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I'm trying to choose between square or round LEDs. I would like to select an LED that will "project" light and I cannot find any information comparing the two types.

Which style of LED will project light better?

Projection, for the purposes of this question, means casting light "in-line" with the LED. For example, an LED right out of the box with straight leads plugged into a breadboard on a flat table will stand vertically. In this case, I would like to project as much light onto the ceiling as possible. I hope this makes sense.

If it matters, I'd like to use water clear blue LEDs.

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    Go with the round ones. The curved top acts like a lens, making it shine light in a bundle. – Gerben Feb 10 '17 at 11:34
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Many of the square or rectangular LEDs with leads – that is, not surface mount devices (SMD) – that I've seen are intended for use as panel indicator lights, so are not very bright. On the other hand, among SMD devices square, rectangular, and round lights run the whole gamut of brightness. Of course many white LEDs, square or round, are extremely bright because of being intended for illumination.

For projecting a beam against a ceiling, adding optics to the LED may be the best approach. For example, buy some 99¢ flashlights like “Waterproof 3500LM Pocket LED Flashlight Zoomable LED Torch Mini Penlight Light” on ebay, and either add a blue filter in front of the lens or replace the LED with an ultrabright blue LED, using the zoomed-out flashlight lens to concentrate the light. Also, search for 10° or 15° “PMMA LED lens” on ebay, Amazon, aliexpress, etc.

Note, for determining if any given LED will project a tight bright beam, look at the angles of its beam pattern. beam diagrams, 30 and 70 degrees This diagram (from Led Buying tips at sunriseled.us) contrasts the intensity of a 30°-beam LED with that of a 70°-beam LED. The diagram at left below (from dimmable-gu10.com) is typical of intensity-vs-angle diagrams, which usually are shown on a polar plot like that, with a narrower oval corresponding to a tighter beam. The diagram at right below shows the same information, in a perhaps more easily comprehended form. typical LED goniometer chart

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