Stair Stringer Calculator

A stair stringer calculator works out the cut dimensions for the diagonal boards that support a staircase. A stringer is a board notched along its top edge to hold each step. Enter the total rise, total run, number of steps, and lumber size, and the calculator returns the riser height, tread depth, stringer angle, stringer length, and the minimum board size needed.

Key terms

Total rise: the full vertical height the staircase climbs, measured from the bottom floor to the top floor.
Total run: the full horizontal distance the staircase covers.
Riser: the vertical part of one step.
Tread: the flat horizontal part of one step, where a foot lands.
Stringer: the diagonal board, notched in a zigzag pattern, that carries the treads and risers.

How to use the calculator

Enter the total rise, in inches.
Enter the total run, in inches.
Enter the number of steps. The calculator does not choose this number automatically; it uses whatever whole number is typed in. A common starting point is to divide the total rise by about 7 inches and round to a whole number, then enter that as the step count.
Choose a lumber size: 2x10, 2x12, or 2x14.
Read the results below the form.

Two presets can fill in the first three fields at once: US/Canada Standard and International Standard. A Custom option is also available for typing in any values.

US/Canada Standard: 84 in total rise, 121 in total run, 12 steps. This works out to a 7 in riser and an 11 in tread.
International Standard: 78 in total rise, 110 in total run, 12 steps. This works out to a 6.5 in riser and a 10 in tread.

Formulas

Riser height and tread depth

riser height = total rise ÷ number of steps
tread depth = total run ÷ (number of steps − 1)

A flight with N steps has N risers but only N − 1 treads, because the top step is the landing itself, not a separate tread.

Stringer angle

stringer angle = arctan(riser height ÷ tread depth)

This is the angle of a single step's slope, sometimes called the pitch. It is not the same as the angle of the line running corner to corner across the whole staircase.

Stringer length

stringer length = √(total rise² + total run²)

This applies the Pythagorean theorem to the total rise and total run, giving the length of the diagonal line from the bottom of the stringer to the top. It is a slightly generous estimate, since the actual notched cutting line is a little shorter than the straight diagonal.

Minimum lumber size

Each lumber size has a fixed actual thickness and depth, independent of the step dimensions:

Nominal size	Actual thickness	Actual depth
2x10	1.5 in	9.25 in
2x12	1.5 in	11.25 in
2x14	1.5 in	13.25 in

The calculator picks the minimum board length by converting the stringer length from inches to feet and rounding up to the next whole foot:

minimum length (feet) = ceiling(stringer length ÷ 12)

Building code limits (IRC)

The International Residential Code, section R311.7, sets two limits that the calculator checks:

Maximum riser height: 7.75 inches. A taller riser makes each step harder to climb safely.
Minimum tread depth: 10 inches. A shallower tread does not give a foot enough room to land fully.

There is no code minimum riser height and no code maximum tread depth. If a riser comes out taller than 7.75 in, the calculator shows a warning. If a tread comes out shallower than 10 in, it shows a different warning. Either way, the results still display, so the number of steps can be adjusted and checked again.

Worked example 1: standard residential stair

Total rise 84 in, total run 121 in, 12 steps, 2x12 lumber.

Riser height = 84 ÷ 12 = 7.00 in
Tread depth = 121 ÷ 11 = 11.00 in
Both values meet code, so no warning appears.
Stringer angle = arctan(7 ÷ 11) ≈ 32.5°
Stringer length = √(84² + 121²) = √21,697 ≈ 147.30 in
Minimum lumber: 2x12 board (1.5 in thick, 11.25 in deep), length = ceiling(147.30 ÷ 12) = 13 ft

Worked example 2: deck stair

Total rise 56 in, total run 96 in, 8 steps, 2x12 lumber.

Riser height = 56 ÷ 8 = 7.00 in
Tread depth = 96 ÷ 7 ≈ 13.71 in
Riser is under 7.75 in and tread is over 10 in, so no warning appears.
Stringer angle = arctan(7 ÷ 13.71) ≈ 27.0°
Stringer length = √(56² + 96²) = √12,352 ≈ 111.14 in
Minimum lumber: 2x12 board, length = ceiling(111.14 ÷ 12) = 10 ft

Choosing a lumber size

The calculator offers three dimensional lumber sizes: 2x10, 2x12, and 2x14. A wider board (greater actual depth) leaves more solid wood after the tread and riser notches are cut, which matters more on steeper stairs with a tall riser and deep tread. 2x12 is the most common choice for residential stringers. The calculator's minimum-length figure is only a lumber-length estimate; it does not check whether a given width is wide enough for the notch pattern, so it is worth sketching the actual cut before buying material.

Frequently asked questions

What is a stair stringer? A stringer is the diagonal board that supports a staircase. It is cut with notches so that a tread and riser board can sit in each notch, forming the steps.

What is the formula for stringer length? Stringer length equals the square root of the total rise squared plus the total run squared, from the Pythagorean theorem: √(total rise² + total run²).

How many steps should a staircase have? There is no single fixed number; it depends on the total rise and run of the space. A common approach is to divide the total rise by roughly 7 inches and round to the nearest whole number, then check that the resulting riser height is 7.75 inches or less and the tread depth is 10 inches or more.

Why does the calculator show a riser or tread warning? The IRC sets a 7.75-inch maximum riser height and a 10-inch minimum tread depth. If the entered numbers produce a riser taller than the maximum, or a tread shallower than the minimum, the calculator flags it. Adjusting the number of steps, the total rise, or the total run changes these values.

What is the difference between the US/Canada and international presets? The US/Canada Standard preset uses a 7-inch riser and an 11-inch tread (84 in total rise, 121 in total run, 12 steps). The International Standard preset uses a 6.5-inch riser and a 10-inch tread (78 in total rise, 110 in total run, 12 steps).

What size lumber do I need for stair stringers? 2x12 is the most common choice for residential stringers and is wide enough for most standard rise-and-tread combinations. 2x10 suits shorter, shallower stringers, and 2x14 suits longer or steeper ones. The calculator reports a minimum board length in feet based on the stringer length; it does not calculate board width.

Stair Stringer Calculator - Rise, Run & Lumber Size