Stair Stringer Rise and Run Calculator

This calculator works out the rise and run for a stair stringer from the total height you need to climb, the number of steps you want, and the tread depth you plan to use. You enter the total rise (floor-to-floor height), the number of risers, and the tread run, and it returns the exact rise per step, the total run of the staircase, and the stringer length. It uses the standard building formula that each riser height and tread depth must stay within safe, code-friendly ranges.

Formula

The core formula is simple division and multiplication:

• Riser height = Total rise ÷ Number of risers
• Total run = Tread depth × (Number of risers − 1)
• Stringer length = √(Total rise² + Total run²)

Where:

• Total rise (in inches or cm) is the vertical distance from the finished floor below to the finished floor above.
• Number of risers is the count of vertical steps. The number of treads is always one less than the number of risers because the top step lands on the upper floor.
• Tread run (in inches or cm) is the horizontal depth of each step, not including any nosing overhang.
• Stringer length is the length of the diagonal board that supports the steps, measured along the slope.

Worked Example

Using the default values from the calculator above:

• Total rise = 105 inches, number of risers = 7, tread run = 10 inches
• Riser height = 105 ÷ 7 = 15 inches
• Total run = 10 × (7 − 1) = 60 inches
• Stringer length = √(105² + 60²) = √(11025 + 3600) = √14625 ≈ 120.94 inches

The calculator shows a riser height of 15.00 inches, a total run of 60.00 inches, and a stringer length of 120.94 inches.

How to Use the Calculator Correctly

Start by measuring the total rise from the finished floor of the lower level to the finished floor of the upper level. Do not measure from subfloor to subfloor if you have already installed flooring – that will give a short rise. Then decide on a target riser height. Most building codes allow risers between 4 and 7.75 inches (100–196 mm) for residential stairs, but check your local code. Divide the total rise by your desired riser height and round to a whole number – that gives you the number of risers. Enter that number and the calculator will give you the exact riser height. Then choose a tread depth that feels comfortable, typically 10–11 inches (254–279 mm). The calculator then shows the total run and stringer length.

Common Mistakes and Misconceptions

One frequent error is using the number of treads instead of the number of risers in the total run calculation. If you have 7 risers, you have only 6 treads – the top step is the upper floor. So total run = tread depth × (risers − 1). Another mistake is measuring the total rise before adding finished flooring thickness. If you plan to add 0.75-inch hardwood on top of a subfloor, the rise increases by that amount. Also, remember that the stringer length is the hypotenuse of a right triangle – it is not simply the sum of rise and run. Finally, do not round the riser height to the nearest whole inch during calculation; keep at least two decimals to maintain accuracy across the whole staircase.

When to Use This Calculator vs. a Full Stair Design

This calculator is ideal for quick estimates – for example, when you are planning a deck stair, a small porch step, or a set of interior stairs and need to know the basic dimensions. It does not account for stair width, nosing overhang, headroom clearance, or landings. For a full staircase with a landing, a turn, or unusual geometry, you need a more detailed design that includes those factors. Also, if your total rise does not divide evenly into a legal riser height, you may need to adjust the number of risers or the floor height. The calculator helps you test different numbers of risers quickly to find a combination that meets code.

Safety and Building Code Considerations

Stair dimensions are regulated for safety. Typical residential codes require:

• Riser height between 4 and 7.75 inches (100–196 mm) – some codes allow up to 8 inches for exterior stairs.
• Tread depth at least 10 inches (254 mm) – some codes require 11 inches for new construction.
• All risers and treads in a single flight must be within 3/16 inch (4.8 mm) of each other – uniformity prevents trips.
• Headroom must be at least 6 feet 8 inches (2032 mm) measured vertically from the nosing line.
• Handrails are required on stairs with more than a few risers, and the height and graspability are regulated.

Always check your local building code before cutting stringers. The calculator gives you the geometry, but the code governs the limits.

Alternatives to Traditional Stringers

If you cannot use a long, straight stringer – for example, because of a low ceiling or a tight space – you have other options. You can build stairs with a landing in the middle, which requires two separate stringer runs. You can use a spiral staircase, which has its own rise and run formulas but is more compact. Or you can use a mono-stringer (a single central steel beam) with cantilevered treads, which is common in modern architecture. Each method has different structural requirements and costs. For a simple outdoor deck, a notched 2×12 stringer is the standard; for interior stairs, you might use a closed stringer with routed grooves for the treads and risers.

Frequently Asked Questions

How do I find the number of risers if I only know the total rise?
Divide the total rise by a comfortable riser height (say 7 inches) and round up to the nearest whole number. For example, 105 ÷ 7 = 15, so you would use 15 risers. Then divide 105 by 15 to get the exact riser height of 7 inches. If the result is not a whole number, round up to avoid a riser that is too tall.

What is the difference between rise and run in stairs?
Rise is the vertical height of each step (the riser). Run is the horizontal depth of each step (the tread). The total rise is the overall vertical distance the stairs cover, and the total run is the overall horizontal distance the stairs occupy.

Why is the total run one tread less than the number of risers?
Because the top step is the upper floor itself. If you have 7 risers, you step up 7 times, but the last step lands on the upper floor, so you only need 6 treads below it. This is a common source of error when calculating total run.

Can I use this calculator for metric measurements?
Yes, the math is the same. Just enter the total rise in centimeters and the tread run in centimeters, and the outputs will be in centimeters. The stringer length will also be in centimeters. The formula does not care about units as long as you are consistent.

What is the maximum riser height allowed?
Most residential codes cap risers at 7.75 inches (196 mm), but some older codes allow 8 inches (203 mm). For commercial buildings, the limit is often 7 inches (178 mm). Always check your local code – the calculator will tell you the exact rise, but you must verify it is within the legal range.

Do I need to add nosing to the tread depth?
Nosing is the protruding edge of the tread that overhangs the riser. It is typically 0.75 to 1.25 inches (19–32 mm). The tread run in the calculator is the horizontal depth of the tread itself, not including nosing. If your code requires a minimum tread depth of 10 inches, that measurement is usually taken from the nosing edge, so you may need a slightly deeper tread to meet the requirement.

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in t | Total rise (floor to floor) | in | 105 | 0
in n | Number of risers | - | 7 | 1
in r | Tread run (depth) | in | 10 | 0
out rise | Riser height | in | t / n | 2
out run | Total run | in | r * (n - 1) | 2
out stringer | Stringer length (hypotenuse) | in | sqrt((t)^2 + (r * (n - 1))^2) | 2