Deck Stair Calculator Metric: Rise, Run & Stringers

This metric deck stair calculator works out the number of steps, the rise and run per step, and the stringer length for a deck staircase. You enter the total rise (deck height to ground), the total run (horizontal distance), and the desired tread depth, and it returns the step dimensions you need to build to code-compliant proportions. The results are given in millimetres and metres, matching metric lumber sizes.

Formula

The calculator uses three standard stair geometry formulas:

• Number of steps: steps = ceil(total_rise / 180) – dividing the total rise by a typical maximum riser height of 180 mm (7 inches) and rounding up to the next whole number.
• Rise per step: rise = total_rise / steps – the actual riser height after rounding the step count.
• Run per step: run = total_run / (steps - 1) – the horizontal tread depth, assuming the top tread lands on the deck surface and the bottom tread lands on the ground.
• Stringer length: stringer = sqrt(total_rise² + total_run²) – the hypotenuse of the right triangle formed by the total rise and total run, giving the straight-line length of the stringer board before cutting notches.

All dimensions are in millimetres (mm) for rise, run, and stringer length. The number of steps is a dimensionless integer.

Worked Example

Using the default values from the calculator: total rise = 900 mm, total run = 1200 mm, desired tread = 280 mm.

1. Number of steps: ceil(900 / 180) = ceil(5) = 5 steps.
2. Rise per step: 900 / 5 = 180.0 mm.
3. Run per step: 1200 / (5 - 1) = 1200 / 4 = 300.0 mm.
4. Stringer length: sqrt(900² + 1200²) = sqrt(810000 + 1440000) = sqrt(2250000) = 1500.0 mm.

The calculator returns 5 steps, 180.0 mm rise, 300.0 mm run, and 1500.0 mm stringer length. Note that the desired tread (280 mm) is not used in the core calculation because the run is derived from the total run and step count – the desired tread is a reference to check against local building guidelines.

When to Use This Calculator

Use this tool when you are designing a deck staircase and need to know how many steps you will cut, what riser height to use, and how long each stringer board must be. It is especially useful for:

• Planning a new deck build where the deck height and horizontal distance to the ground are known.
• Checking an existing staircase against typical comfort ratios (rise + run ≈ 430–460 mm, or rise × run ≈ 63,000–65,000 mm²).
• Estimating lumber needs – you will need at least two stringers, often three or more for wide stairs.
• Converting imperial plans to metric or vice versa (1 inch = 25.4 mm).

The calculator gives you the geometric minimums; it does not replace local building codes, which may specify maximum riser height (often 180–200 mm), minimum tread depth (often 280 mm), and handrail requirements.

How to Read the Results

The number of steps is the total risers you will cut – if you have 5 steps, you will have 5 vertical rises and 4 treads (the top tread is the deck surface itself). The rise per step is the vertical height between each tread; keep it consistent across all steps to avoid tripping hazards. The run per step is the horizontal depth of each tread; this is what you will cut into the stringer. The stringer length is the board length before cutting – you will typically buy a 2×12 (38×286 mm) board longer than this to allow for notching and end trimming.

If the run per step comes out below 280 mm, you likely need a longer total run or fewer steps. If the rise per step exceeds 200 mm, the stairs are too steep and you should increase the total run or lower the deck height.

Common Mistakes and Misconceptions

• Mixing units: Always work in millimetres. A common error is entering centimetres or metres and getting absurd results. Convert everything to mm first.
• Forgetting the top tread: Many people count the deck surface as a step. The calculator correctly subtracts one from the step count for the run calculation, but if you are using a different design (e.g., a landing at the top), adjust accordingly.
• Rounding too early: Round the number of steps up, not down, and then recalculate the rise. Rounding down can make risers too tall.
• Ignoring the stringer thickness: The stringer length is the hypotenuse of the triangle; the actual board must be longer to accommodate the notch depth (usually about 50 mm) and any angle cuts at the top and bottom.
• Assuming the run is the tread depth: The run per step is the horizontal distance between the nose of one tread and the nose of the next. If you use a nosing overhang, the actual tread board may be wider than the run.

Limitations of the Formula

This calculator provides the basic geometry for a straight flight of stairs. It does not account for:

• Landings: If the stairs turn or have a mid-landing, the total run and rise must be split into separate segments, each calculated independently.
• Notch dimensions: The stringer length is the hypotenuse; the actual board length must include the vertical rise of the notch (typically the riser height) and the horizontal run of the notch (the tread depth).
• Material thickness: Tread and riser boards add to the overall dimensions. For example, if you use 50 mm thick treads, the actual rise between finished tread surfaces is reduced by that thickness.
• Local code variations: Building codes differ by region. Some specify a maximum riser of 190 mm, others 200 mm; some require a minimum tread of 300 mm. Always check your local code before cutting.
• Handrail and guardrail requirements: These are safety features that may affect the overall width and design but do not change the rise/run geometry.

Safety and Accuracy Notes

Stair building is safety-critical. A consistent rise and run is essential – variations of even a few millimetres can cause trips and falls. Always measure the total rise from the finished deck surface to the finished ground level, not the bare framing. Use a level and a tape measure, and double-check your measurements before cutting. When cutting stringers, use a framing square with stair gauges to ensure accurate, repeatable notches. Test-fit the stringers before attaching them permanently. If you are unsure about any aspect, consult a professional builder or your local building authority.

Frequently Asked Questions

What is the maximum riser height for deck stairs?

Most building codes in North America and Europe cap riser height at 180–200 mm (7–8 inches). The calculator uses 180 mm as a conservative default, but you should verify your local code. A rise above 200 mm is uncomfortable and often illegal.

What is the minimum tread depth?

Typical minimum tread depth is 280 mm (11 inches) in many jurisdictions. Some codes allow 250 mm for residential, but 280 mm is a safe, comfortable minimum. The calculator lets you enter your desired tread, but the actual run is determined by the total run and step count.

How many stringers do I need?

For a stair width up to 900 mm, two stringers are common. For wider stairs (up to 1200 mm), use three stringers. For stairs wider than 1200 mm, add a stringer every 400–600 mm. The calculator does not determine stringer count – it only gives the length.

Can I use this calculator for interior stairs?

Yes, the geometry is the same, but interior stairs often have different code requirements (e.g., minimum headroom, maximum rise). The calculator works for any straight stair, but verify your local interior stair code.

What if my total run is too short for the desired tread?

If the calculated run per step is less than your desired tread, you have two options: increase the total run (move the bottom of the stairs further out) or reduce the number of steps (which increases the rise per step, possibly exceeding the maximum). You may need to adjust the deck height or add a landing.

How do I convert imperial stair measurements to metric?

Multiply inches by 25.4 to get millimetres. For example, a 7-inch rise is 177.8 mm, and an 11-inch tread is 279.4 mm. Always convert all measurements before using the calculator.

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in total_rise | Total rise (deck height) | mm | 900 | 0
in total_run | Total run (horizontal distance) | mm | 1200 | 0
in tread | Tread depth (desired) | mm | 280 | 0
out steps | Number of steps | - | ceil(total_rise / 180) | 0
out rise | Rise per step | mm | total_rise / steps | 1
out run | Run per step | mm | total_run / max(steps - 1, 1) | 1
out stringer | Stringer length | mm | sqrt((total_rise^2) + (total_run^2)) | 1