Stair calculator

How the riser count and height are worked out

risers = total rise ÷ maximum riser height, rounded up · riser height = total rise ÷ risers · treads = risers − 1 · total run = treads × tread depth · angle = arctan (riser height ÷ tread depth) · sloped length = √(total rise² + total run²) · Blondel: 2 × riser height + tread depth ≈ 63 cm

The starting point is the total rise and the height you do not want to exceed. The rise is divided by that limit and rounded up — which is why the actual riser always lands at or below the limit, never above it. For 280 cm and a 17 cm limit that is 280 ÷ 17 = 16.47, so 17 risers, and the actual height is 280 ÷ 17 = 16.47 cm.

Every step in one flight has to be the same height, so the total rise is always split into equal parts. That is why the calculator also shows what one step fewer would cost: 280 ÷ 16 = 17.5 cm in the example, above the limit you entered. The number is there so you can see the trade-off — the decision is yours.

The tread depth and the number of treads give the run the flight occupies on the floor. If you need the area of the space the stair takes up, or of the room it lands in, work it out in the area calculator, and enter only heights and depths in centimetres here.

The angle comes from ONE step — the arctangent of riser over tread — so it is the real pitch of the flight. The sloped length is the hypotenuse of a right triangle whose legs are the total rise and the total run: the net pitch line, with no allowance for cutting, notching or fixings.

How to measure the total rise

The total rise is the distance from the finished floor below to the finished floor above — from the surface you will walk on to the surface you will walk on, not from concrete slab to concrete slab. This is the most common source of error on a stair.

If the floors are not finished yet, add the thickness of the future covering on both levels: screed, adhesive, tiles or laminate with its underlay. Forgetting two centimetres of tiles upstairs means the last step ends up two centimetres shorter than the others, and that is felt at every use.

Every measurement on this page is in centimetres. A total rise of 2.8 m is 280, not 2.8 — which is why the calculator refuses anything below 30 cm instead of quietly working out a one-step staircase.

By default the finished upper floor counts as the last step, so there is one tread fewer than there are risers. If the top step is a separate tread sitting in front of the upper floor, tick the box: the tread count then equals the riser count and the total run grows by one tread.

The Blondel relationship — and what it is not

Blondel's relationship says that two riser heights plus one tread depth should come to about 63 cm: 2 × riser + tread ≈ 63. The figure is derived from an average stride on the flat and serves as a planning guideline — it is not a regulation, and it is not the measure by which a staircase is approved.

The calculator shows the sum, the distance from 63 cm and how far that is: up to 1 cm is very close, up to 3 cm close, and beyond that it sits well away. That is a distance, not a grade — the word “close” describes the numbers only, not whether the stair is usable.

If you leave the tread depth empty, the calculator derives it from the formula itself: 63 − 2 × riser height. The sum then comes out at exactly 63 cm and the deviation is zero — that follows from the formula, it is not confirmation that the stair came out well. Enter your own tread depth and the deviation becomes real.

The most important limitation: Blondel constrains the proportion of riser to tread, not steepness. A stair with a 20 cm riser and a 22 cm tread sums to 62 and reads as close by this measure, while in reality it is steep and uncomfortable. The sum alone does not decide whether a stair is usable, safe or permitted.

Worked examples

Total rise 280 cm, limit 17 cm, tread depth left empty: 17 risers of 16.47 cm and 16 treads. From Blondel the tread comes to 63 − 2 × 16.47 = 30.06 cm, the total run is 480.94 cm (4.81 m), the angle 28.7° and the sloped length 556.51 cm.

Total rise 305 cm, limit 18 cm, tread 28 cm: 17 risers of 17.94 cm and 16 treads, total run 448 cm, angle 32.6°, sloped length 541.97 cm. The sum is 2 × 17.94 + 28 = 63.88 cm, so 0.88 cm above 63 — very close to the Blondel relationship, yet noticeably steeper than the first example.

Total rise 300 cm, limit 16 cm, tread 35 cm: 19 risers of 15.79 cm and 18 treads, total run 630 cm, angle 24.3°, sloped length 697.78 cm. The sum is 66.58 cm, so 3.58 cm above 63 — well away from the Blondel relationship, because the tread is deep against a low riser.

Put the space you have on the floor into “Available run” and the calculator says whether the flight fits and, if it does not, how many cm too long it is and the deepest tread that would fit. For a 280 cm rise, a 30 cm tread and 400 cm available: the flight is 480 cm long, 80 cm too long, and the deepest tread that fits is 25 cm.

What this calculator does not do

The calculator works out the geometry of a single straight flight and its distance from the Blondel relationship. It does not check regulations: permitted riser heights and tread depths, stair width, railings and headroom differ by country, building type and use, and none of that has been researched or built in here.

It does not handle winders, landings, kite treads or spiral flights, does not size stringers or check load-bearing capacity, does not model the nosing overhang and says nothing about how much finishing material you need. The result is a planning aid — always check the measurements on site before ordering.

If the stair is being cast in concrete, work out the volume for the slab and the steps in the concrete calculator — this page gives you dimensions, not material quantities.