Understanding how recessed lighting spreads its light is integral to coming up with a recessed lighting layout design. Figure out how far the lights really spread the light. It may be 5 feet and it may be 8 or 9 feet. However large the diameter of effective light is, that will determine the spacing the lighting needs in order to be most effective.
Another thing to keep in mind anytime you are planning a recessed lighting layout design is to think about what the area will be used for. If a lot of reading will need to be done in the room, the recessed lights should be closer together. For bathrooms and
kitchens, most people want a bright light that will allow them to see as well as possible. Home offices also need bright lighting.
For a living room or dining room, there may not be as much need for bright overhead lighting. Living rooms, like bedrooms, may not rely on the recessed lighting to provide most of the light. If there are table lamps or floor lamps that are frequently in use in any given room, that room probably doesn’t need as many recessed lights as a room that depends exclusively on the overhead lighting.
For rooms that don’t require bright reading or working light, spacing the recessed lights about 8 or 9 feet apart is enough to provide adequate lighting. For rooms where overhead lighting is extremely important to the function of the room, the lights may be spaced 5 or 6 feet apart. This recessed lighting layout design is not set in stone, but it is a good guideline for most recessed lighting.
So, keep in mind that you have low ceilings, the spread effectiveness will be less (than typical 8 or 9') ceiling, requiring more lights. Another thing to consider, is where the bulb sits in the can, in relation to the trim, is it flush or does it sit up in the can?
If you plan on using the 6, space them 4ft off the (12ft walls) 2 rows of 3, but I would put in 9, evenly spaced at 3ft off the 12ft walls) 3 rows of 3
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Hope this helps - rather have more than not enough, can always tone down with a dimmer.