The rail is longer than the stair
A flight of fourteen risers at seven and a half inches is a rise of one hundred and five inches over thirteen treads, and the pitch line between those two points is longer than either. Then the rail runs past both ends, onto the landing at the bottom and past the top riser at the top, by whatever the manufacturer specifies. So the rail you are quoting for is the pitch line plus two overruns, and the floor it crosses at each end is the overrun multiplied by the cosine of the pitch — a horizontal distance, not the number on the data sheet.
That horizontal figure is the one that matters at the bottom, because it is the floor of a hallway or a landing that the rail is now standing on. Whatever was using that floor — a door swinging onto it, a radiator, the newel, the route past the foot of the stairs — has to coexist with a rail and, if the carriage parks there, with a carriage.
The width everybody else lives with
Two widths matter and only one of them gets quoted. The in-use width is what the stair gives while somebody is riding, and it is briefly relevant. The folded width is what the stair gives for the rest of the day, to everybody else in the house, including the person carrying a laundry basket down at eleven at night. That is the number to write on the plan.
It also decides which side the rail goes on, which is worth treating as a decision rather than as whatever the installer defaults to. A rail on the side away from the handrail leaves the handrail usable. A rail under a window is different from a rail past a doorway. And a stair narrowed by a parked carriage is a stair that somebody may have to leave the building down.
Headroom is measured from a line nobody sits on
Stair headroom is conventionally measured vertically from the nosing line — the imaginary line joining the tread nosings — up to whatever is above. A seated rider is not on that line. They are above it, further out into the stairwell, and moving. So a flight with generous headroom by the ordinary stair measurement can still be tight for a lift, and the clearance that governs is one the manufacturer publishes for their carriage rather than one derived from the stair.
What this page does is take your readings at points along the run and report them against the figure you copied off the data sheet, including where the lowest one is. Take more readings than feel necessary. The low point is nearly always under something structural you were not thinking about — the edge of the floor above, a bulkhead, a boxed duct, a sloping ceiling on the way to an attic — and it is rarely at the point you first measured.
What the landing has to do besides hold a rail
The landing at the parked end is where somebody transfers on and off, which is the part of the whole arrangement with the least margin in it. The calculator subtracts the rail overrun and the parked carriage footprint from the depth you measured, and what is left is what is available for that transfer and for the ordinary business of getting past the bottom of the stairs.
If that number comes out small or negative, the useful next moves are not usually about the lift. Parking at the other end moves the footprint to the other landing. A door at the foot of the stairs that swings the other way, or comes off, frees more floor than any adjustment to the rail will. The door swing planner works out what the door is actually taking, and the turning space calculator works out what is left to turn in.
What this page does not do
It gives no clearance requirement, no equipment dimension of its own, no fixing detail, no structural check and no electrical specification, and it does not say whether a lift can go on your stair. Every equipment figure on it is one you copied from a data sheet for a specific product, and every stair figure is one you measured. What the rail is fixed to and whether that will hold, what supply the lift needs, what the stair has to remain as a means of escape, and whether the installation is permitted at all belong to the manufacturer, a competent installer and your building department.
The failure modes are worth naming plainly and then leaving alone. A lift that stops part way up leaves somebody stranded on a stair, with no good options and nobody necessarily in the house. A stair with a carriage parked on it is narrower for everyone else, in the dark, carrying things. Neither of those is solved by arithmetic, and neither is a reason not to fit a lift — they are reasons to have the conversation with people who install them for a living.
Questions people ask
How long a rail does a flight of stairs need?
The pitch line plus the overrun at each end, and the pitch line is longer than either the rise or the run because it is the hypotenuse. On a fourteen riser flight at seven and a half inches with ten inch treads, the pitch line is about one hundred and sixty seven inches, and then whatever the manufacturer specifies past the bottom riser and past the top gets added to that. The overruns come off the data sheet for the specific lift, which is why the fields for them ship empty here.
How much stair width does a stair lift take?
That depends entirely on the product and this page has no figure of its own for it. What the page does is take the rail projection and the carriage widths from the data sheet, subtract them from the width you measured, and report both the folded width and the in-use width. The folded one is the number worth caring about, because it is what everybody else in the house has for the other twenty three hours of the day.
Why is my headroom fine for the stairs but a problem for a lift?
Because stair headroom is measured vertically from the nosing line, and a seated rider sits above and outside that line while moving. The two measurements answer different questions. The clearance a lift needs is published by its manufacturer for that carriage, and it is not something you can derive from the stair dimensions. Take readings at several points along the flight, because the low spot is usually under a bulkhead, a boxed duct or the edge of the floor above rather than where you first looked.
The landing at the bottom is too shallow. What are the options?
Parking the carriage at the top instead moves the footprint to the other landing, which costs nothing and is often the whole answer. After that, the biggest single gain is usually a door: one that swings onto the landing takes a large arc of floor, and rehanging it to swing the other way or taking it off returns all of it. Adjusting the rail is the last thing to look at, because the overrun is a manufacturer figure rather than a preference.
Does a stair lift block escape from the upstairs?
That is exactly the question to put to your building department, and it is not one this page can answer. A parked carriage narrows the stair, and what width has to remain, and under what conditions, depends on the building and on the rules adopted where you live. It is worth raising early rather than after the rail is up, because it can decide which side the rail goes on and whether the carriage parks at the top or the bottom.