Stair Rise and Run
Calculate the number of risers, actual riser height, number of treads and total run of a staircase. Enter the total rise, desired step height and tread depth to plan a comfortable, code-friendly stair layout.
Plan Your Stairs: Risers, Treads and Total Run
Stair Rise and Run Formula
Where:
- \(H\) — total rise: vertical distance from the finished lower floor to the finished upper floor
- \(r\) — desired riser height (the target step height you aim for)
- \(n\) — number of risers, rounded up so that no single step is higher than your target
- \(R\) — actual riser height, after the total rise is divided evenly among all steps
- \(T\) — tread depth (horizontal going of each step)
- \(L_{nd}\) — landing allowance, extra flat depth added to the total run (0 if none)
- \(L\) — total run: the horizontal distance the staircase occupies
Because the riser count must be a whole number, the actual riser \(R\) rarely equals your target \(r\) exactly — the total rise is simply split into equal steps. The upper floor or landing acts as the final tread, which is why there is always one more riser than treads.
Stair Rise and Run – Calculation Example
Example: a staircase must climb from one finished floor to another 275 cm higher. You want steps of about 17.5 cm and plan treads 28 cm deep, with no landing.
\[ n = \left\lceil \frac{275}{17.5} \right\rceil = \lceil 15.71 \rceil = 16 \text{ risers} \]
\[ R = \frac{275}{16} = 17.19 \text{ cm}, \qquad \text{treads} = 16 - 1 = 15 \]
\[ L = 15 \times 28 + 0 = 420 \text{ cm} = 4.20 \text{ m} \]
Result: 16 equal risers of 17.19 cm each, 15 treads of 28 cm, and a total run of 420 cm (4.20 m). The comfort check \(2R + T = 62.38\) cm falls inside the ideal 61–65 cm range, so this layout will feel comfortable.
How to Use the Calculator
- Measure the Total rise (H) — the vertical distance from the surface of the finished lower floor to the surface of the finished upper floor — and enter it with the matching unit.
- Enter your Desired riser height. The calculator rounds the number of steps up, so the finished riser will never be higher than this value. Aim for 15–19 cm (6–7½ in).
- Enter the Tread depth (T), the horizontal going of each step measured without the nosing overhang.
- If the staircase includes a flat landing part-way up, enter its depth in Landing allowance; otherwise leave 0.
- Read the results: number of risers, the actual (equalized) riser height, number of treads and the total run. The calculator also checks the riser against common comfort limits and applies the Blondel rule \(2R + T \approx 61\text{–}65\) cm.
What Are Rise and Run?
The rise of a stair is its total vertical climb, and the run is its total horizontal footprint. These two dimensions are broken down into individual risers (the vertical face of each step) and treads (the horizontal surface you stand on). Every comfortable staircase shares one property: all risers are exactly the same height. Even a small difference of a centimetre between steps is a classic cause of stumbles, because the body locks into a rhythm after the first two or three steps.
The design always starts from the total rise, because it is fixed by the building. You then choose a target riser height and divide. Since the result is almost never a whole number, the count is rounded up — giving slightly shorter, easier steps — and the actual riser height is recalculated by dividing the rise evenly. The top landing or upper floor counts as the last step, which is why a stair with \(n\) risers has only \(n-1\) treads of built construction.
The total run tells you how much horizontal space the stair will occupy — essential for checking headroom, clearances and whether the stair actually fits the floor plan. Together with the riser height and tread depth, it is all a carpenter needs to lay out stringers and set out the staircase on site.
Comfort Rules and Building Codes
Two rules of thumb govern residential stair design. First, the riser height should stay within roughly 15–19 cm (6–7¾ in); many residential codes cap it at 19.7 cm (7¾ in) and require a minimum tread of about 25 cm (10 in). Second, the Blondel formula — a relation dating back to the 17th century — states that \(2R + T\) should land between 61 and 65 cm (24–25.5 in) for a natural stride. The example above scores 62.38 cm, squarely in the sweet spot.
