Every step costs two metres: slope is bought with length

Whoever designs a ramp for the first time almost always starts from the wrong question — "how steep is it?" — and discovers the right one late: how long is it. Geometry does not negotiate: at the typical 8% limit, a single 16-centimetre step asks for two metres of run; the half-metre raised entrance asks for more than six; one metre of rise asks for twelve and a half, plus the resting platforms. This calculator flips the perspective the right way: given the rise, the applicable rule and the space that actually exists, it returns the required run, the landings and the space index δ — above 1 the compliant ramp fits, below 1 metres are missing, not opinions.

The formula: rise, rule and landings

The core is a proportion: L_req = 100·h/p_max, the minimum continuous run at the maximum allowed slope. On top graft the landings: when the run exceeds the maximum continuous stretch t, the rule imposes horizontal platforms — here 150 cm — and each landing lengthens the path: L_tot = L_req + 150·n. The final comparison is between what is needed and what is there: δ = L_avail/L_tot, dimensionless, equal to itself with the European rule, with the American ADA or with the local code — because the maximum slope is not hard-wired in the model: it is a declared input, to be cited with its source.

The rise scale: the collapse of the index

The index does not fall linearly with the rise: it collapses, because every extra centimetre lengthens the ramp and — past the maximum-run threshold — adds whole landings. The table shows it with the space fixed (6 m available, 8% rule, 9 m run):

At 20 cm the ramp is a detail; at 100 it is a fourteen-metre structure with a platform; at 300 — a whole storey — it is a forty-metre snake no garden contains. That is why the ramp is the queen of small rises and the deception of large ones.

A complete numerical example

A raised entrance of three steps: rise 50 cm, outdoor corridor 6 m long, rule at 8%, maximum run 9 m. The required run is 100 × 50 / 8 = 6.25 m, with no landings. The available space covers 6.00 of it: the index is 6.00 / 6.25 = 0.96 — it almost fits, but almost is not compliant. Using the whole corridor as a continuous ramp would mean 8.3%: out of rule by little, that is, out of rule. The real roads are two: gaining 25 centimetres of run (often moving the start is enough), or changing geometry with a turn. It is the perfect example of the most common case: the project is not decided on metres, it is decided on centimetres.

How to read the space index

The four bands describe four projects. Below 0.8 space commands: the compliant ramp does not fit, and forcing it as a continuous run produces slopes that are dangerous downhill before they are irregular. Between 0.8 and 1.0 it almost fits: the deficit is centimetres, and geometry recovers it. Between 1.0 and 1.3 the ramp is compliant with a physiological margin — and the exact tie (δ = 1.00) belongs to this band: compliant, but without a centimetre to spare. Beyond 1.3 the space is generous, and the mature project does not stop at the limit: it uses the extra metres to drop below the maximum slope, because between the allowed 8% and the possible 5% lies the difference between climbing with effort and climbing.

Where the maximum slope comes from: an input, not a dogma

The limit is not universal. The American ADA reasons in ratios: 1:12, that is 8.33%. In Europe, 8% is the most widespread reference for work on existing buildings, with many rules asking 5-6% on long paths or in public spaces; the German DIN 18040 sets 6% with landings every 6 metres. And the same jurisdiction may allow steeper slopes on very short stretches by exception. That is why the calculator asks for the maximum slope instead of imposing it: the regulatory source belongs in the project, and scenario comparison — "what if 6 applied here?" — is done by changing one number.

The landings: the horizontal metres nobody budgets

The resting platform is the hidden cost of long ramps. It is needed whenever the continuous run exceeds the maximum (parametric here, typically 6-10 m), at every change of direction, and at the top and the bottom — where the chair must be able to stand level without rolling while a door is opened. Each intermediate landing adds 150 cm of run that gains no height: that is why the one-metre rise, which "in theory" asks 12.5 m, in practice asks 14. In U-shaped switchbacks the platform must also allow a full rotation: the design of a ramp is, in good part, the design of its horizontal planes.

