The arc is a quarter circle centred on the pin, not on the jamb
The pivot of a swinging door is the hinge pin, and the pin sits slightly outside the face of the door. That offset is small, usually a quarter inch or so depending on the hinge and how the jamb is mortised, but it means the leading edge sweeps a radius of the door width plus the offset rather than the door width alone. For a 32 inch door that is a 32-1/4 inch radius, an arc a little over 50 inches long, and about 5.7 square feet of floor that has to stay empty.
Everything in this calculation is measured from that pin. An object is inside the arc if its distance from the pin is less than the radius, regardless of whether it is near the wall or out in the room. That is why a low radiator at 20 inches along the wall and 18 inches out is a conflict even though it looks nowhere near the door on a plan: it is only 27 inches from the pin.
The angle at which the door stops is the real answer
Knowing that something is in the arc is only half of it. What you want to know is how far the door gets before it arrives, because the door does not have to open all the way to be useful, and how much use you lose depends steeply on the angle. The clear passage through a doorway with the door part open is the door width times one minus the cosine of the opening angle. That relationship is unkind at the low end.
| Door opens to | Clear passage on a 32 in door | What fits |
|---|---|---|
| 90 degrees | 32 in | Everything the opening allows |
| 75 degrees | 23-3/4 in | A person, most boxes, not a sofa |
| 60 degrees | 16 in | A person turned sideways |
| 45 degrees | 9-3/8 in | An arm and a laundry basket, edgewise |
| 30 degrees | 4-5/16 in | Effectively nothing |
Between 90 and 75 degrees you lose a quarter of the passage. Between 60 and 45 you lose most of what was left. This is why an obstruction that stops a door at eighty degrees is a footnote and one that stops it at fifty is a design problem.
Bathrooms, kitchens and the objects that always turn up
The recurring conflicts are boring and predictable. In a bathroom it is the toilet, the vanity corner and the towel rail on the back of the door, which adds its own depth to the arc that nobody enters. In a kitchen it is a base cabinet corner or the handle of a dishwasher standing proud, and the dishwasher is worse than the cabinet because it is only a conflict when open. In a bedroom it is the corner of the bed and the wardrobe door that opens toward the same patch of floor, giving two arcs that intersect and one of them always loses.
Two arcs that overlap are worth entering deliberately: put the other door leaf in as an object at the position its edge reaches, and see which one stops first. Appliance doors are the same idea, and if that is the question you are chasing, the appliance clearance calculator covers the door swing and pull-out space around fridges, dishwashers and ovens in more detail than this page does.
The walkway question
A door that opens into a route is different from a door that opens into a room. The route check here is simple on purpose: at ninety degrees the door projects its full radius straight out from the wall, so a 32 inch door eats 32-1/4 inches of whatever depth the route had. A 36 inch hall becomes about 4 inches of hall. That is not a near miss, it is a closed corridor, and the practical result is that the door lives closed and gets opened one person at a time.
There are four moves and they are all cheaper than moving the wall. Reverse the hinge side so the arc runs toward the near end of the hall rather than across it. Reverse the swing so the door opens into the room instead. Change the door type, which is where pocket and barn doors earn their place, since neither one sweeps floor. Or accept it and hang the door to open against the wall it is nearest, so at least the open position is out of the way.
What this does not decide
It does not know about fire doors, doors on a means of egress, accessible route requirements, or the manoeuvring clearances that apply on the pull side and push side of a door in work covered by an accessibility standard. Those are set by the code your jurisdiction has adopted and by the standard it references, and they specify things this page does not model, including clear floor space beyond the arc and the force needed to operate the door. If the door is on an exit route, in a rental, or in anything commercial, that conversation belongs with the building department before the frame goes in.
It also assumes the door is a single flat leaf on butt hinges swinging in a plane. Bifolds, sliders, pivots, and doors with a closer that will not hold at an angle all behave differently. If the room is the constraint rather than the door, the furniture fit checker is the other half of this question, and the opening itself is sized on the rough opening calculator.
Questions people ask
How much floor does a door swing use?
A quarter circle with a radius of the door width plus the hinge pin offset. A 30 inch door sweeps about 5 square feet, a 32 inch door about 5.7, and a 36 inch door about 7.2. That floor has to be clear from the wall face all the way out to the radius, and it has to be clear at every height the door passes through, which is why a low radiator and a tall bookcase are both conflicts even though only one of them shows up on a floor plan. Rugs count too, if they are thick enough to catch the bottom of the slab.
Which way should a door swing?
The common conventions are that a door swings into the room it serves rather than into a corridor, that it swings against the nearest wall so the open leaf is out of the way, and that it does not open onto a light switch or into another door. Those are habits, not rules, and they conflict with each other often enough that you end up choosing. What settles it is usually the walkway: if the door blocks a route when open, the other option wins unless it blocks something worse. Doors on an exit route may have direction requirements from the adopted code, so ask the building department about those rather than following the habit.
What does hinge pin offset change?
Very little on its own, and it is included because it is free to include. The pin sits outside the door face by roughly a quarter inch on a standard butt hinge, so the leading edge sweeps a slightly larger circle than the door width suggests. On a 32 inch door that is a quarter inch of extra radius, which matters only when something is sitting within a quarter inch of clearing. If you are using a hinge that throws the door clear of the jamb, a swing clear or wide throw hinge, the offset is larger and worth measuring rather than guessing.
Can I just take the door off when I need the space?
For a move, yes, and it is worth planning for. A slab on loose-pin butt hinges comes off in a couple of minutes and buys back the full opening width plus the space the leaf was occupying. It is a real answer for the once-a-year problem of getting a sofa through. It is not an answer for a door that stops at fifty degrees every day, because the thing it hits will still be there tomorrow and you will still be turning sideways.
The door hits the toilet. What is the cheapest fix?
Reversing the hinge side, if the room allows it. It costs a new mortise on the other jamb, filling the old one, and moving the strike, and it flips the whole arc to the other side of the opening. That is usually cheaper than moving a toilet, which is a drain relocation. If reversing does not help because the room is symmetric about the problem, the next cheapest is reversing the swing to open outward, and after that a pocket or barn door, which removes the arc entirely. Moving plumbing is last for a reason.