Interpreting your results:
- Riser too high (over ~19.7 cm): reduce the desired riser height so the calculator adds a step and lowers every riser.
- Riser too shallow (under ~15.2 cm): increase the desired riser to remove a step; very short steps break the walking rhythm.
- Blondel outside 61–65 cm: adjust the tread depth — a higher riser wants a shallower tread, and vice versa.
Assumptions and Practical Tips
- All risers are assumed equal and the stair is a single straight flight; for L-shaped or U-shaped stairs, compute each flight separately and use the landing allowance for the flat platform depth.
- Measure the total rise from finished floor to finished floor. If you measure from subfloor while flooring is still to be installed, subtract the future floor thickness, or your risers will come out uneven.
- Tread depth excludes the nosing overhang (typically 2–2.5 cm). Codes measure the going, so enter the going, not the total tread board width.
- The calculator does not check headroom, stair width, handrail height or guard requirements — verify these against your local building code before construction.
- The number of risers is rounded up, so the actual riser is always equal to or shorter than your target — a safe direction, since high steps are the main hazard.
When you move from layout to structural design, the stair stringers act as sloped beams carrying the load to the floors. For checking their strength you can use the uniformly loaded simply supported beam calculator, and if the stair is supported on slender posts or columns, the Euler buckling load calculator will help verify they won't buckle under compression.
Frequently Asked Questions
How do I calculate stair rise and run by hand?
First measure the total rise from finished floor to finished floor. Divide it by your desired riser height (aim for 15–19 cm or about 7 in) and round the result up to a whole number — that's your riser count. Divide the total rise by that count to get the actual, equal riser height. Treads are always one fewer than risers, and the total run is treads × tread depth plus any landing depth.
Why is there always one more riser than treads?
The upper floor or landing surface acts as the final step of the staircase. You physically climb every riser, but the top one ends on the finished floor rather than on a built tread, so only \(n-1\) treads need to be constructed. This is also why counting steps on an existing stair off-by-one is such a common mistake when ordering materials.
What is a comfortable riser height and tread depth?
Most residential codes and comfort guidelines call for a riser between roughly 15 and 19.7 cm (6–7¾ in) and a tread going of at least 25 cm (10 in), with 28 cm (11 in) feeling generous. Check the Blondel rule: \(2R + T\) should total 61–65 cm (24–25.5 in). A higher riser pairs better with a shallower tread, and vice versa.
How do I convert the results between metric and imperial units?
The calculator converts everything to metres internally and shows both cm and inches. For manual work: 1 in = 2.54 cm, 1 ft = 30.48 cm, and a common US spec of a 7¾ in riser with a 10 in tread equals about 19.7 cm × 25.4 cm. Keep risers, treads and total rise in one consistent system before dividing — mixing units mid-calculation is a frequent source of errors.
What if my total rise divides unevenly into steps?
That's the normal case. Because the riser count must be a whole number, the rise is split evenly across all steps, so the actual riser rarely equals your target exactly. For example, a 275 cm rise with a 17.5 cm target gives 16 risers of 17.19 cm each. Never absorb the leftover fraction into one or two steps — unequal risers are a leading cause of trips and fail most building inspections.
How do I measure total rise correctly before flooring is installed?
Always measure from the surface of the finished lower floor to the surface of the finished upper floor. If the flooring isn't laid yet, measure the subfloor-to-subfloor distance and add or subtract the final floor thicknesses on each level. A 2 cm tile on one floor and 1.5 cm hardwood on the other, ignored, will make your bottom and top risers wrong even when every middle step is perfect.
Does this calculator handle L-shaped, U-shaped or spiral stairs?
It handles straight flights and, with the landing allowance, single mid-flight landings. For L-shaped or U-shaped stairs, split the total rise between the flights (each flight can have its own riser count, but riser heights must be identical throughout), compute each flight's run separately, and add the landing platform depth. Spiral and curved stairs follow different code rules for tread depth measured at the walk line — consult your local building code for those.