How many downlights

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I have a room that is 10 ft x 17.5 ft that I would like to put some Led downlights in the ones I am using are a 9w warm white with a 60 degree beam angle. I just need to know if 6 or 8 would do for that size of room.
 
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Perhaps you should think about whether needing multiple lights in a room that size shows that the lights aren't very good at the job of lighting up rooms.
 
Using a on line calculator it shows around 2800 lumen or 21 watt, however with any room it is not simply the lumen but colour or walls and size of lamps.

On the bedroom wall I have two GU10 LED lamps either side of the bed, and also two pods on the ceiling, since both could be angled and pointed at different things I did an experiment using the camera to measure the light aimed at some random area of the room. By simply turning lights to reflect off the white wardroom doors and ceiling or aimed at the light coloured bed covers the exposure for camera actually changed by two stops. Clearly same amount of light, just simply where the lights were aimed.

So 10 x 3W lamps 50mm diameter will light a room better than 5 x 6W at 50mm diameter, change to a 100mm diameter light and then two 10W lamps will likely work better than 5 x 6W even when the light output is not as high as it has been defused better so lights the room better.

I have found 3W with 50mm diameter seems to be about the best you can get, over 3W and much of the light is lost, under 3W not bright enough, however you would need 10 x 3W suppose you could arrange in the shape of the great bear and make it like a planetarium, but really the best is to use larger down lights, say 100mm.
 
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I have a room that is 10 ft x 17.5 ft that I would like to put some Led downlights in the ones I am using are a 9w warm white with a 60 degree beam angle. I just need to know if 6 or 8 would do for that size of room.

You might want to consider a wider beam angle. For example, I have 4 like these, that I specifically chose because of the 120 degree beam angle.

https://www.lightrabbit.co.uk/6-watt-frosted-led-ceiling-light-390-lumens-120mm-diameter.html

in half of my kitchen, lighting up approx 4m by 4m, in warm white I think. Plenty bright enough on work surfaces. That being said, the cabinets are off-white high gloss finish, so they bounce the light around.

I only went for downlighters because the ceiling in that half of the kitchen is too low for much else, otherwise I would have gone for pendants or strip lighting.
 

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