International perspective: the same physics, different thresholds

The ramp is the most standardised object of world accessibility, and yet the thresholds diverge: the American ADA at 8.33% with 9-metre runs, most of Europe between 5 and 8%, the German DIN at 6%, many Asian and Australian rules in between. The physics underneath is identical — manual wheelchair, friction, shoulder strength — and indeed the research converges: below 5% almost everyone climbs autonomously, at 8% many need help, beyond 10% the descent becomes the real danger. The calculator is parametric precisely for this: same geometry, your jurisdiction's threshold, and the index δ — a pure ratio — compares a project in Rome, one in Berlin and one in Chicago on the same scale.

Limits of the model and correct use

The model solves the in-line geometry: it does not draw turns and switchbacks (which are modelled by adding the stretches and the manoeuvring platforms), it does not verify width, guardrails, handrails and surfaces — requirements of the rule as much as the slope — and it does not cover vehicle ramps, which follow other rules. The rise must be measured on site, not deduced from the number of steps: two "equal" steps rarely are. When the rise exceeds one metre, the right comparison is no longer between two ramps but between technologies: the home elevator cost calculator completes the decision; and for the geometry of the ramp's vertical sibling there is the staircase calculator.

The length scale: two exact borders

With the rise fixed, every metre gained along the path raises the index. The table grows the available space on the base case (50 cm, 8% rule): two rows fall exactly on the band borders — and the bands' captions are seen at work.

The tie row deserves the look: at 6.25 m the index is exactly 1.00 and the slope using all the space is 8.0% — the limit, not a margin. Compliant, yes: but the first casting error, the first settlement of the ground, and the level will read 8.1. It is the reason the mature project aims for the row below, not the tie row.

The rule scale: from failed to passed by changing one number

Same house, same rise, same corridor: only the jurisdiction's threshold changes. The table crosses the real rules — from the 5% of protected paths to the 12% of short exceptions:

The project crosses all four bands without a brick moving: at 5% it needs eleven and a half metres with a landing, at 12% four are enough. It is the practical demonstration of why the maximum slope is a declared input and not a constant: the same geometry fails in Berlin, sits on the edge in Rome and passes where an exception applies — and the designer must know under which number they are working.

The geometries that save the project: L, U and the inclined plane that turns

When the straight line is not enough, the ramp bends. The L-turn is the first remedy: it splits the run over two sides of the building and costs only the corner platform — 150 cm that gain no height but unlock the project. The U-switchback doubles the run within the same footprint: it is the solution of narrow courtyards, at the price of a deeper manoeuvring platform, because the wheelchair must rotate 180 degrees. The helical ramp around a pillar or inside a stairwell exists, but the inner radius raises the effective slope on the inner edge: the rule is verified there, not on the axis. The rule that holds for all: every change of direction is a platform, and every platform is horizontal metres to budget before drawing.

The descent: the danger the project forgets

The debate about ramps is consumed on the climb — the effort, the autonomy — but the real accidents happen on the way down. A manual wheelchair on a 12% slope accelerates beyond the grip of hands on the wheel rims; a powered one shifts the centre of gravity forward to the tipping limit; with rain or leaves, the friction the rule assumes is no longer there. It is why the regulatory limits look prudent to those who see them from the drawing and sacrosanct to those who use them every day: the maximum slope is not drawn on the effort of climbing, it is drawn on the control of descending. When the calculator shows the slope "using the whole space" above the limit, that is not a more tiring ramp: it is a ramp that selects who can use it.

Measuring on site: the survey that decides everything

The real rise is measured, not deduced. The site procedure: a rigid board level on the high point, the spirit level on top, and the vertical is measured at the low point — or, on long paths, the laser level. Three recurring errors: counting the steps and multiplying by a "standard" riser that does not exist (real risers vary by 2 cm even within the same stair); ignoring the slope of the arrival ground, which can gift or steal precious centimetres; and forgetting the thicknesses — the new paving, the screed, the threshold — that move the zero point. On this calculator's base case, 25 centimetres of run separate compliant from non-compliant: that is a tape-measure error, not a design error.

