Stairs

Working Out Riser Height, Tread Depth, and Stringer Length

A staircase’s step count and dimensions are worked out from the total height it needs to climb and how tall each step is allowed to be. Enter the total floor-to-floor rise, the maximum height a single riser is allowed to be, and a rise + run comfort target, and this calculator works out the number of steps, the exact riser height, the tread depth, the total horizontal run, and the stringer (diagonal) length.

The Formula

Number of risers, rounded UP — rounding down would let a single riser exceed the maximum height you entered:

$$\vD{\text{Risers}} = \left\lceil \dfrac{\vA{\text{Total Rise}}}{\vB{\text{Max Riser Height}}} \right\rceil$$

Actual riser height (always at or below the max, since it just divided the total evenly across however many risers were needed):

$$\vE{\text{Riser Height}} = \dfrac{\vA{\text{Total Rise}}}{\vD{\text{Risers}}}$$

Number of treads = $\vF{\text{Treads}} = \vD{\text{Risers}} - 1$, since the top riser lands you on the upper floor itself, which doesn’t need its own tread.

Tread depth = $\vG{\text{Tread Depth}} = \vC{\text{Rise + Run Target}} - \vE{\text{Riser Height}}$ — the classic “rise + run” stair-comfort guideline (commonly cited as 17–18 in / 43–46 cm) used to derive a comfortable step depth from whatever the actual riser height works out to.

Total run = $\vH{\text{Total Run}} = \vF{\text{Treads}} \times \vG{\text{Tread Depth}}$.

Stringer length (the diagonal cut length), from the Pythagorean theorem:

$$\text{Stringer Length} = \sqrt{{\vA{\text{Total Rise}}}^2 + {\vH{\text{Total Run}}}^2}$$

Worked Example

A 274.32 cm (9 ft) floor-to-floor rise, a 19.685 cm (7.75 in) max riser height, and a 44.45 cm (17.5 in) rise + run target:

1. Risers: $\vA{274.32} \div \vB{19.685} = 13.94$, rounded up to $\vD{14}$.
2. Actual riser height: $\vA{274.32} \div \vD{14} \approx \vE{19.59}$ cm.
3. Treads (steps): $\vD{14} - 1 = \vF{13}$.
4. Tread depth: $\vC{44.45} - \vE{19.59} \approx \vG{24.86}$ cm.
5. Total run: $\vF{13} \times \vG{24.86} \approx \vH{323.12}$ cm.
6. Stringer length: $\sqrt{{\vA{274.32}}^2 + {\vH{323.12}}^2} \approx 423.86$ cm.

Key Factors to Consider

• Every riser in a staircase must be the same height, since inconsistency is a genuine trip hazard. This is exactly why the formula divides the total rise evenly across every step rather than allowing one shorter or taller step — even a small height inconsistency between steps is a well-documented cause of stumbles, since people unconsciously expect uniform steps once they’ve taken the first one.
• Local building codes typically set both maximum riser height and minimum tread depth requirements, and these can vary by jurisdiction. This calculator’s max riser height input should reflect the actual applicable code for the project’s location — treating a commonly-cited figure as universal without checking local code is a real risk for any staircase that needs to pass inspection.
• A steeper staircase (taller risers, shallower treads) takes up less horizontal floor space but is generally less comfortable and safer to use than a gentler one. This tradeoff between footprint and comfort/safety is exactly what the “rise + run” comfort guideline this calculator uses is designed to balance — a tighter space often forces a steeper, less ideal staircase.
• Headroom clearance above a staircase is a separate dimension this calculator doesn’t compute, but is equally important to check. Most codes also specify a minimum vertical clearance above every step — a staircase that satisfies the rise/run/tread dimensions here can still fail to meet code if there isn’t enough headroom above it, which needs to be checked separately against the specific floor plan.

Common Mistakes

• Rounding the riser count down instead of up. Rounding down would let each riser’s actual height exceed the maximum entered — this calculator always rounds the riser count up so no single step ever ends up taller than the limit.
• Confusing total rise with a single riser’s height. Total rise is the entire floor-to-floor height the staircase climbs, not the height of one step — entering one for the other produces a wildly wrong riser count.
• Skipping the local code check because a commonly-cited figure seems reasonable. Maximum riser height and minimum tread depth requirements vary by jurisdiction — a staircase that passes this calculator’s math can still fail an inspection if the inputs don’t match the actual applicable code.

Useful to Know

• Planning a concrete staircase rather than a wood-framed one? Concrete Steps Calculator estimates the concrete volume needed for poured stair steps.
• Need to figure out how much material to order for the treads themselves? Flooring Calculator estimates flooring material and cost from a given area.
• Building the foundation the staircase lands on? Foundation Concrete Calculator estimates the concrete needed for a foundation slab or footing.