What is the difference between roughness and specular in the Principled BSDF shader?

The Documentation says that the roughness input is “microfacet roughness of the surface for diffuse and specular reflection.” and that the specular input is the “Amount of dielectric specular reflection.”

What I don’t really understand is which one to adjust to get a better reflection and when. How do they interact with each other?

If you google “PBR Guide” you’ll find the handy two-part guide to PBR material put together by Allegorithmic. Specular is normally left at default unless it’s for a dielectric material whose specular level falls outside the normal range. Stuff like gemstones and the like.

It’s effect is fairly subtle in most cases.

EDIT: Tweaking Roughness will give you control over reflections. Turn it down for sharper, clearer reflections. Don’t forget to turn metallic up to 1.0 if it’s a shiny metal object. Adding a suitable texture as the input to Roughness can help a lot too - it get’s rid of the perfectly even reflection.

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So if I had a texture that represented the amount of paint and grime on a surface, would that be overlaid on the roughness texture or the specular texture?

Roughness. I had a rummage around to see if I could find an example. In this one its a metal object and I’m using an image to control roughness. Specular will have no effect at all if metallic is set to 1.0 anyway.

Here’s the roughness map (slightly exaggerated as it was a bit more subtle)

This shows the differences between Roughness and Specular (and Metallic chucked in for good measure). The Specular row has Roughness at default (0.5) and the Roughness row has Specular at default (0.5).

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If you turn up matallic all the way you can see what roughness does: it’s the difference between a mirror and something like lead or pewter. Non-matalic materials with very low roughness include smooth plastic or polished wood which you can see a bit of a reflection in.

Yes, roughness is a good thing to put a smudge map on if your dealing with a very smooth surface.