Beyond the ramp: when the right answer is another one

The ramp is the most robust solution — no motor, no maintenance, no waiting — but it is not always the best. Below 50 cm of rise it is nearly unbeatable. Between 50 and 100 cm it competes with the stairlift where space is scarce and the user is one. Beyond the metre, the platform lift almost always wins the comparison: a few square metres against fifteen and more metres of snake, no effort, and a total cost that at those numbers becomes comparable — the home elevator calculator serves exactly that comparison. The mature decision is not "ramp yes or no": it is the point of the path at which each technology stops being the simplest and starts being a fallback.

Frequently asked questions

How do you calculate the length of a wheelchair ramp?

With L = 100·h/p_max: the rise in centimetres divided by the maximum allowed slope. With a 50 cm rise and an 8% rule, 6.25 m of continuous ramp are needed; if the run exceeds the maximum stretch, 150 cm intermediate landings are added.

What is the space index?

It is the ratio δ between the length available along the path and the compliant run required, landings included. It is dimensionless: 0.96 means 4% of the metres are missing; above 1 the compliant ramp fits; above 1.3 it pays to design it gentler than the limit.

What is the maximum slope for a wheelchair ramp?

It depends on the applicable rule: the American ADA allows 8.33% (1:12), in Europe 8% is the most widespread reference on existing buildings with many contexts at 5-6%, the German DIN 18040 asks 6%. That is why the calculator treats it as a declared input, to be cited with its source.

How long must a ramp be for one step?

A typical 16 cm step asks for about 2 m of ramp at 8% (16 × 12.5). It is the quick rule to remember: every centimetre of rise costs 12.5 cm of run at 8%, and exactly 12 cm with the ADA 1:12.

When are resting landings needed?

Whenever the continuous run exceeds the rule's maximum (typically 6-10 m; 9 for the ADA, 6 for DIN 18040), at every change of direction, and at the top and bottom of the ramp. Each intermediate landing adds about 150 cm of level run that gains no height.

What do I do if the compliant ramp does not fit?

If the index is just under 1, centimetres are recovered by moving the start or with an L-turn; if it is far below, you change geometry (a U-switchback with its manoeuvring platform) or route; if the rise is large, you change technology — a platform lift or a stairlift.

Why can't I simply make the ramp steeper?

Because beyond the limit the manual wheelchair does not climb autonomously and — more dangerous — accelerates beyond control on the way down. An out-of-rule slope is not a bureaucratic irregularity: it is the point where help becomes mandatory and braking uncertain.

Is the slope measured per stretch or on average?

Per stretch: every segment of ramp must respect the limit, and the average does not offset a steep stretch with a flat one. That is why the calculation is done on the real path — start, arrival and landings included — with a level, not on the crow-fly line.

What is the difference between ADA 1:12 and the European 8%?

The ADA expresses the limit as a 1:12 ratio (8.33%), slightly more permissive than the European 8%; in exchange it imposes maximum runs of 30 feet (about 9 m) and rigorous landings. The calculator handles both: just enter 8.33 or 8 as the maximum slope.

Does the calculator work for portable or telescopic ramps?

The geometry yes — rise and length determine the slope for a leaned ramp too. But portable ramps are used with an assistant and manufacturers state their own usage slopes, often steeper than building limits: for autonomy the rule's threshold applies, not the leaflet's.

When is a platform lift better than a ramp?

Indicatively beyond one metre of rise: the ramp exceeds 12-14 m of run with landings and guardrails, occupies the garden or the stairwell and is tiring anyway. The platform occupies a few square metres, serves far greater rises and at those numbers the total cost becomes comparable.

What does this calculation NOT verify?

The clear width, handrails and guardrails, side kerbs, the anti-slip surface and outdoor drainage, the lighting: requirements of the rule as much as the slope. The model solves the in-line geometry; turns and switchbacks are modelled by adding the stretches and the manoeuvring platforms.

Updated July 2026