Stair Stringer Size Calculator

Last updated: 27 Nov 2025 | Author: Brij | Review By: Irshad

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A simple Stair Stringer Size Calculator to determine the correct lumber size, notch depth, stair angle, and stringer length. Includes complete formulas, and a real example for accurate stair construction.

Total Rise:

Total Run:

Tread Depth:

Riser Height:

Stringer Type:

Stair Stringer Size Calculation Results

Recommended Stringer Size:

lumber

Maximum Notch Depth:

Actual Notch Depth:

Stringer Safety Status:

status

Stringer Length:

Stair Angle:

Step Diagonal Cut Length

A stair stringer must be strong, safe, and properly sized before cutting notches for treads and risers. If the notch is too deep, the stringer becomes weak and risks breaking.

This Stair Stringer Size Calculator helps you determine:

Safe stringer lumber size (2×10 or 2×12)
Maximum notch depth (40% rule)
Actual notch depth (based on your riser height + tread depth)
Diagonal cut length
Stair angle
Total stringer length

Below is a complete guide that explains how the calculator works, with formulas, and an example.

Formulas Used in the Calculator

1. Total Number of Risers

$R = \text{round}\left(\frac{Total\ Rise}{Riser\ Height}\right)$

2. Total Number of Treads

$T = R - 1$

3. Actual Tread Run

$Actual\ Tread = \frac{Total\ Run}{T}$

4. Stair Angle

Angle is based on per-step geometry:

$\theta = \tan^{-1}\left(\frac{Riser\ Height}{Actual\ Tread}\right)$

5. Stringer Length

The length of the stringer is the hypotenuse of total rise and total run:

$L = \sqrt{(Total\ Rise)^2 + (Total\ Run)^2}$

6. Step Diagonal (Cut Length)

$Step\ Diagonal = \sqrt{(Riser\ Height)^2 + (Tread\ Depth)^2}$

7. Actual Notch Depth

Your code uses:

$Actual\ Notch\ Depth = Step\ Diagonal \times \sin(\theta)$

8. Maximum Notch Depth (40% Rule)

$Max\ Notch\ Depth = (Actual\ Board\ Depth) \times 0.40$

For common boards:

2×10 actual depth = 9.25 in
2×12 actual depth = 11.25 in

9. Safety Check

$Pass\ if:\ Actual\ Notch\ Depth \le Max\ Notch\ Depth$

Example Calculation

Using your code’s formulas:

Given:

Total Rise = 108 in
Total Run = 140 in
Riser Height = 7.5 in
Tread Depth = 10 in
Stringer = 2×12 (actual 11.25 in → max notch = 4.5 in)

Step 1 — Total Risers

$R = round(108 / 7.5) = 14$

Step 2 — Total Treads

$T = 14 - 1 = 13$

Step 3 — Actual Tread

$Actual\ Tread = 140 / 13 = 10.77\ in$

Step 4 — Stair Angle

$θ = atan(7.5 / 10.77) = 34.7^\circ$

Step 5 — Step Diagonal

$Step\ Diagonal = \sqrt{7.5^2 + 10^2} = 12.5\ \text{in}$

Step 6 — Actual Notch Depth (your code logic)

$Actual\ Notch\ Depth = 12.5 × sin(34.7°) = 7.11\ in$

Step 7 — Maximum Notch Depth

$MaxNotch = 11.25 × 0.40 = 4.5\ in$

Step 8 — Safety Check

Since:

$7.11 > 4.5 → Fail$

FAQs

1. What determines the correct stair stringer size?

The correct stringer size mainly depends on how deep the notches are. A deeper notch weakens the board. Most building guidelines follow the 40% rule, which means you should remove no more than 40% of the stringer’s actual depth when cutting the steps.

For example:

2×10 → actual depth = 9.25 in → max notch ≈ 3.7 in
2×12 → actual depth = 11.25 in → max notch ≈ 4.5 in

2. What is the “actual notch depth”?

Actual notch depth is the amount of wood removed from the top of the stringer for each step.

Your calculator finds it using:

Riser height
Tread depth
Stair angle

The vertical depth removed must stay within the allowed safety limit to avoid weakening the board.

3. What is the difference between “actual notch depth” and the “step diagonal” cut length?

Actual Notch Depth → The vertical material removed (used for safety checks).
Step Diagonal → The angled cut length across the notch (useful for marking and cutting).
These values are related but not the same. Only notch depth affects the structural strength of the stringer.

4. When should I use a 2×12 stringer instead of a 2×10?

A 2×12 stringer is recommended when:

Your riser height is large
Your tread depth is large
The calculated notch depth exceeds the safe limit for a 2×10

If the notch depth is too deep, a 2×12 gives you extra wood so the stringer remains strong and safe.

5. What happens if the notch depth exceeds the maximum safe limit?

If the notch depth is deeper than the allowed maximum (40% rule), the stringer becomes structurally weak and may crack or fail under load.

Your calculator will display Fail and may recommend:

Switching to a larger board (e.g., 2×12 or 4×12)
Reducing tread depth
Reducing riser height

Check out 1 Similar Calculators:

Stair Stringer Size Calculator

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