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We can't see your stairs from here, nor can we determine how the structure is built so mostly we are going to ask a lot of questions in this article to get you thinking.
Caution: Before removing any walls or wall sections always determine if there is a "load", it supports something else, on the wall you are removing.
Now let's take at the space under your stairs. It takes different forms and shapes, depending on which way the stairs run and how wide they are, but it is nearly always underused. Would the space be more useful if it were not boxed in but became part of the main space, whether in the hall or the living room? Is it deep enough to take a desk, or a chair and telephone table? If the staircase is in the kitchen, will the refrigerator fit under it? Or would the run of kitchen fittings and cupboards carry right on under it so that it becomes part of the main kitchen? Would it be better to fit the staircase space with cupboards and drawers rather than opening up the whole space?
Is it big enough to get a small shower room into, or a tiny bath? Very small baths, slightly deeper than normal for sitting in seats, are available and can be fitted under a staircase if there is enough headroom and the plumbing can be organized without too much expense. An oval bath takes up much less space than a conventional one and can be angled to fit very narrow rooms. If you can bear to give up the idea of a bath altogether, a luxurious shower cubicle can be installed in a very small space.
If the stairs slope quite steeply, it may be possible to put a lavatory under the lower part so that when standing there will be plenty of headroom and when sitting, closer to the slope, there will be still be headroom. A small basin is all that is necessary in an under stairs loo. Tiny spaces such as these can be made attractive with pretty ceramic tiles and fitted cupboards can provide extra storage for shoe-cleaning equipment, extra toilet rolls, etc. There may even be room to house the washing machine under a shelf in a downstairs cloakroom, alongside the outdoor boots. This would mean that the space needs to be near another bathroom or the kitchen, so that it will not be too expensive to run the pipes to it and so that drainage is also nearby.
It is possible to remove the concealing wall from the stairs so that the whole staircase becomes part of the neighboring room. Even so, it can be a separate part, providing an area for telephoning, study or storage. A wooden staircase with elegant banisters would complement an antique desk and, with a set of bookshelves, would become an efficient and workable office space without encroaching on the main living area. In a ground-floor flat, a tiny but workmanlike kitchen can sometimes be opened out under the taller part of the house's main staircase, extending as an alcove from the living room. When a kitchen is as tiny as this, it must be very well planned and thought out. Such a kitchen would suit a single person. What is usually lacking is worktop space but this can often be provided by the dining table.
What can you do with that wasted space under the stairs?