Stair Stringer Calculations: How to Measure

This calculator works out the rise, run, and stringer length for a straight staircase. You enter the total rise (floor-to-floor height), the total run (horizontal distance), or the number of steps, and it returns the individual step rise, step run, stringer length, and the angle of the stringer. The result is the exact length and cutting angle for the stringer, so you can mark and cut it correctly.

Formula

The stair stringer is the diagonal board that supports the treads and risers. Its length is the hypotenuse of a right triangle formed by the total rise (vertical distance between finished floors) and the total run (horizontal distance from the face of the first riser to the face of the last riser).

Stringer length = √(total rise² + total run²)

Step rise = total rise ÷ number of risers

Step run = total run ÷ (number of risers − 1)

Stringer angle = arctan(total rise ÷ total run)

All lengths are in inches (or any consistent unit). The angle is in degrees.

Worked Example

Using the default values: total rise = 105 in, total run = 110 in, number of risers = 7.

1. Step rise = 105 ÷ 7 = 15.00 in
2. Step run = 110 ÷ (7 − 1) = 110 ÷ 6 = 18.33 in
3. Stringer length = √(105² + 110²) = √(11025 + 12100) = √23125 ≈ 152.07 in
4. Angle = arctan(105 ÷ 110) ≈ 43.7°

The calculator displays the same results: step rise 15.00 in, step run 18.33 in, stringer length 152.07 in, angle 43.7°.

How to Use the Results

The stringer length is the diagonal measurement from the top of the stringer to the bottom, measured along the back of the notches. When you lay out the stringer on a 2×12 board, you mark the step rise and step run on the edge of the board, then cut out the notches. The angle tells you how to cut the top and bottom of the stringer to sit flush against the floor and the upper landing.

Typical residential stair dimensions are:

• Step rise: 7 to 7.75 inches (178 to 197 mm)
• Step run: 10 to 11 inches (254 to 279 mm)
• Stringer board: 2×12 (actual 1.5 x 11.25 inches) for most residential stairs

If your calculated step rise or run falls outside these ranges, adjust the number of risers or the total run and recalculate.

Common Mistakes and Misconceptions

One frequent error is confusing the number of risers with the number of treads. A staircase with 7 risers has only 6 treads because the top riser meets the upper floor. That is why the formula divides total run by (risers − 1).

Another mistake is measuring the total rise from the subfloor instead of the finished floor. If you plan to install hardwood or tile, the finished floor height is higher. Measure from the finished surface of the lower floor to the finished surface of the upper floor.

Also, the stringer length calculated here is the theoretical diagonal. Real stringers need additional length at the top and bottom for bearing on the floor and the landing—often 2 to 4 inches extra. Check your local building code for the required overlap.

Safety and Building Code Considerations

Stair building is regulated by local building codes, and the numbers vary by jurisdiction. Most codes in the United States follow the International Residential Code (IRC) for residential stairs:

• Maximum step rise: 7.75 inches
• Minimum step run: 10 inches
• Minimum width: 36 inches above the handrail
• Headroom: at least 6 feet 8 inches

These are minimums and maximums—you cannot simply use any number. The rise and run must fall within the allowed range, and the difference between the tallest and shortest step on a staircase cannot exceed 3/8 inch. Always verify with your local building department before cutting.

For safety, use at least three stringers for stairs wider than 36 inches, and attach them securely to the floor and the upper landing. The stringer notches reduce the effective strength of the board, so using a 2×12 instead of a 2×10 is recommended for most residential work.

Alternatives to Traditional Stringers

Not every staircase uses a cut stringer. Common alternatives include:

• Solid stringers with brackets: The stringer is a plain board, and metal or wood brackets are attached to support each tread. This is easier for curved or angled stairs.
• Pre-fabricated stringers: Some lumber yards sell stringers already cut for common rise/run combinations, but they may not match your exact floor height.
• Steel or concrete stringers: Used in commercial or outdoor settings, these are often engineered and not cut on site.

For a simple straight stair, a cut stringer is usually the most cost-effective and straightforward method.

Frequently Asked Questions

How many stringers do I need?

Most residential codes require stringers every 16 inches on center. For a 36-inch-wide stair, that means three stringers. For wider stairs, add more. If you use a center carriage or a solid stringer, you may need fewer.

What is the maximum rise for a stair?

Under the IRC, the maximum step rise is 7.75 inches. Some older codes allowed 8 inches, but most current U.S. codes cap it at 7.75. Check your local code, as some areas have stricter limits.

Can I use a 2×10 for a stringer?

Yes, but only if the step run is short enough that the notch depth does not weaken the board. A common rule is that the remaining uncut portion of the stringer must be at least 3.5 inches. For most stairs with a 10-inch run, a 2×12 is safer. When in doubt, use a 2×12.

How do I measure the total rise?

Measure vertically from the finished floor of the lower level to the finished floor of the upper level. If you are building a deck, measure from the deck surface to the ground. Use a straightedge and a level to get an accurate vertical measurement—do not measure along the stairs.

What does the stringer angle mean for cutting?

The angle is the slope of the stringer relative to the floor. You use it to cut the top and bottom of the stringer so they sit flush on the floor and the upper landing. Most carpenters mark the angle using a framing square rather than a protractor, but knowing the angle helps when using a miter saw.

Why does my calculated stringer length seem too short?

The calculated length is the diagonal between the top of the first riser and the bottom of the last riser. It does not include the extra material needed at the top and bottom for bearing. Add 2 to 4 inches to each end for the actual board length. Also, check that you entered the total run correctly—it is the horizontal distance, not the diagonal.

Related

• Dividing Fractions by Whole Numbers KS2
• Confidence Intervals and P-Values: What They Mean
• Two Unknown Equation Solver: How to Solve Systems

in rise | Total rise (floor to floor) | in | 105 | 0
in run | Total run (horizontal) | in | 110 | 0
in n | Number of risers | - | 7 | 1
out step_rise | Step rise | in | rise / n | 2
out step_run | Step run | in | run / (n - 1) | 2
out stringer | Stringer length | in | sqrt(rise^2 + run^2) | 2
out angle | Stringer angle | deg | atand(rise / run) | 1