Stair Stringer Cut Calculator: Rise, Run & Layout

This stair stringer cut calculator works out the exact rise and run for each step on a straight stair stringer, plus the total stringer length and the angle of the cut. You enter the total rise (floor-to-floor height), the total run (horizontal distance), and the number of steps, and it returns the individual step rise, step run, stringer length, and cut angle so you can lay out and cut your stringers accurately.

Formula

The calculator uses the basic geometry of a right triangle. The stringer is the hypotenuse, the total rise is the vertical leg, and the total run is the horizontal leg.

• Step rise = Total rise ÷ Number of steps
• Step run = Total run ÷ (Number of steps − 1)
• Stringer length = √(Total rise² + Total run²)
• Cut angle = arctan(Total rise ÷ Total run)

All lengths are in inches (or any consistent unit). The angle is in degrees. The step run divides by (steps − 1) because the last step lands on the upper floor – the treads are spaced one fewer than the number of risers.

Worked Example

Using the default values: total rise = 105 in, total run = 120 in, steps = 7.

1. Step rise = 105 ÷ 7 = 15.00 in
2. Step run = 120 ÷ (7 − 1) = 120 ÷ 6 = 20.00 in
3. Stringer length = √(105² + 120²) = √(11025 + 14400) = √25425 ≈ 159.45 in
4. Cut angle = arctan(105 ÷ 120) = arctan(0.875) ≈ 41.2°

So each step rises 15 inches and runs 20 inches, the stringer is about 159.5 inches long, and the cut angle is about 41 degrees. These match the calculator outputs.

What the Results Mean

The step rise and step run are the two critical dimensions for cutting the notches into a 2×12 or other stringer board. The stringer length tells you the minimum board length you need (add a few inches for waste). The cut angle is the angle at the top and bottom of the stringer where it meets the floor and the upper landing – you’ll mark this angle on the board to make the end cuts.

Remember that the step run is the horizontal depth of each tread, not including any nosing (the overhang). If you plan to add a nosing, you may need to adjust the tread depth or the run accordingly. The calculator gives the basic layout – building codes and finish materials will affect final dimensions.

How to Use the Calculator

Measure your total rise from the finished floor below to the finished floor above. Measure the total run from the face of the lower floor to the face of the upper floor (or the edge of the upper landing). Decide how many steps you want – typically you divide the total rise by a desired riser height (7–8 inches is common) and round to a whole number.

• Enter the total rise and total run in inches.
• Enter the number of steps (risers).
• Read the step rise, step run, stringer length, and cut angle.

If the step rise comes out too high (over 8 inches) or too low (under 4 inches), adjust the number of steps and recalculate. Most building codes limit riser height to about 7.75 inches, so check your local code.

Common Mistakes and Misconceptions

One frequent error is dividing the total run by the number of steps instead of steps minus one. The last step doesn’t have a tread – it’s the upper floor. That mistake makes every tread too shallow.

Another mistake is mixing units – if you measure rise in inches and run in feet, the angle and length will be wrong. Use the same unit for both.

Also, the stringer length is the straight-line distance along the slope. It is not the sum of the step rises and runs. Many people think they can add up the step dimensions – that gives a longer, incorrect length.

Choosing the Right Stringer Board

Stringers are usually cut from 2×12 lumber (actual size 1.5″ x 11.25″). The board must be wide enough to accommodate the step run and the throat (the remaining wood below the notch). A common rule is that the throat should be at least 3.5 inches for a 2×12, so the step run cannot exceed about 10–11 inches when using a 2×12. If your step run is larger, you may need a wider board or a different design.

Use straight, dry, structurally graded lumber. Avoid knots near the notches. For outdoor stairs, use pressure-treated or naturally rot-resistant wood. The stringer length from the calculator tells you the minimum board length – add 6–12 inches for end cuts and waste.

Safety and Building Code Considerations

Stairs are structural and safety-critical. Incorrect stringer cuts can lead to uneven steps, trips, and falls. Always follow local building codes for riser height, tread depth, and handrail requirements. The calculator gives you the geometry, but it does not replace a professional review.

• Check that the step rise is within code limits (typically 4–7.75 inches).
• Check that the step run is at least 10 inches (varies by code).
• Ensure the throat of the stringer is not too thin – at least 3.5 inches for 2×12.
• Use proper fasteners and structural connectors when attaching stringers.

If you are not experienced with stair layout, consider having a professional check your cuts before installation. A small error in the angle can compound over many steps.

Frequently Asked Questions

Do I divide the run by steps or steps minus one?

Divide by steps minus one. The top step lands on the upper floor, so there is no tread there. For 7 steps, you have 6 treads, so the run is divided by 6.

What is the maximum riser height allowed?

Most residential building codes limit riser height to 7.75 inches (some to 8 inches). The minimum is usually 4 inches. Check your local code for exact values.

Can I use this calculator for outdoor stairs?

Yes, the geometry is the same. But outdoor stairs may have different code requirements (e.g., tread depth, slip resistance) and you should use weather-resistant lumber and fasteners.

What is the throat of a stringer and why does it matter?

The throat is the shortest distance from the notch to the bottom edge of the board. If it’s too thin, the stringer can crack under load. For a 2×12, keep the throat at least 3.5 inches.

How do I measure the total run if the stairs are open on one side?

Measure horizontally from the face of the lower floor to the face of the upper floor (or the edge of the landing). If the upper floor has a nosing or overhang, measure to the point where the treads will end.

What if my step rise is not a whole number?

That’s fine – the calculator gives decimals. You’ll mark the rise and run on the framing square using the decimal values (e.g., 7.5 inches). Use a sharp pencil and a square for accuracy.

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in total_rise | Total rise | in | 105 | 0
in total_run | Total run | in | 120 | 0
in n_steps | Number of steps | - | 7 | 1
out step_rise | Step rise | in | total_rise / n_steps | 2
out step_run | Step run | in | total_run / (n_steps - 1) | 2
out stringer_len | Stringer length | in | sqrt((total_rise)^2 + (total_run)^2) | 2
out cut_angle | Cut angle | deg | atand(total_rise / total_run) | 1