10.5 inches = 147 inches. The stringer length is the square root of 108 squared plus 147 squared = 182.4 inches (15.2 feet). The throat depth is 11.25 minus (7.2 times 10.5) divided by the square root of (7.2 squared + 10.5 squared) = 11.25 minus 5.94 = 5.31 inches, which is adequate.
Factors That Affect Stringer Sizing
Riser Height
A taller riser cuts a deeper notch, reducing the throat depth. Going from a 7-inch to a 7.75-inch riser can reduce the throat by half an inch on a 2×12.
Tread Run
A longer tread run also increases the notch depth. The notch is a right triangle of rise by run, and the perpendicular depth to the hypotenuse determines how much board is removed.
Board Size
A 2×12 (11.25 in actual) is standard. A 2×10 (9.25 in) works for shallow stairs but leaves a thinner throat. Some builders use engineered lumber for long flights.
Number of Stringers
Three stringers across a 36-inch stair is typical. Wider stairs or heavy loads may need four. Each stringer shares the load equally if the treads and risers are stiff enough to distribute it.
Flight Length
Longer flights put more bending stress on the stringer. A STRUCTURE Magazine analysis found that a 15-riser 2×12 flight at 7.25-inch rise and 10.5-inch run can exceed deflection limits.
Stringer Cost Comparison
Material cost comparison for different stringer configurations on a 108-inch rise, 10.5-inch run stair.
| Board | Stringers | Length each | Total LF | Throat |
|---|---|---|---|---|
| 2×12 | 3 | 15.2 ft | 45.6 lf | 5.31 in |
| 2×12 | 4 | 15.2 ft | 60.8 lf | 5.31 in |
| 2×10 | 3 | 15.2 ft | 45.6 lf | 3.31 in |
A 2×10 stringer on this stair has only a 3.31-inch throat, which is marginal. A 2×12 at 5.31 inches is the safer choice.
When to Use a Stair Stringer Calculator
Ordering Stringer Lumber
Find the stringer length and multiply by the count to know how many board feet or linear feet to order.
Checking Board Adequacy
Confirm that a 2×12 leaves enough throat for your rise and run before cutting. A thin throat can deflect and crack under load.
Comparing 2×10 vs 2×12
See whether a 2×10 provides enough throat, or whether you need to step up to a 2×12 or sister a 2×6 to the stringer.
Estimating Project Cost
Enter the price per linear foot to get a quick cost estimate for the stringer stock.
Common Stringer Calculation Mistakes
1. Overcutting the Notch
Cutting past the intersection of the rise and run lines weakens the stringer. Drill a 1/4-inch relief hole at the notch corner and cut to it.
2. Using a 2×10 on a Tall Riser
A 7.5-inch riser with a 10.5-inch run leaves only about 3.3 inches of throat on a 2×10, which is structurally marginal.
3. Forgetting to Account for the Top and Bottom Cuts
The stringer needs extra length for the seat cut at the bottom and the connection at the top. Add a few inches to the calculated length when ordering.
4. Assuming Two Stringers Are Enough
Three stringers is the standard minimum for cut stringers on a 36-inch stair. Two stringers leave the middle of each tread unsupported.
5. Ignoring Deflection on Long Flights
A long stringer can deflect under load even with adequate throat. Have an engineer check flights longer than 12 feet.
Accuracy and Limitations
The calculator computes stringer geometry from standard carpentry formulas. It does not perform structural analysis or check local code amendments.
What it covers
- Stringer length from total rise and run
- Throat depth from board width and notch geometry
- Adequacy check at 3.5 and 5 inch thresholds
- Material estimate in linear feet
What it does not cover
- Structural bending or deflection analysis
- Closed (housed) stringers
- Engineered wood or steel stringers
- Top and bottom connection details
How We Calculate Stringer Dimensions
Frequently Asked Questions About Stair Stringers
What size board do I need for stair stringers?
A 2×12 (11.25 in actual width) is standard for residential stair stringers. A 2×10 works only for shallow risers with short runs, where the throat stays above 5 inches.
What is throat depth on a stair stringer?
Throat depth is the narrowest remaining width of the stringer board after the notch is cut, measured perpendicular to the long edge. A deeper throat means a stronger stringer.
What is the minimum throat depth?
The IRC does not prescribe a minimum throat depth. Industry practice considers 5 inches adequate, 3.5 to 5 inches marginal, and below 3.5 inches structurally inadequate for a 2×12.
How many stringers do I need?
Three cut stringers is the standard minimum for a 36-inch residential stair. Add a fourth stringer for wider stairs or heavy loads.
How long should my stringer board be?
The stringer length is the hypotenuse of the total rise and total run. For a 108-inch rise with a 147-inch run, the stringer is about 182 inches (15.2 feet). Buy boards at least that long plus a few inches for end cuts.
Can I use a 2×10 instead of a 2×12?
Only if the throat depth stays above 5 inches. A 7.2-inch riser with a 10.5-inch run leaves only 3.31 inches of throat on a 2×10, which is structurally marginal.
What is a relief hole?
A small hole (typically 1/4 inch) drilled at the inside corner of each notch before cutting. It prevents overcuts and reduces the stress concentration that can crack the stringer.
Do I need to reinforce my stringers?
If the throat is marginal (3.5 to 5 inches) or the flight is longer than about 12 feet, consider sistering a 2×6 or a 2×4 strongback to the bottom edge of each stringer.
How do I calculate stringer cost?
Multiply the number of stringers by the stringer length in feet, then multiply by the price per linear foot of your stringer stock.
Is my data saved?
No. The calculation runs entirely in your browser and nothing you enter is stored or sent anywhere.
Sources
- STRUCTURE Magazine, Wood-Framed Stair Stringer Design (stringer structural analysis, throat depth examples, deflection limits for notched 2×12 stringers).
- IRC 2021 Section R311.7, Stairways (residential stair riser, tread, width and headroom requirements).
- Fine Homebuilding, Laying Out Basic Stair Stringers (stringer layout technique, notch cutting, relief holes).
Related Calculators
Cutting stair stringers?
This calculator estimates stair stringer geometry and material from rise, run and board size. The IRC does not set a prescriptive minimum throat depth. Confirm stringer sizing with your local building department or a structural engineer, especially for long flights. Spotted an error? Let us know.